[THIS NUMBER IS ESPECIALLY DEVOTED TO MATHEMATICS AND PHYSICS.]

JOHNS HOPKINS

CIRCULARS.AiblisAedwz~’k Ike a~5fro1~ationofIke Boardof Truslees.

No. 3.] BALTIMORE, FEBRUARY, i88o. [PRICE 5 CENTs.

CALENDAR.

February10—March30. Dr. Adams’sCourseon the Italian Renaissance,etc.February16—March 19. Dr. Lanman’sCourseon the Vedas.February18—May 5. ProfessorGildersleeve’sReadingsin the Greek Tragic Poets.February21—April 24. M. Rabillon’s Readings(in French) in FrenchLiterature.February23. Fourth Anniversary of the University.February23—May 3. Prof. Morfis’s Courseon British ThoughtandThinkers.February24-26. Lectureson Celestial Chemistry,at the Peabody,by Prof. G. F. Barker.March2-4. Lectureson Color Blindness,at the Peabody,by Dr. B. J. Jeifries.

CONTENTS.

PAGE. rAGE.

Calendar, . . . . 21 Hopkins Hall Lectures, . . . 32

Times of Meetingof University Societies,etc., . . . 21 Reportof Meetings of University Societies, . . . 33-35

Public Lecturesin Progress, 21 ScientificAssociation, . . . . . . . 33

MathematicsandPhysics,1876-80, . . . . . 22-3o Philological Association, . . . . . . 33-34

GeneralStatement, . . . . . . . . 22 HistoricalandPolitical ScienceAssociation, . . . 34

InstructorsandStudents, . . . . . . . 23 MetaphysicalClub, . . . . . . . 34Coursesof Instruction, . . . . . . 24-25 MathematicalSeminary, . . . . . . 34-35

List of Apparatusin Physics, . . . . . 26-27 CommemorationDay, . . . . . . . . 35List of Periodicals, . . . . . . . 28 Additions to Roll of Students, . . . . . 35

List of PapersPublished, . . . . . . ~ Brief Announcements, . 30, 35Note from ProfessorRowland, . . . . . . 30 Scientific Periodicals, . . . . . . . . 36

Comparisonof Standards, . . . . . . . 31

Scient’iflc. First Wednesdayof eachmonth, at 8 P. M. Next meeting, March 3.

S. F. Clarke, Sec’y.

Philological. First Friday of each

month, at 12 M. Next meeting, March 5.C. R. Lanman,Sec’y.

ilistorical and Political Science.

Third Fridayof eachmonth, at 8 P. M. Nextmeeting, March 19. H. B. Adams,Sec’y.

Metaphysical, SecondTuesdayof eachmonth, at 8 P. M. Next meeting, March

9. Allan Marquand,Sec’y.

Biological. Thursday of each week, at4 P.M.

Mathematical Seminary. Third

Wednesdayof each month, at 8 P. M. Nextmeeting,March 17.

Greek Seminary. Wednesdayof eachweek, at 12 M.

PUBLIC LECTURES.

Lecturesarein progressin Hopkins Hall

at ~ P. M:Prof. Morris, Mondays,till May 3.Dr. Adams,Tuesdays,till March 30, and

Thursdays,March 18 and25.

Prof. Gildersleeve,Wednesdays,till May5.

Dr. Lanman, Thursdays,till March ii,

andFriday, March i~.

M. Rabillon, Saturdays,til] April 24.

MEETINCS OF SOCIETIES, Etc.

22 2OHNS HOPKINS [No. 3.

MAT E ATICS AN PHYSICS,

1876-80.

The following statementsarebrought togetherin a connectedform, so that studentswho desireto devotetheir time to MathematicsandPhysicsmay seewhat opportunitiesareoffered in the JohnsHopkins University.

Although the precisecoursesto be given in the future are not stated,there is everyreasonto believe thatthey will be at leastas varied andadvancedas heretofore; and that studentsresidingherefor two or threeyearswill have the opportunity to pursuethe study of Mathematicsand Physics,in any direction which they maychoo8e,under competentguidance,andwith the requisitebooks andapparatus.

The organization of this part of the University hasbeen directedin Mathematicsby ProfessorSYLVESTER,

LL. ID., F. R. S., formerly of London and Woolwich, and in Physics by Professor ROWLAND, and by theirAssociates,W. E. STORY, Ph. ID., and C. S. LIAsTINGs, Ph. ID. Lectures have also been given by non-residentprofessors,who have likewiserenderedaid in the mathematical and physical examinations; andtherehavebeenseveralassistantinstructorsand private teachersactingunder the generalguidanceof the professors.

The advancementof mathematicaland physicalstudiesis herepromotedby the following agencies:

1. C’omrsesof Lecturesand Class-BoomInstructions,coveringthe most important subjects in Pure andApplied Mathematics,including Analytical Mechanics,and Physics. Some of thesecourseswill be repeatedannually, and others will be given as they may be called for by students. The annual programmescontaindetailedannouncements.

2. Mhthematical~5”eminary. The studentsof Mathematicsareaccustomedto meetProfessorSylvesterandDr. Story in monthly assemblies,known as meetingsof the “Mathematical Seminary.” At thesemeetings,besidesoccasionalpapers,such topicsas mayfrom time to time suggestthemselvesin the courseof readingof thestudents or instructors,or may otherwisehe of general interest to personspursuing mathematicalstudies,arediscussed.

The resultsof specialstudiesupon the following subjects,amongothers, were examinedduring thelast academicyear:Nexvton’srule for the limit of roots of algebraic equations.—Therule of signsin trigonometry.—Barycentricco-ordi-

nates.—Doublepoints of plane curves.—Thequasi evolute.—Centralharmonic transformation.—Specialcasesof Pascal’shexagram.—Transformationby elliptic co-ordinates.—Regularfigures in spaceof n dimensions.

3. Physical Journal Society. The physicists hold a weekly meetingunder the direction of ProfessorRowlandandDr. Hastings,for time purposeof reviewingthe recentnumbersof journalsdevotedto Physics.

4. Johns Iiliopkins Scientific Association. A meeting of this Associationis held monthly, at which anopportunity is afforded for communicatingabstracts of recentmathematicaland physicalprogress,as well asthe results of individual research.

5. American Journal of iJfathematics. The University encouragesthe publicationof paperson scientificsubjects producedby its members. Some of these are printed in the AmericanJournalof Mathematics,pub-lished underthe auspicesof theUniversity,andothersappearelsewhere. A partial list of thesepapersis appended.

6. Apparatus. Additions areconstantlymadeto the physical apparatus,which is alreadyextensive,andis especially adaptedto researchesin Heat Electricity, and Magnetism. The University employs a skilledmechanicianin the manufactureand repair of instrumentsof precision.

7. Book8 and Periodicals In the Peabodyand Hopkins Libraries may be found the TransactionsoflearnedSocieties,completesets of the PhilosophicalMagazine, Crelle, Liouville, Grunert, Poggendorff,Dingler,etc. A list of the periodicalscurrently receivedis appended.

8. Fellowships. Among the twenty fellowships of the Unive~rsity, each yielding five hundred dollarsannually,threeareordinarily held by mathematical,andthreeby physicalstudents.

UNIVERSITY GIRCULARS.

INSTRUCTORS AND STUDENTS.Professors, Associates, and Lee urers.

J. J. SYLVESTER, Professorof Mathematics. IA. M., University of Cambridge; F. R. S., Londonand Edinburgh;

CorrespondingMember Institute of France Member Academy ofSciencesin Berlin, Gbttingen, Naples, Milan, St. Petersburg,etc.;LL. D., University of Dublin, University of Edinburgh; late Pro-fessor of Mathematics in the Royal Military Academy, Woolwich.

WILLIAM E. STORY, Associatein M~zthe;nalics.A. B., Harvard University, 1871 ; Ph. D., University of Leipsic, 18Th

Tutor of Mathematics in HarvardUniversity, 1875-76.

CHARLES S. PEIRCE, Lectureron Logic.A. B., Harvard College, 1859, A. M., and S. B., 1863; of the U. S.

Coastand GeodeticSurvey.THOMAS CRAIG, Lectureron Mathematics.

C. E., Lafayette College, 1875; Ph. D., Johns Hopkins University,1878; of theU. S. CoastandGeodeticSurvey.

HENRY A. ROWLAND, Professorof Physics.C. E., RensselaerPolytechnic Institute,Troy, 1870; AssistantProfessor

in the same, 1872-75.

CHARLES S. HASTINGS, Associatein Physics.

Ph. B, Yale College,1870, and Ph. D., 1873; Holder of the TyndallScholarshipin Paris, 1875.

J. WILLARD GIBBS, Lectureron Mechanics.A. B., Yale College,1858; A. M., andPh. D., 1863; Professorin Yale

College.

FABIAN FRANKLIN,Ph. B., ColombianUniversity, 1869.

Assistantin Mathematics.

Public Lectureshave also been given by:

PROFESSORSIMON NEWCOMB, of theU. S. Naval Observatory. Ills- PROFESSORJOHN TROWBRIDGE, of Harvard University, Philosophytory ofAstronomy,(1876-77); of Physics,(1879-80).

PROFESSORJ. E. HILGARD, of the U. S. Coastand GeodeticSurvey.On GeodeticSurveys,(1876-77)

Students.

The following list includes the namesof those only who have made Mathematicsor Physics their principal study

NEWTON M. ANDERSON, (from Columbus,0., Ohio StateUniversity; Mas-sachusettsInstitute of Technology)-

BROWN AYRES, (from New Orleans,La.; WashingtonandLee University;S. B., StevensInstitute of Technology, 1878; Graduate Student,JohnsHopkins University, 1878-79). Fellowin Physics.

GUSTAV BISSING, (from Baltimore; Baltimore City College).JOHN C. BLAND, (from Washington, D. C.; C. E., American Institute of

Civil Engineers). Officeof the SupervisiugArchitectof the Treasury,Washington,D. 6’.

JOHNW. BROWN, (from GovanstownMd.; Mr. G. G. Carey’s School).

ROBERT J. COLEMAN, (from Fayette, Mo.; A. B., Central College, Mo.,1875).

CHARLES M. CONE, (from Hartford, Vt.; S. B., DartmouthCollege, 1875).THOMAS CRAIG, (from Pittston, Pa.; C. E., LafayetteCollege,1875; Ph. 1).,

Johns Hopkins University, 1878, and Fellow in MathematicsandPhysics,1876-79). U.S. Coastand GeodeticSurvey, f’f/ashington,.D. C.;Lectureron .llJathe,natics.

H. ROZIER DULANY, (from Upperville, Va.; University of Virginia, 1878).Instructor in AZathe,naticsin Air. C. C. Carey’sSchoolBaltimore.

BURR K. FIELD, (from Mt. Washington,Md.; Ph. B., Vale College, 1877).Engineer C’or~5s, St.L. c6 S. F. F. R., Wichita, Kansas.

LAWRENCE B. FLETCHER, (from Marlboro’, N. Y.; A. B., ColumbiaCollege,1877, andFellow of Science,1877-80).

FABIAN FRANKLIN, (from Baltimore, Md.; Ph. B., Columbian University,1869; GraduateStudent, Johns Hopkins University, 1876-77, andFellow in Mathematics,1877.79). Assistant in Mathematics.

SPENCERH. FREEMAN, (from Penfield,N. V.; A. B., Universityof Roches-ter, 1875, andA. M., 1878).

HENRY L. GANTY, (from OwingsMills, Md.; McDonoghSchool).JOSHUA W. GORE,(from Frederick County Va - C E , University of Vir-

ginia, 1875; Fellow in Mathematics,1876-78). Professor of NaturalScience,SouthwesternBaptist University, 7achson, Tennessee.

EDWIN H. HALL (from Gorham, Me.; A. 13., Bowdoin College, 1875;Graduate Student of Physics,Johns Hopkins University, 1877-78).Fellow in Physics.

GEORGE B. HALSTED, (from New York City; A. B., Princeton College,1875; Ph. D., JohnsHopkins University, 1879, and Fellow in Mathe-matics,1876.78). Tutorin Princeton College.

ARTHUR S. HATHAWAY, (from Ithaca, N. Y.; S. B., Cornell University,1879). Teacherof Mathematics in Mr. B. AL Lamnh’s School Balti-more.

DANIEL XV. HERING, (from Mechanicstown, Md.; Ph. B., Yale College,1872, and C. E., 1878; Fcllow in En~ioeering,Johns ilookins Uni-versity,1876-78). Assist En’4neer -~

Pennsylvania. - , B. C’. V. K. B., Wavne~aoro,

MAXWELL S. HUDGINS, (from MatthewsCourt House,Va.; C. E., Washing-ton and Lee University, 1876). Teacher of Mathematics, DabneyUniversity School,New Yorh City.

WILLIAM W. JACQUES, (from Newburyport, Mass.; S. B., MassachusettsInstitute of Technology, 1876; Ph. D., Johns Hopkins University,1879, and Fellow in Physics,1876-79).

JAMES E. KEELER, (from Mayport, Fla.; La Salle (Ill.) High School).C. HERSCHEL KOYL, (from London, Ontario; A. B., Victoria University,

(Ont.), 1877).

WILLIAM S. MARSTON, (from Cambridge,Mass.; A. B., harvard University,1874). Private TeacherofMathematics,Baltimore.

OSCARH. MITCHELL, (from Marietta, 0.; A. B., Marietta College, 1875, andA. M., 1878 ; GraduateStudent,Johns Hopkins University, 1878-79).Fellow in Mathematics.

WILLIAM S. MOORE, (from RockHill, S. C.; A. B., DavidsonCollege,1877).EDWARD L. NICHoLs, (from Peekskill, N. V.; S. B., Cornell University,

1875; Ph. D., Universityof Gdltingen, 1879). Fellow in Physics.CHALMERS C. NORWOOD,(from Fort Valley, Ga.; A. B., Davidson College,

1878).

JAMES PAGE, (from Baltimore; Baltimore City College).

ROBERT W. PRENTISS, (from New Brunswick, N. J.; S. B., RutgersCollege,1878; GraduateStudent,JohnsHopkinsUniversity, 1878-79). Fellowin Mathematics.

PHILIP M. PRESCOTT,(from Waukegan,Ill.; ChandlerSc. Dept.,DartmouthCollege).

E. DARWIN PRESTON,(from SpruceGrove, Pa.; B. C. E., Cornell Univer-sity, 1875; Fellow in Engineering,1876-78). Aid, U. S. CoastandGeodeticSurvey.

HENRY F. REID, (from Baltimore; C. E., PennsylvaniaMilitary Academy,1876).

GEORGE L. SMITH, (from Canandaigua,N. V.; C. E., Cornell University,1874). Teacher, StateZVormalSchoolBaltimore.

WASHINGTON I. STRINGHAM, (from Topeka,Kansas; A. B., Ilarvard Uni-versity, 1877; GraduateStudent,JohnsHopkins University, 1877-78).Fellow in Mathematics.

WILLIAM J THOMAS, (from Baltimore; Randolph-MaconCollege).

CHARLES A. VAN VELZER, (from Ithaca,N. V.; S. B., Cornell University,1876). Fellow in Mathematics.

HERMAN VOORHEES, (from Troy, N. V.; C. E., Rensselaer PolytechnicInstitute, 1873). Deceased.

FRANK P. XVHIrMAN, (from Troy, N. V.; A. B., Brown University, 1874,and A. M., 1877; MassachusettsInstitute of Technology).

LEWIS XV. XVILHELM, (from Baltimore; Baltimore City College, 1871).

FEB., i8Soj 23

7OHNS HOPKINS

COURSES OF INSTRUCTION.(Thenumberof studentsisgiven in parenthesis.)

1. Determinantsand Modern Algebra: PROFESSOR

SYLVESTER, 1876-77, secondhalf-year, twice weekly, (7);1877-78,twice weekly, (5); 1878-79, twice weekly, (8).

The courseon Determinantsasa connectin~link betweenAlgebra,asformerlyunderstood,and the Modern Al~ebra,which has grown np in the last quarterof acentury,was designedfor mathematicalstudentspossessedof only an elementaryknowledgeof thesubject.

Thelecteresin the session,1876-77,werechiefly confinedto this subject,that ofModernAlgebrain its widersensebeingonly enteredupon.

In 1877—79 the coursein Modern Algebra wascontinued. This subjectwas de-velopedin an original manner,thetheoryof differentiantsbeing madethe basisoftbatof invariantsandcovenants. In particular,thedeterminationof thenumberofindependentinvariantsandcovariantsof a ~iveu quanticw s treatedvery fully.

Salmon’s Modern Higher Al~ebra, and Fafl de Brunos Th6es’ie dee FormesBineie’eswere to someextent usedas books of reference.

Manyoriginal investigationsof thelecturer, including new aswell aspreviouslypublishedmatter,wereincorporatedinto the substanceof thesecourses;severalofthe former, (among which maybe specifiedthe proof of the previously nudemon-stratedFundamentalTheoremof the Denumerationof invariants,broughtoutforthe first time in thelecture-roomof theUniversity), weresubsequentlypublishedinvariousmathematicaljournals.

2. Theoryof Numbers: PROFESSORSYLVESTER, 1879-80,twice weekly, (8).

Thesubjectis treatedby v nunsmethods,manyof which arenew and original.Thecourseembracesa statementof theresultof independentinvestigationsby thelecturer,amongwhich may he specified an extensionof the methodof ContinuedFractionsto Quaternious;and researchesinto theDivisors of CyclotomicFunctions,with applications to a new theory of cubic-form equations. Dirichiets Zehlen-theorie. Legendres Thioris dee Nombres, and l3achmann’s Theorie desKreistheilenq,areusedasbooksof reference.

3. Quaternions: DR. STORY, ~877-78, twice weekly, (2);1879-80,thrice weekly, (4).

Text-Book: Tait’s ElementaryTreatiseon Quaternions.This courseis designedto give a practicalknowledgeof themethodsof quater-

nions; andtheelementarychaptersof thetext-bookaretreatedwith asmuchhrevityasis consistentwith a thoroughlogical foundationof thesubject.

4. Elliptic Functions: DR. STORY, 1878-79 (beginningof a two years’ course),twice weekly, (2) ; 1879-80,thriceweekly, (4).

Text-Book: CayleysElementaryTreatiseon Elliptic Functions.Thecourseduringthe currentyearis a continuationof that of thelast year,and

presumesa knowledgeof the equivalent of chapters1—JY., XII—XJIJ. of the text-book.

5. HigherPlaneCurves: DR. STORY, 1878-79,first half-year,thriceweekly, (6) ; 1879-80,first half-year,four timesweekly, (5).

Text-Book Salmon’sHigher PlaneCurves.Particularattentionis paid to the generalpropertiesand methodsof treatment

of algebraiccurves and systems of curves,so asto preparethe way for a morethoroughstudy of specialcases.

6. Solid Analytic Geometry: DR. STORY, 1878-79,thrice weekly, secondhalf-year,(7) ; 1879-80,four timesweekly, secondhalf-year.

Text-Book: Salmon’sGeometryof ThreeDimensions.An elementarycourse embracing mite a thoroub treatmentof the plane,and

the more important propertiesof the quadricsurfaces,with a free use of modernmethods.

7. Differential Equations: Da. CRAIG, 1877-78, thriceweekly, (4); DR. STORY, 1878-79, twice weekly, (5);1879-80, thriceweekly, (8).

Text-Book: Boole’s Treatiseon DifferentialEquations.A practical course. Thesecondhalf-year is devoted especiallyto partial differ-

ential equations.

8. Calculusof Variations: DR. CRAIG, 1879-80, twelvelectures,(9).

Thiscoursewasdesignedaspreparatoryto that of ProfessorGibbsnfl RationalMechanics.

9. SphericalHarmonics: DR. CRAIG, 1878-79, ten lec-tures,(6) ; 1879-80, twenty lectures,(6).

This courseembodieda statementof the generaltheoryofSphericalHarmonicsand theirapplicationto somenewproblemsin Hydrodynamics.

10. Cylindric or Bessel’sFunctions: DR. CRAIG,

1879-80,ten lectures,(2).

An examinationof their generaltheoryand application to vortex motion in aviscousfluid.

II, GeneralTheory of Functions,including lie-mann’sTheory: DR. CRAIG, 1879-80,thirty lectures.

The~eneral theoryof fonctionsof a complex variable,as given by Neumannhis work entitled,RiemanneT/zeorie.

12. Theoryof Equations: DR. STORY, 1876-77, twiceweekly, (7) ; Ma. FRANKLIN, 1877-78,twice weekly, (1);1878-79,twice weekly, (1); 1879-80, twice weekly, (6).

Text-Book: Todhunter’sTheory ofEquations.An elementarycourse,including themostimportantmethodsfor theexactor ap-

proximatesolution of algebraicalequationsand the determinationof limits for theroots and of theirreality.

13. Definite Integrals: DR. CRAIG, 1876-77, first half-year, thrice weekly, (5).

Text-Book: Meyer’s BestimmfeIntegsvde.This wasa courseof lecturesuponthe generaltheoryof definite integrals,par-

ticularly theEulerianIntegrals.

14. Differential and Integral Calculus: DR. CRAIG,1876-77, daily, (5); MR. FRANKLIN, 1877-78, thriceweekly, (4); 1878-79, thrice weekly, (12) ; 1879-80,thrice weekly, (9)~

Text.BookS Williamson’s Difierential CalculusandIntegral Calculus.Embracingthe elementsof the differential and integral calculus,and themost

fundamentalapplicationsto geometry.

15. Conic Sections: DR. SToRY, 1876-77, first half-year,daily, (6) ; 1877-78,four timesweekly, (5); MR. FRANK-

LIN, 1878-79, thrice weekly, (5); 1879-80, thrice weekly,

(5).

Lecturesgiven fromnotespreparedby Dr. Story.Thiscourseis the outgrowthof a successfulattemptto teachconicsections,by

modern methods, from the beginning. A thorough knowledge of the analyticgeometryof the straight line in rectanenlarco-ordinatesis the only prerequisite.As a mentaldiscipline,aswell asa preparationfor future geometricalstudies,thesemethodsare greatly to be preferredto the old methodsstill in general use inelementarytext-bookspublishedin this country, howeverlittle employedin origi-nalinvestigationson thedescriptivepropertiesof the conies.

16. Modern Synthetic Geometry: MR. FRAN KLIN,1877-78,twice weekly, (2).

Text-Book: Mulcahy’sModern Geometry.

17. MathematicalAstronomy: DR. STORY, 187778,thrice weekly, (2).

24 [No. 3•

Text-Book: Gauss’ Theoria Moles.

UNIVERSILY CIRCULARS.

18. Rational Mechanics: PROFESSOR GIBBS, 1879-80,four timesweekly, duringJanuaryand February,1880,(10).

The object of this course is to develop the general principles of mechanicsintheir mutual connections,and to explain its most importantmethods. A full state-ment of the characterof thecourse is madeiii University Circulars,No. 1, page7.

A knowledgeof theCalculusof Variationsis indispensableto all pnrsuiu~ thiscourse.

19. Elementary Mechanics: DR. CRAIG, 1876-77,secondhalf-year,(8).

This course was intended especially for studentsbeginning the study ofPhysics;no text-hookwasemptoyed.

20. Analytical Mechanics: DR. CRAIG, 1877-78, firsthalf-year,(6).

This conrsewasbasedupon Kirchhoff’s JfathematisehePhysik,and principallyconsideredthemotionof a rigid body.

21. TheoreticalDynamics: DR CRAIG, 1878-79, fifteenmathematicallectures,(6).

This coursewasbasedupon Jacobi’sVorlesungeed&er Dynernilc. Thegreatgun-eral priuciplesofDyuamicswereeaplainedveryfully,aud Hamilton’sandLagrauge’smethodswerediscussedandillustrated.

22. MathematicalTheoryof Elasticity: DR. STORY,

1876-77, twice weekly, second half-year, (4); 1877-78,

twice weekly, (2).Themethodoftre Imeetempi yedwasthat of Riemaun(D(tfereetialgleichustgen,

~§79—89), with numerousapplications.

23. General Physics DR. HASTINGS, 1876-77, daily;1877-78, daily; 1878-79, daily, (13); 1879-80, daily, (15).

Text-Book: Atkinson’s Ganot.This courseis givee every year,and it discussesall the principal subjects in

Physics,(Mechanics,Li~ht, Sound,Heat,Electricity and Magiietlsm.)There are daily lessonsthrouJh the year,including every week two lectures,

three recitatiomis,and one practical lessonin the Laboratory,to which a selectnumberof studentsis admitted.

24. Thermodynamics: PROFESSOR ROWLAND, 1876-77;1878-79, thirty mathematical lectures, and ten con-ferences,(7).

This coursewas adaptedto the use of physicists,rather than to that of thosewho desireto study the theoryof the steam-engineonly.

25. ElectricityandMagnetism: PROFESSORROWLAND

1878-79,eighty matiematical lectures,and twenty-sevenconferences,(3) ; 1879-8~),twenty lecturesand five con-ferences,(:3).

In this courseXImxwell’s Treatiseon Electricity and Magnetismwas used,tosomeextent,asa bookof reference.

26. TheoryofHeatConduction: PROFESSORROWLAND,

1879-80,threelecturesand oneconferenceweekly, (5).

Thelecturesarenot basedup-in any works of reference.but thesubjectis treatedfrom a new standpoint,so asto be adaptedto physicist~. Constantreferenceismadeto thesimilarity ofthe subjectwith the theoryof electricity.

25

27. Theory of Sound in its Relation to Music:DR. HASTINGS, 1877-78,51X public lectures.

‘I’hese lectures,given to a generalaudience,brou~ht forwarti, with experimentalilltistratious, the presentstate of physical investigations in respect to musicalsounds.

28. Hydrodynamics: DR. CRAIG, 1878-79, twenty-fourmathematicallectures,(7).

Thesubstanceofthis coursewasgiven a secondtiucein elevenlecturesaddressedto Civil andMilitary Engineers.

29. Theory of Observations,and Selected Pro-blems in Physics: DR. HASTINGS, 187677, (3);1877-78, 1878-79, (6); 1879-80, (9); once weekly,

Saturday.This work is planned to meetthe requirementsof suchasaretaking a major

course in Physics,or who are pursuin~ that study as a subsidiarysubjectin pre-paration for a second degree. In this course specialattention is given to themethodsof discussingobservations.

30. Experimental Physics: PROF. ROWLAND, daily;Da. HASFINGS, Saturdays.

Theroomsdevotedto ExperimentalPhysicsareopendaily from 9 A. at. to 5 r. M.

They are speciallyadaptedto those mvho areengagedin conductinginvestigationsor wbo are training themselvesto becoiueprofessionalphysicists. In addition totheseadvancedstudents,thosewho are engagediu studiesantecedentto medicine,and otherpersous,including studentsof Chenaistry,Biology, etc.,who showaspe-cial aptitettefor thepursuit of Physics,haveanopportunityto work in the Labora-tory one dayin the week.

‘Ihe University is sapplieti with the~necessaryapparatusfor study in any de-partmentof Physics;but for work iu respectto Heat,Electricity and Magnetism,its resourcesareunusuallygood. Thelist subsequentlygiven (whichwasoriginallyprinted,with othercorrespondiu~lists, in the Bulletin of Harvard CollegeLibrary,)exhibits the characterof the collection.

31. Logic: MR. C. S. PEIRCE, 1879-80,thrice weekly, (14).A generalcourse,treatingthe foundationof logic antI deducingthe theoryof the

subject from physiological facts. Subjects treated:clearnessof apprehension;doctrine of limits; syllogistic (a new analysis); the doctrineof logical breadth,depth,andarea; logical algebraaud the logic of relatives; probabililies; theoryoferrors; iuductiou aud hypothesis.

A courseof lecturesem MedievalLogic, tiesigueti to showthe spirit andleadingdoctimnesol the logic of the Midtlle Ages,wasalso givenby Mr. Peirce.

32. Probabilities: MR. C. S. PEIRCE, 1879-80.Developingthemathematicsof probabilities.

33. History of Astronomy: PROFESSOR NEWCOMB, of

the U. S. Naval Observatory,1876-77,twenty public lec-tures.

TheseLectures,(part of which were subsequentlyprinted in a volume), wereadaptedto studentsmud others who desired to becomeacquaintedwith thegeneralprogressof astronomuicalresearch,both ancient and modern. The spirit and me-thod of the ancientAstronomy,and the stepsby which the sciencehas reacheditsprasentstateof perfection~verefully discussed.

34. Geodesy PROFESSORHILGARD, of the U. S. CoastandGeodetic Survey. 1876-77,twenty public lectures.

Thiscourseof Lectures,attendedchiefly by thosedevotedto thepursuit of CivilEngineerin,,,exhibited thenauthodsand resultsof extended topographicalsurveysin Europeand America.

35. Philosophy of Physics: PROFESSOR JOHN TROW-

BRIDGE, of Harvard University, 1879-80, twelve publiclectures.

This courseillustrated before a generalaudiencethe modernmodeof investi-gationrespectingheat,Sound,Light,Electricity and-~tagnetism,and drewattentionto the Philosophyof Physics,andthe importanceof this branchof science.

FEB., i88o.]

JOHNS HOPKINS

LIST OF APPARATUS IN PHYSICS.Designed for Scientific Researches and involving Accurate Measurement.

272e Universily has also the o~7I(1rolus eqaisitefor denions/ralions.

(Repnblishcd,with additions,from theLibrary Bnllctin of Harvard University No. 12, l8~9.)

ACOUSTICS.

All the ordinary apparatusby Koenig of Paris, including Helm-holtz’s double siren, Lissajousvibrating microscope,Hastings’ pen-dulum comparator,&c.

OPTIcs.

i. Aleyerstein Sfectrometer—largemodel. The circle is of i6centimetersradius,divided on silver to 6’ and reading by two micro-scopesto 2”. The probableand periodic errors of graduation havebeen investigated, and are given in the “American Journal ofScience,” vol. xv. p. 270. Having a common axis with the largecircle is a table rotating independently, 6.~ centimeters radius,graduatedon a silver limb, and by two verniers to single minutes.The massivestand hasa joint by which the circle maybe broughtinto a vertical plane. Aperture of telescopeand collimator 4.0 centi-meters, focal length 34 centimeters,powers from 13 upward. Asmaller telescope 2.0 centimeters aperture, i8.o centimeters focallength, power 7, may be placed on a third support rigidly connectedwith the microscope bearers. The accessoriesof this instrumentare

(a). Two telescopeswith Nicol prisms before objectives longerdiagonalsof prisms, 2.0 centimeters; lennth of telescopes,20.0 centi-meters; power, 3 ; position angles of prisms read by circles of 3.5centimetersradius to minutesof arc.

(b). Babinet’s compensatorwith wedgeof 3 centimetersavailablelength.

(C). High powercollimating ocular.(a’). Low powercollimating ocular. -

(e). Threemicrometereye-pieces.2. Sfectrorneter,by Schmidt and Haensch. The circle hasa silver

limb i6 centimetersradius,divided to 6’ and readby microscopesto2”. Table in centreh~sa nraduation6.o centimetersradius,readingbby verniersto 1’. Aperture of objectivesof telescopeand collimator,3.9 centimeters; focal length, 35.0 centimeters; power, 13. Theanglebetweenlines of collimation of telescopeand tile collimatormaybe readby small circle to single degrees.

3. Stein/wit’s S~ectrosco~e. The clear aperture of train, includingt~o

60n prisms,is 4.0 centimeters. Focal length of collimator anrltelescope32.5 centimeters,powers,8, 12, etc. Photographicscale.

4. Silbermana’s Heliostat, etc. This instrument by Duboscq,hastwo mirrors, i8.o centimetersby 9.0 centimeters,one silver underglass andthe other silver. Also, Jorte-lumi~re.

5. Heliostat,with perfectplanemirror i6.8 c. m.diameter. Designedby Rowlandand madeby Schneider.

6. 7amin’s Interferezitial Refractometer,with tubes100 centimeterslong, for the study of refraction in gasesanda glass trough 20 centi-meterslong for liquids, by Duboscq.

7. Complete apparatusfor thestudy of phenomenaof interference,by Duboscq.

8. Phiotografli/c AAparatus. Objective 6. centimeters aperture,and about40 centimetersfocal length for plates; 10 X 12 inches,bySteinheil. Dark room,collection of chemicalsand everythingneces-sary for experimentson this subject.

9. Becquerel’sF/ios1s5/ioroscofe,by Duboscq.10. Polarizing Af~aratus, by Steeg; also by Duboscq.ii. Apparatus for producing monochromaticlight of any color.

Designedby Hastings and madeby Schneider.12. Prisms,gratings, etc.a. Hollow prism by Meyerstein; aperture, 6.i X 5.2 centimeters.b. Hollow prism by Steinheil ; aperture,2.2 centimeters.c. Thallium glass prism by Steinheil ; aperture,4.8 centimeters.a’. Two flint glass prisms by Steinheil aperture,4.7 centimeters.e. Crownglass prisms by Steinheil; aperture,4.8 centimeters.f. Two quartzprisms by Steeg; faces,3.4 X 3.0 centimeters.g. Iceland spar prism ; faces,2.6 X 2.2 centimeters,by Steeg.ii. Two rocksalt prisms; faces, 5.o X 4.0 centimeters,by Steeg.

Also rocksalt lens.i. Large Nicol prism, largest diagonal 6.~ centimeters. Also a

numberof smallerones.f Gratings on speculuin metal 4.3 X 3.9 centimeters with 8648

lines to the inch, and 4.4 X 4.4 centimeterswith 17,396 lines to theinch,and a smaller glass grating with 8648 lines to the inch, all byChapmanwith Rutherfurd’sengine.

Kirchoff’s, Angstrom’s, and Rutherfurd’s maps of the solar spec-trurn.

k. Oldl telescopeby Dollond. Objective about4 in. diameterand6 ft. focal length.

ELECTRICITy AND MAGNETISM.

The distinguishingfeatureof the apparatusfor thesesubjectsis its.accuracyandthe determinationof the constants in absolutemeasure.The collection is unique in this respect.

13. Rosolanel’sAbsoluteElectrometerfor potentials representedbysparks of about 0.1 to inch. Designed on Sir Win. Thomsonsguard-ringprinciple andconstructedby Edelmaunof Munich. Guard-ring 33.5 centimetersdiameter,and can be separatedabout 7 centi-meters,the distancebeing readby vernier to o.oi centimeter. Mov-able disc io centimetersdiameter,and firmly attached to arm of abalancesensitive to I mgr. Balancemovesonly .01 centimeter,andmeansof two distancesof the discs are taken, the one to move it toupper and the other to lower stop. Weights of from to 5 grammesordlinarily used. Discsground and ~olisked to mirror surl=zceafterinc/ce/plating.

14. Rosa/and’sElectrostatic StandardGondenser. ConstructedbyGrunow of New York. One spherewithin the other nickel platedand ~round to mirror siciface, with extra ball for interior. Balls, 7and 8 inches diameter. Hollow sphere,10 inches diameter. Appa-ratus for centering. Radii determined by loss of xveight in water.Canbe charged and dischargedany number of times at the rateofthreeper second,by meansof fine wires which pass in momentarilyfrom outsideand thus do not changethe capacitygreatly. Any con-densercan be coml)aredwith it by meansof anelectrometer.

i~. Thomson’sQuadrant Electrometer,by White of Glasgow,withThomson’skey.

i6. Gondenser-J microfarad by Elliott.17. Goinmutatorsfor hinh (say I inch spark)as well as low tension.i8. Rowland’s Ga/vanometerfor the absolute measurementof

dischargesof high tension. Constructedby Rowlandand Schneider.Coils wound with paper between,and boiled in parafin in vacua atioo

0 C. to be thoroughly dry. Needle shieldedi from electrostaticaction, and deflection read by mirror and scale. Number of coils.about11,000. Constant on the cm. gr. second system 19,091. = Gof Maxwell asdeterminedby comparisonwith gaivanometerdescribedin American Journalof Science,vol. xv, p. 334. See No. 19 below.

19. Rosa/and’s absolute Galvanometer for the measure of quiteweakcurrents. Constant 1833.2. See AmericanJournalof Science,vol. xv., p. 334. Constant very accurately known. 1790 turns.Can be used as sine galvanometeror with mirror and scale. Hori-zontal circle readsto I’, but is readily estimatedto 30”. Telescopeand bar for determining horizontal intensity in exact position ofinstruin ent.

20. Rosa/and’sTangent Galvanometer,brass circle ~o centimetersdiameter. Circle gradluated to i~’ and 20 centimeters diameter.From I to 243 turns can be used,the constantof each set beingknown with great accuracy. Made by Meyerstein,but altered andwoundaudi coils measuredby Rowland.

21. Tsao T/zomson’sGalvanometersof high and low resistance,thefirst differential with coils around both needilesand setof shunts,byElliott of Londlon.

22. TzooNob/li Astatic Galvanometersby Elliott, and one by Sal-leron.

23. W/edemannGa/vanomete;swith two sets of coils and two kindsof needles. Readingby mirror and scale.

24. Galvanometerwith large wire for experimentson the dampingeffect of the coils on the needle,and for determiningresistanceinabsolutemeasure. Designedby Rowlandand madeby Schneider.

25. TangentGa/vanometer,wooden circle, with variety of coils ofknown constant.

26. Mirror Ga/vanometer.27. Rosa/asia’s wooden circle, 84 centimeters diameter,carefully

laid up out of maple wood, and containing severalgrooves on theedgeto containsiogle wires. It is used to surrounda galvanometer,wilen, by the aidi of tile electrodynamometer,the horizontal intensitycan bemeasuredat any instant. Extremely useful.

26 [No. 3.

UNIVERSITY CIRCULAES.

28. Electrodynamometerof form given in Maxwell’s Electricity,vol. ii, p. 330. Outer circles about 27.5 centimetersdiameter with240 windingson eachside. Constant,G, of outercoils 78,371 on cm.gin. secondsystem. Inner coils about 5.5 centimetersdiameterwith63 coils in each. Moment of inertia of suspendedcoil accuratelyknown. Constantcalculatedand alsodeterminedby comparisonwitha tangent galvanometermadeof the circle describedabove. Made(partly) by Gurley of Troy, and circles woundand measuredby Row-land.

29. Electrodyin-unometer,Quincke’s form for weak currents, byEdelmanoof Munich.

30. Standardsof Resistancemountedso that theycan be placedinwater. i and io ohms by Elliott; io, 100, and i,ooo ohms by War-den, Muirhead, and Clark of London alsomounted in anotherstylei, io and ioo Siemens’units, by Siemens and Haiske of BerlinAlso three copies of coil whose al)solute resistancewas determinedby Rowlandas 34.719 earti?qnad-Fsec.

31. Resistancecoils in boxes to io,ooo and io,oo~to ioo,000 ohmsby Elliott, and to io,ooo Siemens’units by Edelmann.

32. Rowland’sResistanceComparator. Ten coils of io ohms each,arrangedso that they can be joined in seriesor abreast,thus makingi, io, and ioo ohms besidesintermediateones. Made by Schneiderand adjustedby Rowland.

33. Two bridges of Jenkins’ form for the accurate comparisonofequal resistances,and also a Wheatstonebridge, having a wire ofplatinum-iridium alloy one meterlong, by Elliott.

34. Magneto-electric Mackine for 1,200 candies, by SiemensBrothers,London, with engine to drive it, and both Siemens’andFoucault’s lamps. Also battery of 6o largebichromatecells.

35. Ruhnzkorfcoil; spark i~ or 20 centimeters,by Ruhmkorff ofParis.

36. Rowla;ids Earth inductor with brass circle. 30 centimetersliameter,wound and measuredby Rowland. Made by MeyersteinofGdtti ngen.

37. Ruhmhorjf’s Afparatus for diamagnetism,by Ruhmkorff ofParis.

38. Electric Clocksbeatingsecondsfrom regulator.39. Rowland’sStandardof ElectromagneticInduction. Three coils

on brass cylinders which can be l)laced accuratelyon top of eachother. See American Journal of Science,vol. xv. Mutual poten-tial of coils with unit current3775500., 2561974., 2051320., etc., on thecm. grin. secondsystem.

40. Telescopes,Scales, and Mirrors. Silvered brass millimeterscaleby Brown and Sharp. Mounted telescopeby Steinheil,objective4.0 centimetersdiameter,with three oculars, giving powersof 20, 40,and 8o. Unmountedtelescopeby Steinheil, objective 2.7 centimetersdiameters,and 3 oculars.

Mounted telescopeand paper scaleby Meyerstein: objective, 2.7centimetersdiameter.

41. Thin mirrors and plain parallel glassesby Steinheil. Themirrors gavea perfect imagewith theiitghestmagnifyingrower.

Thomson’sReplenisheron large scale for use with electrometerHoltz andfriction machines,Leyden jar batteries,Geisslertubes,&c.

HEAT.

42. Rowland’s Instrumentfor comfaring the mercurial with theair Thermometerbetween o and ioo

0 C. Constructed by Schneider.Readingsseldomdiffer more than 0.020 or 0030 C. at any one point,especiallyup to 400 C., and a changeis contemplatedwhich will im-prove it.

43. Rowland’sI;istru’nent for comparingThermometersfrom ~ toabout3oo~ C. Constructedby Schneider. Accurate to abouto. i0 C.

44. Regnault’sAir Thermometer,by Golaz, Paris.45. ~7olly’s Air Thermometer, by Berberich, Praeparator, Phys.

- Inst., Univ. of Munich.46. Regnault’s Apparatusfor Expansion of Gasesboth at con-

stant pressureand constant volume,also Regnault’s form of Rud-berg’sapparatus,by Golaz, Paris.

47. Regnault’s Apparatus for Tension of Vipors, including: a.the boiler; b. the reservoir for compressed air; c. a rotary pumpfor compressinggases;d. mercurial manometer,by Goiaz, Paris.

48. Regnault’s Apparatus for specific Heat of solids, by Golaz,Paris.

49. Regnault’sHygrometerwith Aspirator, by Golaz, Paris.

50. Thermometers,about 30 01. 40, principally by Baudin,Paris,and Geissler, Bonn. . Many of these have been compared with theair thermometeras well as with standardsby Fastrd, Casella,or fromKew. The thermometersup to 400 C. undoubtedlyrepresent theairthermometermore accuratelythan any so far constructed,and aresul)posed to agreewith it to about o.oi0 C. They have been com-paredwith it eight times cluring about one yearor more. The errorin calorimetric investigations from using uncomparedthermometersniay amount to two per cent.

51. Rowland’s Apparatusfor determiningChangeof spec~ftcI-leafof Liquids with temperature,by Schneider.

52. Diilo;ig’s Apparatusfor the Heat 01 Cbnibustion, by Salleron,Paris.

53. Melloni’s Apparatus for radiant energy,by Salleron,Paris.54. Two .Jnstru,nentsfor thecalibration of mercurial thermometers,

one by Golazand the otherby Salleron.~ Rowland’sApparatusfor deterniining the niechanical Equiv.

alent of Heat,or for investigating the specific heat of liquids and theirchancre with rise of temperature.

This instrument was constructed by the aid of funds contributed bythe Rumfordcommitteeof the AmericanAcademyof Artsand Sciences,but the instrumentxviii remainfor the presentat Baltimore. It wasconstructedby Schneider. It is run by a petroleum engine,No. 67below

* * * To be constructedsoonApparatusfor compressinggasesto 1000 atmospheres.Apparatusfor accurately cietermining the form of the adiabatic

curve of gasesand vaporsat aiiy teniperatureup to about 1000 C.

MISCELLANEOUS.

~6. Cbniparator,by Meyerstein,for bars i meterlong. Microscopescannot beset nearerthan 10 centimeters. One division of head ofmicrometerscrexvsis about millimeter.

57. MicroscopeCbinparator, designed by Rowland after Rogersplan and madeby Grunow.

~8. Dividing Engine,by Perreaux. Free motion about ~5 centi-meters Screw ~.. millimeter thread. Head divided into 250 parts.2~oi divisionsof head give i millimeter almost exactly. Subsidiaryscrewatright-angles to the other.

59. Air Funips. Rotaryand common,by Ritchie, of Boston; mer-cury, on Jolly’s plan, by Berberich,of Munich.

6o. Rotary Fiinip for compressinggases to i~ atmospheres,byGolaz, Paris.

6i. ThreeMercury Gauges;one about25 metershigh, and measur-ing pressuresup to about33 atmospheres;one movableand measur-ing pressurefrom I to 4 atmospheres and one measuringfrom oto i atmosphere.

62. Ilaronieter, by JamesGreenof New York, with very large tube.63. Two Cathetonieters,one by Meyerstein, and the other by

Saileron.64. StandardMeters,comparedat Washington.6~. Ralancesand Wei~hts. One balanceweighing to 5 kilo. and

accurate to about ing. xvith weights from 5 kilo. to mg. Oneweiohinu to 200 crrms. accurateto about 0.1 mg. xv ith weights froma100 gr. to mg. These are by Schickert of Dresden. One heavybalanceweighing to about25 kilo. and accurate to abouta. grin, bySch n eider.

Standardglass kilogramme on Jolly’s plan, and compared withBerlin standard,by Berberich of Munich.

The first balancementioned is mounted on top of a case,so thatglobesfor weighinggasescan be suspendedbeneathit.

66. Clock-work with Foucault’s regulator for running small appa-ratusat a regular velocity.

67. Petroleuni Engineof three-horsepower. It is capableof givinga large amount of compressed air at more than ioo pounds to thesquareinch pressure,and might beusedfor repeatingThomson’s andJoule’s experiments,or any otherson the foxy of gases.

68 Two Spheronieters,largeby Meyerstein,and small by Salleron.69. Severalextra micrometereye-pieces.70. Apparatusfor Researcheson theFlow of Liquids. Greatest

availableheadabout1.4 meters. -

71. Revolving niirror capable of 250 revolutions per second.Mirror of glass silveredon both sides and 4.7 cm. diameter. Drivingpower, compressedair from a Root blower. Designed by Rowlandand madeby Schneider.

72. Metallic /l=tanonieterfor very minutedifferencesof pressure,byEdelmannof Munich.

5 * Nos. 19, 25, 26, and 28,and the silveredscaleof No. 40belong to ProfessorRow-land, but are usedin the laboratory.

FEB., i88o.] 27

28 7OHNS HOPKINS [No. 3~

LIST OF PERIODICALS.Thefollowin.~ list containsan ennmerationof theprincipal periodicals,devotedeitherwholly orpartially to thediscussionof mathematicaland physicalsubjects,which

aretakenby the Libraryof the JohnsHopkinsUniversity,andtheLibraryofthePeabodyInstitote.

The publicationsof learnedsocietiesare nsnally given nuder the nameof the place wherethe meetingsareheld. TheUniversity Library is designatedby H. ThePeabodyLibrary is designatedby P. A completesetis thusindicatedP

5 etc.

Americanacad.of arts and sciences: Memoirs. Proceedings. Boston. P.*

Americanassocn for the advancementof sci.: Proceedings. Salem. H. P.*Americanephemerisand nautical almanac. Washington. H. P.

American journal of mathematics. Baltimore. l1.~ P9~

Americanjournal of scienceand arts. New Haven. H * P *

Analyst. Des Moines. H.Annalenderphysik und chemie. (Poggeudorif.) Leipzig. H.* P.~

Annalesde chimie et dephysique. Paris. H. PA~

Annalesde l’ohservatoirede Paris: M~moires. Observations. P2~Annalesdesmines. Paris.

Annalesdes poutset chauss~es. Paris.

Annalesdu conservatoiredes arts et in~tiers. Paris.Annali di matematica. (l3rioschi.) Milan. H.

Aunnaire du bureaudeslongitudes. Paris. P.5

Annual recordof scienceand industry. New York. H. P.~

Archiv dermathematikund physik. (Grunert.) Leipzig. 11. P.~Archives dessciencesphysiqueset naturelles. Geneva. PA~

Astronomische nachrichten. Kiel. H. P.

Bollettino di bihliogr. e storia delle scienzematemat.e fisiche. Rome. H.*

Berlin. Kbnigliche akad.derwissensch.:Physikal. Abhdl.Mathemat.Abhdl. H. PA~Monaisberichie. II.

British assoc’nfor the advancementof sci.: Proceedings. London. H.* P.~Reports. London. H.* PA~

Brussels. Acad~miedes sciencesde Belgique : Aunnaire. Bulletins. P.*M~moires couronn~sdes savants~trangers.

M~moires et nouveauxm6moires.

Buffalo. Academyof science: Bulletin.

Bulletin de la soci~t~mathfmatiquede France. Paris. H.

Bulletin dessciencesmath~matiqueset de lastronomie. Paris. H.

Cambridge (Mass.) Annalsof Harv. coil, observatory. H.

Cambridge(England). Philosophical society. Proceedings. H.Transactions. H. P.*

Cherbourg. Soci~t6 nationale des sciences naturelles et math6-

matiques: M~moires. H.

Chicago. Academyof sciences: Transactions. p.Comptesrendusdes s6ancesde l’acad~miedessciences. Paris. H. P.*

Connecticutacademyof arts and sciences: Transactions. H. P)~Dingler’s polytechnisehesjournal. Augshurg. H. P.~

Dublin : Royal Irish academy: Transactions.

Edinburgh. Royal society: TransactionsEducationaltimes. London. H.

Engineer. London. P.

Engineering. London. p .*

Engineeringandmining journal. New York. H. P*

Fortschritteder Physik. Berlin. H.

Franklin Institute : Journal. Philadelphia. H. P.*

Giornale di matematiche. Naples. H.Gbttingen. Kiinigliche gesellschaftderwissenchaften:Nachrichten. H. P.~5

Gbttingischegelehrteauzeigen. H. P.*

Great Britain and Ireland: Governmentpublications. P.Institut de France: Acad~mie dessciences: Comptesrendus.

M6moires. M6moires pr~sent6spar diverssavants.

Sciencesmath~matiqueset physiques.

Institution of civil engineers:Minutes. London.

Irish acadeuty(royal): Transactions. Dublin.Jahrbuchflber die fortschritteder mathematik. Berlin. H.

Jahresberichtliberdie chemie und physik. Giessen. H.Journalde l’&ole polytechnique. Paris. I-I. P.*Journal de math6matiquespureset appliqu~es. Paris. H. P.*

Journalde physiquethf~oriqueet appliqu6e. Paris. H.

Journal fUr d. reine und angewandtemathematik. (Crelle.) Berlin.

Leipzig. Astronomischegesselischaft:Vierteljahrsschrift.

Li~ee : Soci~t6 royaledesscieners: M~muires.London. Institution of civil engineers: Minutes.

Mathematicalsociety: Proceedings.

Royal astronomicalsociety: Memoirs.Monthly notices. Proceedings.

Royal society: Philosophicaltransactions.Proceedings.

London, Edinburghand Dublin philosophicalmagazine. London.

Mathematischeannalen(Clebsch.) Leipzig.Messengerof mathematics. London.

Munich. Kdnigliche akademieder wissenschaften:

Abbandlungendermath~mat.physik. classe.Sitzungsberichteder mathemat.physik. classe.

Nature. London.

Natitical almanac. (London.)Nautical almanac. (Washington.)

Nouvellecorrespondancemath~matique. Liege.

Paris. Bureaudeslongitudes: Anunaire.

Conservatoiredesarts et m6tiers : Annales.

Ecolepolytechnique: Journal.Observatnire: M ~cmoires. Observations.

Soci~6 mathematique: Bulletin.See Institut de France.

Philadelphia. Franklin Institute : Journal.

Amer. philosophicalsociety; Proc. and Trans.

Philosophicaltransactions. London.

Poiytechnischesjournal. (Dingier.) Augsburg.

Popularsciencemonthly. Ne~v York.Quarterlyjournal of pureand appliedmathematics. London.

Quarterlyjournal ofscience. London.Radcliffe observatory. Astronomical observations. Oxford.

Rendiconti dcl realeinstituto Lombardo di scienzee lettere. Milano.

Repertorium d. rein. u. angewandt.mathematik. Leipzig.

Repertorium fur experimental.physik. Miinchen.

Revuedescoursscientifiques. Paris.Rome. Atti della realeaccad.dei Lincei: Transunti. Memorie.

Royal society: Philosophical transactions. London.Proceedings. London.

Scientific american. New York.

St. Louis. Academyof sciences: Transactions.

St. Petersburg. Acad~mie imp~riale des sciences:Bulletin de la classephysico-math~m.

Bulletin scientifique.

M~langesmath~matiques.M6langesphysiqueset chimiques.

M6moires : Sciencesmath. l)hys. et natur.

M~moires pr~sent~spardivers savants.

Technologiste,Le. Paris.

Telegraphicjournal and electrical review. London.

U ni ted States: Governmentpublications.

Van Nostrand’sengineeringmagazine. New York.Vienna. K. K. akademieder tvissenschaften

Denkschriften: Mathemat-naturwissenclasse.

Sitzungsherichte: Mathemat..naturwissen.classe.Vierteljahrsschrilt derastronomisehengesellschaft. Leipzig.

Washington. Smithsonian institution : Contributions.

Miscellaneouscollections. Annual rel)orts.

Zeitschrift fur angewanclieelekiricitUislebre. Milnehen.Zeilsebrift dir mathematikund physik (Schlbmilch). Leipzig.

H. P.*H.

H. P*H. P.*H. P.~H. P.*H. PA’

H.

P..

H. P.*H.P.H. P.

H.

H. PA’

H.PA~

H. p*

H. PA~H.* P.’~

H. P.*H. PA’H. P.*H. PA~

H’.H.H.H.

H. P.*H. p*

H.P.

~~ *

P.P.

H.H. p*

H.

H. P.*H.

H.* P.~11*

H. p*

UNI VERSITY CIACULAKS.

LIST OF MATHEMATICAL AND PHYSICAL PAPERS,Published by Members of the University, September, 1876,to February, 1880.

B~ PuoFxssoxSYLVESTER.

Zn the American 7ozi;ma/of Mathematics, (1878—80.)

Application of the New Atomic Theory to the Graphical Repre-sentationof the Invariantsand Covariantsof Binary Quantics.

On Differentiants Expressedin Terms of the Differences of theRoots of their ParentQuantics.

Note on M. Hermite’s Law of Reciprocity.Completionof the Theory of Principal Forms.Additional Illustrations of the Law of Reciprocity.On the Principal Forms of the General Sextinvariantto a Quartic

and Quartinvariantto a Sextic.On the ProbableRelation of the SkewInvariantsof Binary Quintics

and Sextics to one another,and to the Skew Invariantof the sameWeight of the Binary Nonics.

On Clebsch’s EinfachstesSystemassoclirterFormen and its Gen-erali zation.

Note on the LadenburgCarbon-graph.Note on the Theoremcontainedin Prof. Lipschitz’s Paperentitled

“Demonstration of a FundamentalTheorem obtained by Mr. Syl-vester” in Am. Jour Math., I, pages336-341.

A Synoptical Table of the Irreducible Invariants and Covariantsto a Binary Quintic, with a Scholium on a Theoremin ConditionalHyperdeterminants

Noteson Determinantsand Duadic Disynthemes Two papers.On the CompleteSystemof the Grundformenof the Binary Quantic

of the Ninth Order.Tables of the Generating Functions and Gr6undforms for the

Binary Quanticsof the First Ten Orders.On the Resolutionof Numbers into theSum or Difference of two

Cubes.Tablesof the FundamentalCovariantsof a Systemof two Binary

Quanticsfor all Combinationsof Ordersnot exceedingFour, and Ob-servationson the preceding.

On the Divisors of Cyclotomic Functions.

Zn the Proceedingsof tile RoyalSociety,London.

On the Limits to the Orderand Degreeof the FundamentalInva-

riants of Binary Quantics. (1878.)

Zn the Messengerof ilfathe;natics, London.

Rule for Abbreviating the Calculation of the Number of In- orCo-Variants of a given Order and Weight in the Coefficients of aBinary Quantic of a given Degree. (1878).

Note on Continuants. (1878).On a Theoremconnectedwith Newton’s Rule for the Discoveryof

the ImaginaryRootsof Equations. (1879).On the Strict Relation betweenDiscriminantsand Remittants,and

the Productof Differencesof Rootsof Binary Forms. (188o).

In the London, Edinbnrgh a/id Diebli/i PhilosophicalMagazine,Lo/idon.

Two paperson Spherical Harmonics,containing the New Theoryof the Bipotential. (1876).

On a Generalizationof Taylor’s Theorem. (1877).Proof of the Hitherto UndemonstratedFundamentalTheoremof

Invariants. (1878).Note on an Equationof Finite Differences. (1879).

Zn the Edncatio/ial Ti/nes, London.

MathematicalQuestionsfor Solution, of an original characterandembodying distinct theories, monthly during the years 1876-79,in continuanceof a series begun manyyears ago.

7onral fur reine /1/id a/igezoa/idte Mathematik, (Crelle,) Berlin.

Sur les actionsmutuellesdesformes invariantivesd~riv6es. (1878).Sur les d6terminantscompos6s. (1879).Sur un d6terminantsym6trique qui comprendcommecas particulier

Ia premi~repartie de lYquation s6culaire. (1879).Note surune propri6t6 des6quations dont toutes lesracinessoot

r~elles. (1879).Sur lentrelacementd’une fonction par rapport ~t une autre. (1879).Preuveinstantan6ed’apr~sla m~thodede Fourier, de la r6alit6 des

racinesde l’6quations~culaire. (1879).

in the ComptesRe/id/is de l’Academie desSciencesde l’Institut deEra/ice.

Sum~ les invariants fondamentauxde Ia forme binaire du huiti~meordre. (1877).

Sur une m6thodealg6brique pourobtenir lensembledes invariantset descovariantsfondamentauxdune forme binaire. (1877).

Sur une m6thoclealg6brique pour obtenir l’ensembledesinvariantset descovariantsfondamentauxrl’une forme binaire et d’une combi-naisonquelconquedeformes binaires. (1877).

Sur le vrai nombre des covariants6l6mentairesdun svst~mededeuxformes biquadratiquesbinaires (1877).

Th6orie pour trouver le nombredescovariantset descontrevaniantsd’ordre et ded~gr6,donn~s lin6airement ind6pendantsd’un syst~mequelconquecle formes smmultan6es,contenant un nombre quelconquede variables. (1877).

Sur lesinvariants. (3 papers.) (1877).Sur la loi der~ciprocit6 pour lesinvariantset covariantsdesquantics

binaires. (1878).Sur la th6orie des formes associ6esde MM. Clebschet Gordan.

(1878).D6terminationdune limite sup6rieureaunombretotal desinvariants

et covariantsirr6ductibles desformes binaires. (1878).Sur les covariantsfonclamentauxd’un syst~me cubo-quadra(ique

binaire. (1878).Sur le vrai nombredesformesirr6ductibles dusyst~mecubo-biquad-

ratique. (1878).D6termination du nombre exact des covariants irr~ductibles du

syst~mecul)o-biquadratiquebinaire. (1878).Sur lescovariantsirr6ductiblesdu quanticdu septi~meordre. (1878).Sur la forme binaire du septi~meor7lre (1878).Sur la valeur moyennedes coefficients dansle d~veloppementd’un

d6terminantgaucheon sym6trique rl’un ordre infiniment grand,et surlesd6terminantsdoublementgauches. (1879).

Table des nombresde d6riv6es invariannives d’ordre et de ddgr~donn6s,apl)artenantsk Ia forme binaire du dixi~me ordre. ([879).

Sur la valeur moyennedes coefficients num6riques dans un d6ter-minant gauchedun ordre infiniment grand. (1879).

Sur une propri6t6 arithm6tiquedune certaine s6rie des nombresentiers. (1879).

Sur le vrai nombre descovariantsfondamentauxd’un syst~mededeuxcubiquesbinaires. (1879).

Sur les diviseursdesfonctionscyclotomiques. Two papers. (1880.)

B~ DR. W. E. SToRy.

Zn the A/ne/-ica/i 7onr/ial of Mathe/natics.

On the Elastic Potential of Crystals. (1878.)Note on the Paper of MR. KEMPE, entitled the “Geographical

Problem of the Four Colors,” in theAm. Jour.of Math., II, 3. (1879.)

B~ DR. T. CRAIG.

Motion of a Point on the Surface of an Ellipsoid. (Am. 7our. ofMath., 1878).

The Motion of a Solid in a Fluid. (A/n. 7ozir. of Math., 1878).Mathematical Theory of Fluid Motion (Va/i Nostra/id’s Eng.

Mag., 1879; also y5ri/ited i/i a vol/i/ne, New York, Va/i Nostrandi88o).

GeneralDifferential Equationfor DevelopableSurfaces. (7onr. ofFranklin 1/ist., 1879).

Projectionof the General Locusof Spaceof Four DimensionsintoSpaceof Three Dimensions. (A//i. ~o;ir. of Math., 1879).

The Motion of an Ellipsoid in a Fluid. (A//i. 70/u. of Math., 1879.)On the Spherewhich cuts Five given Spheresatthe sameAngle.

(A/ialyst, i88o).

B~ MR. F. FRANKLIN.

Bipunctual Coordinates. (A/n. 7onr. of Math., 1878).On a Problem of Isomerism. (A//i. 7our. of Math.. 1878).Notes on Partitions of Numbers,etc. (A/n. 7oiir. of Math., 1878,

1879).

FEB., i88o.] 29

2OHNS HOPKINS

Bx’ DR. G. 13. HALSTED.

Bibliography of Hyper-Spaceand Non-EuclicleanGeometry. (Aiii.7our. of Mat/i., 1878).

Note on the First English Euclid. (Am. 7our. of Mat/i., 1878).B~ Miss CHRISTINE LADD.

Quaternions. (Analyst, 1877).The Polynomial Theorem. (Analyst, 1878).On some Propertiesof Four Circles Inscribed in One and Circum-

scribed aboutAnother. (Analyst, 1878).On Pascal’sHexagram. (Am. 7our. of Mat/i., 1879).

By Mn. W. I. STRINGHAM.

SomeGeneralFormulaefor Integralsof Irrational Functions. (A;;i.7our. of Mat/i., 1879).

The Quaternion Formulae for Quantification of Curv~s, Surfacesand Solids for Barycentres. (Am. 7onr. of Mat/i., 1879).

B~ PROFESSOR ROWLAND.

The Magnetic Effect of Electrical Convection. (Am. 7our. ofScience, 1878; abstract by I-IeIm/ioltz in Monatsberic/it d. Berlin.Akad..

Researchon the Absolute Unit of Electrical Resistance. (Avi.7onr. of Science,1878).

Note on the Theory of Electrical Absorption. (.4m. j7onr. ofMat/i., 1878).

On Professor Ayrton and Perry’s New Theory of the Earth’sMagnetism,with a Note on a New Theory of the Aurora. (F/il/os.Mag., 1879).

Note on the Magnetic Effect of Electrical Convection. (P/iiYos.A/ag., 1879).

On the DiamagneticConstantsof Bismuth and Calc-Sparin Abso-lute Measure,part I. (Am. ,7’oiir. of Science,1879).

On the MechanicalEquivalent of Heat,with SubsidiaryResearcheson the Variation of the Mercurial from the Air Thermometer,and onthe Variation of the Specific Heat of Water. (Anier. Acad., Boston,I 88o; alsopri;ited se75arately,Cambridgs,7. Wilson &-‘ Son, 126 ~8vo.,one75/ate.)

By DR. C. S. HASTINGS.

The Influence of Temperatureon the Optical Constantsof Glass.(Am. 7onr. of Science,1878).

On Lockyer’s Hypothesis,that theso-calledElementsare CompoundBodies. (Am. G/iem. 7onr., 1879).

On thePerfectColor Correction in Triple Objectives. (A in. 7our.of Science,1879).

B~ Mit. C. S. PEIRCE.

On the Ghosts in Rutherfurd’s Diffraction Spectra. (A in. 7our.of/i/at/i., i88o).

A Quincuncial Projection of the Sphere. (A iii. 7our. of Mat/i.,i88o).

BY DR. W. W. JACQUES.

Effect of the Motion of Air within anAuditorium upon its AcousticQualities. (7our. of Fi-aii/i/in lust., 1878; P/i/os. Mag., 1879).

Velocity of Very Loud Sounds.(Am. 7on’. of Science,1879; P/i/os.Mag., 1879).

Diamagnetic Constants of Bismuth and Calc-Spar Crystals inAbsolute Measure. (Ani. 7our. of Scieiice,1879).

Distribution of Heat in the Spectraof Various Sourcesof Radia-tion. (A vi. Acad.,Boston, 1879).

B~ MR. E. H. HALL.

On a New Action of the Magnet on Electric Currents. (Am. 7ozir.

of Mat/i., 1879).By DII. E. L. NICHOLS.

A New Explanationof theColors of theSky. (P/i/os. Mag., 1879).Characterand Intensity of the Rays emitted by glowinr Platinum.

(Am. 7onr. of Scieiice,1879).Optical Method for the Measurementof High Temperatures.

(A in. 7our. of Science,i88o).

NoTa.—~1heforegoinglist doesnotincludethe papersof any xvriter published previouslyto his connectionwith this institution, or after he left. it; and it omits lightarticlesandthoseof a merely transientinterest. It duesnutinclude the papersof non-residentlecturers.

Thefollowinl note may beregardedasa Postscriptto the Memoir by ProfessorRowlandon the MechanicalEquiv eat or Heat. tCambildge.1881.) recently published in the Pro’ceedingsof theAmericanAcademyor Arts and ~clencesin Boston.

NOTE FROM PROFESSOR ROWLAND.[Gomparison with Di’. Joule’s Therinometei’.]

Di’. Joulehaskindly sent me the comparisonof my therinometei’,No.6166,with his, andthe i’esult will bepublished in full in the Proceed-ings of the American Academy of Sciences.” In this mannerI havebeenable to makethe exactreduction of Isis i’esults to the nil’ thermo.metei’. The following aretheresults:

METhOD.

Filetionof watei’...

n~ercury

lion

Electric beating...

Friction ofwater...‘‘ ‘‘ ‘‘

~o %o. 0.0

8e o 0

100 781 5

140 7707

90 772.8

90 775.4

90 776.0

90~ 773.9

180.6

140.7 772.7

120.7 774.6

150.5 773.1

140.5 767.0

l7~.3 774.0

Joule’svalue re-]ducedto the airthermometerand

,t.o the latiturle uSBaltimore.En2ish MetricSystem.System.

787.0 442.8

I 778.0 426.8

779.2 427.5

I 781.4 428.7

782.2 429.1

780.2 428.04280

776.1 425.8

778.5 427.1

776.4 426.0

770.5 422.7

777.0 426.3

0

a

427.4

427.7

42.8.8

428.8

428.8

428.8

426.7

427.6

428.0

427.3

427.5

426.9

0

0

+15.4

—‘9

— 13

—.1

+3—.8

+1.3

—18

—.9

— 1.3

— 4.8

—.6

Brief Announcements.DR. C. SIHLER, Assistant in the Biological Laboratory, will give,

under thedirection of theProfessorof Biology, a courseof eighteenpractical lessonsin the lilse of t/ie Microscofe,and in Microsco75icAnatoniy. The lessons will begin Saturday,March 6, and will begiven on Wednesdaysand Saturdaysof eachweek at 3 P. M., con-tinuing for about one hourand a half each. The courseis intendedfor medical studentsand physicians. Fee,ten dollars, to bepaid atthe Treasurer’soffice, in the University building.

MR. A. S. COOK, Associate in English, hasformed a class for thestudy of 5/enientary Ang/o-Saxomi. It will meeton Tuesdays,Wed-nesdaysand Fridays, at 4 P. M., in rooms A and B, No. 187 NorthHoward St., beginning Februaryto.

D~. H. B. ADAMS, Associate in History, hasorganizeda class forthe study of the history amid Eleniemitsof Political Ecomioniy,whichwill meeton Mondays,Wednesdays,ThursdaysandFridays,at 4 P. M.,in room 3, commencing February9

DR. MINTON WARREN, Associate in? Latin, has formed classesforreadingLivy, books xxi and xxii, and Lucretimis, books i, iii and v,meetingfour tim~s a week,beginningTuesday,February17.

HENRY C. ADAMS, Ph. D., lately a Fellow of JohnsHopkins Uni-versity, and now lecttirer at Cornell University, will commence acourseof instruction in Political Ecomioniy,at this University in theearly spring.

MR. SYDNEY LANIER, Lecturer on, English Literature,hasformeda classfor expositoryreadingsin Emig/is/i Literature.

DR. THOMAS CRAIG, Lectureron Mathematics,will give a courseofthirty lectureson thegeneralT/ieory of Enmictiomisof A Gomn75/exVan-~zble,includimig Riemmiamin’s T/ieory, on Tuesdays,Thursdaysand Fri-days, at 7 P. M., beginning Tuesday, February24. The followingworks of reference are recommended: Briot et Bouquet—T/i/oriedesFomictiomis Elli75tiqnes. Neumann—Vorlesmingemiilber Riemnamimi‘5T/ieorie. Durege—Elememite der T/ieorie denFunctionemi.

30 [No. 3.

1847

1850

1867

1878

The meandifferenceof thetwo amountsto only 1 in 430, almostexactlythe sameas I estimatedin the body of my pal)el’, an extremelysutisfac-tory result. H. A. ROWLAND.

BALTIMORE, February 16th, 1880.

UNI VERSITY GII?CULA RS. 3’

PHYSICAL bABORATORY: COMPARISON OF STANDARDS.BALTIMORE, February, 1880.

In order to secureuniformity throughout the country in certain physicalstandards,and to facilitate the useof the absolutesystemof heatmeasure-ment, it hasbeenthought advisableto organizein thel)hysical departmentofthis Universitya sub-department,wherecomparisonsofstandardscaohemade.

Comparisonof Thermomelers. At presentwe areonly able to makecom-parisonsof thermometers,and so to reducetheir degreesto theabsolutescaleof theperfettgasthermometer.

As the work is very laborious,it is prol)osedto makethis sub-departmentself-supporting,by a system of fees sufficient to cover the bare costof thelabor,so that all may avail themselvesofthe facilities hereoffered.

In a recentstudy of standardthermometersby Geissler,Baudin, Fastrb,CasellaantI from Kew and the comparisonof the samewith the air ther-mometer,the differencesdue to thevariety of the glass amountedto 00. 2 or00. 3 C., andthedifferencesfrom the air thermometerwere ashigh sometimesas00. 3 C. at the400 point.

The error from using uncomparedmercurial thermometersin calorimetricinvestigatioLs mayamount to one or two per cent. For thisreasontheairthermometerhas been taken as the standard, and all c~mparisonswill hereducedto thefinal absolutestandardofthe perfectgasthermometer.

Very completestudiesof thermometershavebeenmade between0 and400

C. and a less completestudyhetween0 and1000, andbetween1000 and2500.

Up to 1000, our thermometershave not only been comparedwith the airthermometer,but also with standardsby Fastri, Geissler,Casella,Baudinandfrom Kew.

The studyfrom 0 to 400 hasbeen publishedby the AmericanAcademyofSciences,at Boston, in a memoir on the Mechanical Equivalent of [feat.One of our thermometersis alsonow in the handsof Dr. Joule,who hascomparedit uith theoriginal thermometersusedby him in the determinationof theMechanicalEquivalentof Heat.

The apparatusfor thecomparisonup to 1000 C., is describedin thepaperabove referredto. The thermometersaretotally immersedin the waterwiththeir stems very near the bulb of the air thermometers. From 1000 up to

2500 an oil bath is used,the bulbs only being in the oil, but the stemsareheatedto thesamedegreeby beingin contactwith a heavy copperbar, whosetemperatureis noted by separatethermometers.

The ordinarycomparisonis madewith thestemsof the thermometersin avertical position. Where theyare usedin a horizontalpositiona correctionwill have to be made,and this correction will be determinedwhen it is sodesired. When thecomparisonis madeonly to 400, we cancomparethem ina horizontal position,but we cannot then insure thesameaccuracyaswhenthey arevertical, andit is neveradvisableto use them in that position.

Where desired, a study will bemadeof the changesof the zero point asafunction of the teml)eratureto which it hasbeen heated,and of the time, butthis study is not advised,asit doesnot lead to very valuableresults.

Thermometerswith metal,woodenor paper scales,are generallytoo poorto be worth comparison,aiftl would often be sl)oiledl by theimmersion in thewater. Thermometerswith metal caps of Geisslersform areoften injured,especiallywhen heatedto 250~ C. Therefore,comparisonsof thermometersof these classeswill not be undertaken,exceptin thecaseof standardslongusedfor someparticularpurpose,or in that of fine Geisslerthermometers.

Threeintervals (or thecomparisonhavebeen selected.A. Between0 and40~ for thermometersusedfor meteorologicalobserva.

tions, determinationof the temperatureof standardsof length,calorimetricdeterminations,and all purposeswhere extremeaccuracyis desired withinthat limit. To obtain thefull value of sucha comparison;thermometersshould begraduatedat leastasfine as00. 1 C. or 0~. 2 F.

B. Between0 and 1000 C. It is advised that the thermometerssent begraduatedat leastas fine as 0~. 2 C. or U

0. 5 F.C. Between1000 and2500 for thermometersusedby chemistsin thedeter.

mination of melting or boiling points. Thermometersshould be graduatedto 10 C. or 10 F.

Three kinds of comparisonwill bemadefor eachof theintervals 0 to 400,

0 to 1000, and 1000 to 250~ asfollows.1st. Direct comparisonwith theair thermometer,andalsoa primary stan-

dard. This comparisonis very laborious,andis not recommendedexceptinvery exceptionalcases,as morethan one comparisonshouldbemadeto insuregood results.

2nd. Comparisonwith primary standardswhich havebeen comparedmanytimes with the air thermometer. This is recommendedwherean error of1o is of someimportance.

TOo3rd. Comparison with secondarystandardswhich have been compared

many timeswith theprimary standards,andnot very often directly with theairthermometer. This is recommendedin all ordinarycases,wherean errorof

canbe tolerated.1~0 0

Whenseveralcomparisonsaremade,thefollowing intervalswill beallowedbetweenthe experiments,so that the zeroreadingmaybeallowedto return toits primitive value.

Thermometersheatedto 4C0 C. about 1 week.U 0 100~ C. 6 weeks.

250~ C. “ 4 months.The latter interval is too small for anaccuratereturn.For theexactdetailsofthemethod of comparison,I must refer to theabove

mentionedpaperon theMechanicalEquivalentof Heat.It is advisablein all caseswheie greataccuracyis desired, that a number

of comparisonsbe utade,seeing that delicate thermometersare constantlyvarying throughslight limits, andthe averagestatecan only bedeterminedbyrepeatedexperiments.

Re~ports. In the report of the comparison,the original readingswill begiventogetherwith the reducedones,andthe plot of the curve of errorsofthe thermometerat every point. From this curve, tile error of the ther-mometerat any readingcan be found.

It is proposedto publish at theendof theyear a completereportof all thecomparisonsmadeduring the year,together with all new determinationsoftheerrorsof thestandards,andto sendit to anyaddressata price which wewill hereafterannounce.

Fees. The comparatorsallow five thermometersonly to be placedin them,of which two are our own standardsin ordinary comparisons,and one indirect comparisonswith the air thermometer. Therefore,threethermometerscan be comparedas easily asone in ordinary cases,and four in direct coin•

parisons. Hencethefollowing systemof feeshasbeenmadeout.A. Whena nuniber of Tizermometersore sent.

Comparisonbetween0 and400 C. for 3 or 4 thermometers.$20 00

11 00800

Direct, probableerror at each point,

Primary Standards = TOOSecondary “ =

0 and l00~ for 3 or 4 thermometers.

Direct, probableerror at eachpoint, =

Primary Standards U U T~0

Secondary

1000 to 25cc for 3 or 4 thermometers.Direct, probableerrorat eachpoint, i1~0

Primary Standards 1100

Secondary

$25 0012 00

9 00

$20 0012 009 00

B. For Single Thermometers.For single thermometers,the feesfor the direct comparisonsshould be

reducedto one-third,and for the ordinary onesto one-half theabove figures.But in this case thethermometerwill have to remain hereuntil enoughaccu-mulateto fill the comparators.

Directions for Sending. With eachthermometer,sendthenameof maker,the date when madle, laurlaosefor which it is used,andthehighesttemperatureto which it has lately beenheatedl,and thedateof suchbeating,togetherwiththe kindl of comparisondlesired,and whether the thermometeris generallyusedin thehorizontal or theverticalposition.

In packing, the thermometershouldbe placedin a small box, whichshouldagainbe packedwith straxvin a largerbox.

The thermometers,both dluring transit audI while here, must be at the

owners’ risk. Only sufficient fees have been chargedto coverthebarecostof the comparison,and we bear the risk of our own standards,which areprobably more valuable than any of thosewhich will be sentto us. Buteverycarewill be taken,andtheprobability of an accidentis very small.

We expectsoonto be ableto make othercomparisons,and noticewill thenbegivenof thefactby the issue ofanothercircular.

II. A. ROWLAND,Professor of Physics.

FEB., 188o.]

32 70/INS HOPKINS [No. 3.

HOPKINS HALL LECTURES AND READINGS~AT 5 P. M.Thefollowing coursesof lecturesand readings,to begiven in HopkinsHall, at 5 P. M., will be opento the publicsubjectto the regulationsasto tickets, etc.,heretofore

announced.

History, by DR. H. B. ADAMS, Associatein History. Ten lectureson the Italian Renaissance(V ‘14 the Beqinitinqs of Modernhistory.

Dates a~ (1 ~SpecialThpics.I. Tuesday,February ic. The Unity and Transitions of History.2. Tuesday,February 17. Venice and the Beginnings of Modern

Commerce.3. Tuesday,February 24. Papal Rome and the States of the

Church.4. Tuesday,March 2. The Renaissanceof PaganRome.5. Tuesday, March 9. Florence and the Beoinninos of Modernb ~

Politics. The Medici. Savonarola.6. iuesday,March i6. The Beginnings of Modern Literature.

Dante.7. Tlotrstlay, .ili/arch 18. Petrarch,Boccaccio,and Chaucer8. Tuesday,A/arch23. The Beginningsof Modern Art.9. Thursday, March 25. The Revival of Learning and the Dis-

coveries of Science.10. T~astlay, March 30. The Renaissanceof Geographyand the

Discoveryof the New World.

The Vedas, by Dr. C. R. LANMAN, Associate in Sanskrit. Sixlectures on the Ancient Literature of India.

Datesaud Sj5ecia/Topics.

I. Mbatlay, February i6. India. Its peoples. The periods ofits history. Our kinship with the Aryans.

2. Thursday, Februaiy~19. The grand divisions of the literature.First period. The Vedic literature. (a) Sanhita, (b) Brah-

mana. (c) SutraSecondperiod. The Sanskrit literature. Epic. Dramatic.

Didactic. Scientific. Juristic. Buddhistic.3. Thursday, February 26. The Sanhitas or Vedic Scriptures

proper. Rig-veda. Atharva-veda. Yajur-veda. Sama-veda.The Rig-vecla. Its character,form, extent,date,origin, tradi-tion, and relative i ruportance.

4. §ihtersday, Miarch 4. The borne and civilization of the VedicAryans. The Vedic divinities, mythology, and folk-lore.

~. Thursday, March I I. The Vedic Religion. The Godsof theLight.

6. Frtday, March 19. The Vedic Religion. The Gods of theEarth and Sky. The Vedic cosmogony. The doctrineof afuture life.

History of Philosophy, by ProfessorG. S. MORRIs, of the Univer-sity of Michigan. Eleven lectures on British Thoa~ht andThinkeis.

Datesand Special Thpics.I. Monday, February 23. The General Characteristicsof the

English Mind.2, Monday, March i. Mediaeval Anticipations of Modern

English Thought. (JohnScotusErigena,Johnof Salisbury,Roger Bacon,JohnDons Scotus,William of Occam.)

3. Monday,March8. Englishmenof the Renaissance. (Edmunde~penser, Sir John Davies, Richard Hooker.)

4. Mozday, March i~. William Shakespeare.5. Monday, A/arch 22. FrancisBacon.6. Monday, J[hrch 29. ThomasHobbes.7. Monday, April 5. John Locke.8. Monday, April 12. GeorgeBerkeley.9. Monday, April 19. David Home.

To. Alonday, April 26. Sir William Hamilton.I’. Aloaday, May 3. John Stuart Mill.

Greek, by PROFESSORGILDERSLEEVE, Professorof Greek. Twelve

lecturesand readings in the Greek Traqic Poets.

Dates andSpecial Topics.

I. Wednesday,Febrna~y i8. Introductory: The beginnings of

tragic art.

2. Wednesday,February 25. Aeschylus: Life and art,— with

readings.

3. Wednesday,Alarch 3.

4. Wednesday,March Ia.

5. Wednesday,Alarch 17.

6. TYednesd , Alarch 24.

7. Wednesday,Aliarch 3’.

pus Coloneus.

Wednesday,April 7.

Wednesday,April 14.

Wednesda?,,April 2 1.

Wednesday,April 28.

8.

9.TO.

II.

12.

The Oresteia.

Macbethand Agamemnon.

Sophodes.

Readingsin Antigone and Electra.

Readings in Oedipus Rex and Oedi-

Readingsin Ajax and Philoctetes.

Euripides.

Illustrative Readingsin Euripides.

Illustrative Readingsin Euripides.

Wednesday,May5. On some characterscommon to the three

tragic poets.

French, by PROFESSOR RABILLON, Lecturer on French Literature:

Twelve readingsin French Literature. (In French).

Datesand Special Topics.

1. Saturday,February21. Corneille: Le (‘id.

2. Saturday,February28. Corneille : Le (2id.3. Saturday,March 6. Corneille Le Cid.4. Saturday,Aiarch 13. Racine: Jphig~nie.

5. Saturday,March20. Racine: Jphig4nie.

6. Saturdat,,March27. Racine: fphiq6nie.7. Saturday,April 3. Voltaire : Zaire..

8. Saturday, April io. Voltaire: Zaire.

9. Saturday,April i7. Voltaire : Zaire.io. Saturday, April 24. Moli~re.

I’. Saturday, May i. Moli~re.

12. Saturday, May 8. La Fontaine.

Thedesignof thesereadin~sis not only to explain thosepaasagesin the worksread.which may presentdifficulties, and to statethe changesundergoneby thelanguage,but also to point out the literary beauties xvhich might escape thenoticeof a reader.

~ Those who P~OPO5Cto follow these readingsare expectedto bring withthemthetext of theauthorsnamed.

History, by DR. AUSTIN SCOTT. Ten lectureson the Methodsof

Historical Inquiry, beginningTuesday,April 6.

Scheduleof Datesof Current Courses.

Mondays, . . . . . . . PROF. G. S. MORRIS.

Tuesdays,(with two exceptions) . . . DR. H. B. ADAMS.

Wednesdays, . . . . . PROF. B. L. GILDERSLEEVE.

Thursdays,(with oneexception) . . . DR. C. R. LANMAN.

Saturdays, . . . . . . . PROF. L. RABILLON.

UNIVERSITY CIRCULARS.

MEETINGS OF UNIVERSITY SOCIETIES.Scientific Association

.

January 7, 1880.

(i) MR. W. I. STRINGHAM presenteda paper on GeometricalFigures in Spaceof Four Dimensions.

A regularfigure in spaceof four dimensionsis definedasonewhich is com-pletely boundedby equal regular figures of threedimensionsand whosevertices lie on the four-fold sphere. Threeof suchfigures are, (1) theFour-fold Pen/aid, boundedby five tetrahedra,(2) the Four-fold Ocloid, boundedby eight cubes,(3) theFour-fold Hexadekoid,boundedby sixteentetrahedra.

If V== vertices(zero-dimensional),E edges(one-dimensional),F faces(two-dimensional), S= solids (three-dimensional), then the numbers ofvertices,edges,faces andsolids which make up the above threefigures are

(1), V = 5, E== 10, F== 10, S==5;(2), V= 16, E==32,F==24, S==8;(3), V= 8, E = 24, F 32, S =46.

By an interchangeof V with S and E with F, (2) becomes(3) and viceversa,and hence(2) and (3) are called reciprocals of each other. Hencealso (1) is self-reciprocal. The reciprocalof a regularfigure is itself a regu-lar figure; hence,except in thecaseof self-reciprocals,regular figures occurin pairs.

The figures(1), (2), (3) give therelation,E + S = F + V, which becomesEuler’sequationfor figures in spaceof threedimensionsonsubstitutingS 2,which is the right valuefor this case, the polyhedron counting as one andthe spacewhich surrounds it as one. It can be proven that this formulais true for all four-fold figures.

The number of regular figures in four-dimensionalspaceis finite, for thenumberof three dimensionalfigures by which theycan be boundedis onlyfive, and in order to form a four-dimensionalangle by combining three di-mensionalfigures abouta given point, thesefigures mustfall short of fillingspaceof threedimensionsandmustthereforebe finite in number.

The figure formed by taking as vertices the middle pointsof the edges ofthe Four-fold Pentoid,is a Four-fold Dekoid,boundedby five tetrahedraandfive octahedra,and satisfies the relations V 10, E =30 F—30 S=10.whenceasbefore E + S = F + V.

This paper was discussedby PROF. REMSEN, MR. E. H. HALL,and DR. E. L. NICHoLs.

(2) MR. L. B. FLETCHER gave an accountof a peculiar MolecularChangein Iron at Red Heat.

An iron wire heatedto whiteness,andallowedto cool gradually, contractsuntil a dull red heat is reached,when a suddenexpansiontakesplace, fol-lowedby a gradual contractionasthe wire cools to still lower temperatures.At theinstantof this momentaryexpansionthewire is seento glow suddenlyand brilliantly. At aboutthe same temperaturea suddenand momentarycontractionis observedduringtheheatingofthe wire.

It was thought that these changesmight be ordinary thermal effectsasso-ciated with somechangein the superficialoxidation. To decidethis point,Mr. Fletcherheatedwires of iron and steel, and allowed them to cool inatmospheresof air, carbondioxide, and coal-gas,aswell asin a vacuumof afraction of a millimetre, theeffectobservedin eachcasebeing thesame. Thecause of the phenomenamust thereforebe a molecularchangeoccurringthroughoutthemassof themetal.

This was followed by remarksby PROFESSOR ROWLAND, on thephenomenonreferredto in the last paper.

Thephenomenonconsideredseemsto beanalogouswith that of theretard-ation of thesolidification of water. Waterin a clearglasstubecanbecooledbelowzero,andthensuddenlysolidifies with anexpansionof volume.

(3) DR. C. SIHLER presenteda communicationOn the Histological

Changesin Developing Bone as a Prototype of Abnormal Growths.Theview wasbroughtforward, that in growingbone,it is alwaystheyoung

and undifferentiatedtissuewhich is the producerof the final tissues,andwhich invadesandremovestheold tissues;while theold tissueshavenot thepowerofgiving rise to new ones.

This paperwas discussedby DR. BARTON.

January 19, 1880.

A special meetingof the Association was held, to listen to a com-munication from DR. EMIL BESSELS, late Naturalist of the PolarisExpedition, and now of the SmithsonianInstitution, on “Arctic Ex-plorations.’~

Dr. Besselsnarratedthe history of explorationsin the Arctic Circle, anddiscussedthe best method of conductingthem. He approvedof the lalan,suggestedby therecentcongressof geographersatHamburg,of establishingstationsatdifferent points as far North aspossible,from which expeditionscouldbesentout toward thePolein favorableseasons.

February 4, 1880.

(I) DR. W. K. BROOKS presenteda paper on Partial and TotalSegmentation.

He showed by comparisonof the eggs of a numberof Molluscs, duringthe earlystagesof development,that theLamellibranchsarethe descendantsof an ancestorwhose eggs were few in number,large,and furnished with afoodyolk, like the eggs which are laid at present by representativesof thegenusNassa.

A discussion followed, participated in by Professor Martin andMr. L. B. Fletcher.

(2) DR. J. R. MCD. IRBT reada communicationon CrystallographicCalculations.

A number of new and useful formulae for calcufating the angles and

indicesof crystal faceswasgiven.

Philological Association

.

January 9, 1880.

(i) The principal paper was by PROFESSOR ELLIOTT, on Noun-flexion in the OldestFrench Texts.

Theclassificationof infiexion is herefoundedexclusivelyon gender. Thefiexional phenomenaup to thetwelfth centuryare taken asthe basisof thisclassification. The difficulties werestatedwhich attendanysystemnof classi-fication whatever. Theservicesparticularlyof l)iez,GastonParis,Paul Meyer,Littr6, Tobler and Lebinski werediscussed. Accordingto gender,thewholeinfiexional systemdivides itself naturallyinto two greatcategories,Masculinesand Feminines theformerwere split into two distinctsets,accordingto thevariability or invariability of the Latin accent;the latter likewise give adouble division, according to the final letter, whethervowel or consonant.G. Paris’ andTobler’s theories,with referenceto the Feminineanomaliesofthe Passionda C’kris/, were reviewed at length: the former’s position wasshownto be tenableand stronglysupportedby data.

Resultsof this investigation: Genderasa basisof classificationfor the OldFrenchflexional system offersus fewer exceptionsthananyother principle.The systemthus constituted held its own up to the twelfth century. Theexceptionsactuallyfound did not belongto thefirst periodof thelanguage.In the twelfth centurymutilations of this primitive systemcreptin: the firststageofconfusionis representedby a simple encroachmentof the casusoh.liquns in both numbers respectively,on the donmain of the casusrectus;thesecondstage, by the fiexional s beinghungon to thealreadyanomalouslyemployedcasusobliquus. This stateof things, however,hasnot yetbecomea general rule. Rhyme is yet the greatconservatorof syntheticforms, andpreventsa headlongrush to theanalyticstate. Analogyandassimilationarethe too strongestprinciples at work up to the thirteenth century in theprocessof levelingthe fiexional differenc9sin theFrenchlanguage.

(2) PROFESSOR BRANDT thenreada paperon Briicke’s “ImperfectVowels.’

It wasclaimedthat such a classof vowels, said to be peculiarto English,doesnot exist. The idea is basedon prejudice,and on carelessobservationof English sounds.

(3) PROFESSOR LANMAN read a paperon Unconscious Duplicationof EquivalentLinguistic Elements.

This explainedthe origin of the double article in combinationslike //leAlcoran, le lierre, le lariat, and of the double preterit-sign in a/tack/ed,drozvnded,foaleded etc. The double plurals, like breeckes,belluses,galluse.r(gallows-es),werealsonoticed.

(~) PROFESSOR COOK reviewedLounsbury’s History of the EnglishLanguage.

February 6, 1880.(I) PROFESSOR BRANDT read the principal paper, which was on

Verner’s Law.

The paperreadconsistedof partsof a longer investigationupon Grimm’sLaw, viz.: the generalintroduction,and the part treatingof Verner’s Law.Grimm’s Law was restatedin three formulas with x, y, z. Y is thesonantstop; z, the surd one. Both are fixed quantities. X representsthat veryuncertainquantitycalled “aspirate.” The advantageof thesesymbolswasclaimed to be, that they necessitatethe inquiry into their phoneticvalue,which is too generallyneglectedwhen“hard, soft, aspirate,”and the letters,e g., bk, dk,gk areused. Parent-speech,GeneralTeutonic,andHigh Germanare the only true representativesof three groupsof languagesaffected byGrimm’s Law. ThenVerner’s Law wasdiscussed,which explainsthelargeclassof exceptionsto the shifting of theformula “Parent-speech.z: G. T.x: H. G. y.,” by thedifferencein theoriginal accent.

FEB., i88o.] 33

7OHNS HOPKINS

(2) MR. J. W. BRIGHT read a paperon The Views of Begemannrespectingthe Teutonic WeakPreterite.

The aim of the paperwas to present Begemaun’sattitude towards the‘‘composition theory‘‘ along the line o f its history from Bopp and Grimmto the present,and thus gradually to develop l3egemann’sown theory hy itssharpandargumentativecontrasts,andto indicatedetailsof argumentattach-ing to thewholediscussionwhichyet await conclusivedemonstration.

(3) PROFESSOR LANMAN reada paperon the Origin of the Beliefin the Transmigrationof Souls.

The belief mayhavearisen independentlyamongtheEgyptians,Shemites,andAryans. SeveralVedic passagessupposedto contain thegermsof theMetempsychosiswere examined. The developmentof thedoctrinein Indiawasreferredto thePost-Vedicage.

(4) MR. B. F. O’CONNOR read a paper on the Principles ofOrthographyof Frenchverbs endingin -elerand-eter.

These verbs, numberingahout230, present the peculiarity that some ofthem double the consonantbefore mute e, whereasothersunder the samecircumstancesaccent the precedinge. The reasonfor this distinction isunknown,andthereis muchconfusionamonggrammarianson thesuhject.

A careful study of eachverb shows that the principle which originallygovernedthem was Etymology, and that theyshould he classifiedaccordingto this principle. The simplestway out of the difficulty would be to con-jugatethem all alike.

(5) PROFESSOR CRoss read a paper on The Testamentaof theTwelve Patriarchs.

This showedtheuncertaintyof theresultsreachedin attemptingto establishthe dependenceof one documentupon another,from isolated verbalcoinci-dences;and that the argumentfor the previousacquaintanceof the writerof the 7estame;ztawith certainhooks of theNew Testamentis inconclusive,becausethewordsadvancedto supportthis view are not peculiarto the twoalone,hut areof commonoccurrencein otherGreekwriters andin theLXX.;andthat the dateusuallyassignedfor its compositioncannotbe established.

Historical and Political ScienceAssociation

.

The regular Januarymeeting of the Association was postponedon accountof the semi-annual examinations.

Metaphysical Club

.

December 9, 1879.

(i) The principal paper,by MR. E. M. HARTWELL) was on Reflex

Action and its Analogiesin the Fixing of Belief.

The variousfactorsof reflex actionwere discussedseparatelyandin theirrelationsto oneanother. Simpleandtetanicmu.cularcontractionwereshownby experimentsupon the nervemusclepreparationof a frog. Severalexpe-riments were made upon frogs, in order to show reflex action, indicatingpurposewithout volition. Thestepswherebythemind resolvesits doubtsorreachesits beliefs were pointed out as analogousto thosein the reflexaction of a brainlessfrog.

(2) MR. DAVID STEWART presenteda communication on TheEthics of Belief.

This paperdiscussedthemoralgroundsof a belief in the supernatural,andpointedout thedishonestyof treatingas positivefact,dogmaswhich aremat-ters of doubtor dispute.

January 13, 1880.

(i) MR. ALLAN MARQUAND presenteda translation,which hehad

made,of the treatiseof Philodemus,,~ p~ ea~rs ~covxa~ rrriercov.

This treatise,recoveredfrom the ruins of Herculaneum,at theendof lastcentury,revealsto us themethodof induction taught in the school of Zeno,the Epicurean. The inferencepassesfrom the known to the unknown bymeansof resemblance. The method is contrastedwith the xu~” &s’~exiva~vof the rhetoricians, and argumentsare presentedto show that the methodof resemblanceunderliesthe other. Various objectionsare considered,andit is shownin a very interestingway that the method cannotbe attacked,exceptby assumptionswhich canbeobtainedonly by induction itself. In thetreatmentof inductivefallacies we arereferredto a lost work of Demetrius,theEpicurean,wherethissubjectis saidto havebeentreatedvery compactly.

MR. C. S. PEIRCE remarked upon the value of this treatiseto thehistory of Inductive Logic and EpicureanPhilosophy.

(2) MR. C. W. NICHOLS read a paper on Moral Insanity as aCauseof Crime.

This paper, basedupon M. Despine’s Fs~’cJzoiogie Nolurelie, called at-tention to manycasesof n~aniaandmonomania,and urgeda more scientificandhumanetreatmentof themorally insane.

(~) M~. W. S. PRATT offered an abstractof Grant Allen’s PAysi-ological Aes//ze/ics(London andNew York, 1877).

Starting with the doctrine that pleasureand painaresubjectiveconcomi-tants of nervous states Mr. Allen first distinguishesthe truly aestheticpleasures,and then discussesat length the stimulations, both actual andideal, to which thesensoryorgansandthecobrdinatingcentresof theintellectaresubject,with a view to ana priori determinationof their relativeaestheticvalues. Applications of the conclusionsreachedare madeto paintingandsculpture, andespeciallyto poetry. Attention wascalledby Mr. Prattto theadmirablemethodof thebook, andto its importanceasa treatiseon thesen-suouselementsof aestheticenjoyment.

February 10, 1880.

(I) The principal paperwas by Ma, W. S. PRATT on Helmholtz’sTheory of the Developmentof Musical Scales.

After calling attention to a few of the scalesnow in use, the answersthatHelmholtz gives to the questions, (I) Why are scales with determinatedegreesuniversally used?; and (II) Why are certain degreespreferred toothers?werediscussedatlength.

His answerto (i) was objectedto, and the early developmentof a-kyilzmsuggestedasa more satisfactoryreasonfor the practice. This view wassupportedby a priori considerations,and by observationson the musicofbarbaroustribes. (2) Ilis theoryof thefurtherprogressof scaledevelopmentwas divided into five parts: (a) The acousticdoctrines of partial-tonesandof tone relationship; (b) The physiologicaldoctrine that theearis essentiallya setof resonatorssensitive to thesepartial-tonesandto the naturalkinshipsestablishedby them ; (c) Resting upon these,the mentaltendencyto choosescales containing only tonesnearly akin to each other; the operationofwhich tendencyis limited by (d) The smallest interval toleratedbetweenconsecutivenotes, and by (e) Thedesirefor uniform intervals. The inter-action of these elementsin the evolution of nwdernscales,was explainedand illustrated.

A legitimateextensionof this rationalizationof theaction of tastedevelopsa largenumberof theoreticalscalesthat areasyet unknownin practicaluse.Theactualformsareoften inferior in tonal correlationto the theoretical,anda fuller explanation is neededof the exclusion of the latter by the former.Helmholtz’s failure to recognizethe probability of someharmonic influenceon thescalesof even the most barbarouspeoples,was alsonoted. In con-clusion, a brief mentionwas madeof the currentdisputeas to what shall beadoptedasthestandardscale.

(2) A paperon the Evolution of Nervesand NervousSystemswasreadby MR. E. M. HARTWELL.

This gaveanaccountof theinvestigationsof Messrs.RomanesandSchaeferon the contractileandconductiletissuesin theMedusidjelly fishes. It wasclaimed that theyhad demonstratedcertainprogressivestagesof genesisandspecializationin the nervous systemsof various generaof the Medusaeand that theirresultsaffordednew andvaluable inductiveevidencein favor ofthe deductive theory propounded by Mr. Herbert Spencer, concerning thedevelopmentof thenervoussystemfrom undifferentiatedprotoplasm.

]Jliathemat~c~’1 Semina~y

.

November19, 1879.

DR. STORY, on a Generalizedfornzof Analytical Triangle.

The methodof Newton’s parallelogramorof the “analytical triangle,” isindependentof the angle betweenthecoordinateaxes,andmaythereforebeal)plied to any trilinear system to determinethe natureof a curve in thevicinity of theintersectionof any two axes, if thethird coordinatebe regardedasconstant. If therefore,thecurvebe referredto a bilinear system,xvemay,by regardingtheinfinite straightline as the third axisof a trilinear system,determinethenatureof thecurveat theinfinite pointsofthebilinear axes,andthetangents(asymptotes)at thepointswherethecurve cutseither axis. Thegeneralizedanalytical triangle is equilateralandshowsthecoordinationof thethree origins (so to speak),vix : the origin, in the ordinary sense,and theinfinite points of the bilinear axes. The coefficientsof the equationof thecurvearearrangedin the triangle in rows parallelto the tkree sides accord-ing to the powers of the three coordinateswhich the correspondingtermswould contain, if the equation were made homogeneous.The essentialdifference between this arrangementand that of the ordinary analyticaltriaogie, is theuseof therows parailelto thethird side.

34 [No. 3.

UNIVERSITY CJRCULARS.

December 22, 1879.

(i) Mit. STRINGHAM: On Vector Ratios consideredas TrigonometricFunctionsof Angles.

If c~, /3, 3 formthevectorsidesof a right triangle, (c~ —I-- ~), then cq

is the quaternioncosineof the acuteanglebetween~ and /3, and sq/3

is thequaternionsineof the sameangle. Starting from thesetwo definitions,a completequaterniontrigonometrymay be developed,giving analoguesofall the formulae of the ordinary scalartrigonometry, such a trigonometryevidently includin~ the scalar trigonometry as a special case. Thus thequaternionformula,

/3 /3sq ~eq

givesatoncethescalarforta~ula

T2sq/3~T2cq/3=~ici

If we consider comolanar angles only, the two fundamental additionformulaeare

sq(/3~Y~~sq/3cqY ~cq sq V/3,

(2) MR. VAN VELZER: On a Condition that the Total Differen-tial Equation

Pd~+Qdy+ftdx+.. . -t-Tdv=omayadmit of asingle Primitive.

Thecondition isPQI? ..T’Jd d d ddx dy dz •dv

H~ Q Ri. e. anyandevery one of the symbolic determinantsformed by taking threecolumns of theabovematrix mustvanish.

If thereis a singleprimitive, let it be~ o then— _ dcp dp,Q==m,... 7½=rnd1~

dx dy dvandtheabovematrix becomes

ft ...§/‘P Qd d d ddx dy dz dv K

d mi... ~ ddx dy dz dv

Considerthefirst threecolumns. Since

irni’ _ _ _

dz — dm dcp d dpdy dy dz± dydzd m ~ _ drn dq m ddcp,

_ +dz dy ~ -79;. de dy

PQ ftd d d

d,p dp dcpm7~hv -;~ij7 “~ dz

35

I P Q ft P Q ft-— dm dvi dvi d d d

~ ~dq mdPj dq dcp d~pdx dy dzi dx dy dz

The first determinant of the right hand membervanishes, becauseof theidentity of the first and third rows, and the second vanishesbecauseddq ddp

~ etc. The same is true of any other thcee columns of thefirstmatrix.

(3) MR. FRANKLIN made some remarks on the Remainder inTaylor’s Theorem.

lz~ 1Writing ft~ —, fn (x + ~ k), the limit of~ as Ii approacheszerois

January 21, 1880.

(i) MR. STRINGEAM: A Generalization,for ic-fold Space,of Euler’sEquationfor Polyhedra.

Let N5 , N, , , N, , - . - N~S denoterespectivelythe number of zero-,

one-, two-, three-, . . - n-dimensionalboundariesof a completegeometricalfigure in u-fold space. Then thegeneralizedformula is,No±N,+. - .±Nn N,+AKo+. - .±N11i+2, ifn be even;Ne~N,~. . .+Nn.,~=N,+N,+. . .—f--N,~, if n be odd.For these equationsaretrue for thesimplestfigures, andtheyarenot invalidatedby addingto suchfiguresanynumberof (n-l )-dimensionalboundaries.

A descriptionwas given of threeregular geometricalfigures belonging to4-fold space,additional to thethree describedat thelast meetingof theSci-entific Association; viz., (I) the4./old Ikotetroid a self-reciprocal figure i (2)the 4-fold Tetradekoid; and (3) its reciprocal, the 4-fold Rebdomekontoid.Thesesix seemto completethelist of regular figures in 4-fold space,exclud.ing stellatedfigures. The analogues, in n-fold space, of the tetrahedron,cube,andoctahedronwerealsodescribed.

This paper was discussedby PROFESSOR SYLVESTER, MR. C. S.PEIRcE, DR. STORY, and MR. MITCHELL.

(3) DR. STORY: On the Reduction,by Determinants,of theexpres-sion for Radius of Curvature,given in Salmon’sHigher PlaneCurves,p. 83.

The determinantto be calculatedis,o— a Ii, (n—l)L—gz, o

lz,b, (n—l) ilI—fz, og,f, o —cz n—lL, M; 0 —oz, —z

(n—I)’ (bL’ —2IeLM+aM’ ) + a2 H, where N is the Hessian. Hence

a(bL’—2kLM+ oAf’) == ~ ‘~, and R _____________

(n—i) ~‘ A’

(3) PROFESSOR SYLVESTER: On a ProbableGeneralizationof theTheorem,

xP—1— X’ +pY2

x-l

CommemorationDay.The fourth anniversaryof the Johns Hopkins University will be

observedon Monday, February 23d, i88o, by a public ceremony inHopkins Hall, when it is expectedthat three Matriculates will beadvancedto the degree of Bachelor of Arts, and one Bachelor ofPhilosophywill be promoted to the degreeof Doctor of Philosophy.Afterthepublic exercisesareconcludedtherewill beasocialassemblyofthe officersand studentsandtheir friends in theLibraryandotherHallsof thg University. On similar occasions,in previous years,the Presi-dentof theUniversity hasdeliveredan addressand theother speakershave beenas follows:

February 22, 1876.—Addressesby Reverdy Johnson, Esq., andPresidentEliot, of Harvard University, followed by the President’sInauguralAddress.

Feb.22, I877.—Addressesby ProfessorsSylvesterand Gildersleeve,and the readingof a Poem by JamesRussellLowell.

Feb. 22, 1878.—Addressesby Hon. Geo. Win. Il3roxvn, ProfessorRemsen,andPresidentEliot, of Harvard University.

‘Feb. 22, 1879.—An addressby Judge Geo. W. Dobbin; a Latincongratulationby ProfessorC. D. Morris, and an Oration by Presi-dentWhite, of Cornell University.

At the close of the public exercisesin 1879, the college graduatesresidentin Baltimore,with theirinvited guests,partook of a collation,at which Hon. S. T. Wallis presided,andseveralspeeches~ere made.

Reisterstown, Md.DELLA FORRE,FRANKUniversity of virginia.

Downs, HOwARD F.Bottinore Uity college, i8i6.

HOWARD, CURTIS C. 267 N. EutawSt.5. 13., Ohio State Agricultoral college, 1018

PATTERsON, J. WILSON 79 Park Ave.A.’ B., Princeton Colle

11e, 1863.

SurRo, ALFRED E.Loyolo lJeltcge.

Any persons who havecopies of the FirstUniversity that theyare willing to part with,sendingthem to the University.

64 William St.

198 Bolton St.

Chemistry.

Matriculate.

Chemistry.

Greek.

Candidate.

Annual Report of thewill confer a favor by

The first numberof the AMERICAN JOURNAL OF PHILOLOGY, underthe editorial chargeof ProfessorGildersleeve,is expectedto appearon Monday, Feb.23, i88o.

FEB., i88o.]

Additions to the Roll of Students.(For other lists seepp. 1-5 and 20, University Circulars).

36 7OHNS HOPKINS UNIVERSITY CIRCULARS. [No.3, FEB., i88o.

]

AMERICAN JOURNAL OF MATHEMATICS.FU1R~~ AITD A~E~IjLED.

Editor in Chief,J. J. SYLVESTER,Professorof Mathematics; Associate Editor in Charge,WILLIAM E. STORY, Associate in Mathe-matics; with the co-operationof SIMON NEWcOMB, H. A. NEWTON and H. A. ROWLAND.

Issuedunder the auspicesof the Johns Hopkins University.

Publishedin the quarto form and in numbersappearingfour times a year. Subscriptionl)rice per Volume, of about384 pages, $5.00; price pernumber$1.50. Vol. I, 18~T8—79 (388 pp., 4 l)latCs), can still be furnishedat the subscriptionprice.

All communicationsshould be addressedto the AssociateEditor in charge.

CONTENTS FOR FEBRUARY, 1880, Vol. II. No. 4.I. TABLES OF THE GENERATING FUNCTIOBS AND GROUND-FORMS FOR SIML’L- V. ON THE GHOSTS IN JIUTHERFURD’S DIFFRAcTION SPECTRA. By C. S. PEIRcE.

TANEOUS BINARY QUANTICS OF THE FIRST FOUR ORDERS, TAKEN TWO VI. ON A THEOREM FOR EXPANDING FUNCTIONS OF FUNCTIONS. By EMORY

AND TWO TOGETHER. By .1. J. SYLVESTER, assisted by F. FRANKLIN. McCLINToCK.

H. REMARKS ON THE PRECEDING TARLES. By J. J. SYLVESTER. VII. PRELIMINARY NOTES ON MR. HALL’S RECENT DISCOVERY. By B. A. Row.LAND.

III. A NEW GENERAL METHOD OF INTERPOLATION. By EMORY MCCLINTOCK.VIII. ON CERTAIN TERNARY CURIC-FORM EQUATIONS. EXCURSUS A. ON THE

IV. A CERTAIN CLASS OF CURIC SURFACES TREATED RY QUATERNIONS. By A. DIVISORS OF CYCLOTOMIC FUNCTIONS. By J. J. SYLVESTER.

B. CHACE. I IX. A QUINCUNCIAL PROJECTION OF THE SPHERE. By C. S. PEIRCE.

AMERICAN CHEMICAL JOURNAL.EDITED, WITH THE AID OF CHEMISTS AT HOME AND ABROAD,

By IRA REMSEN, Professorof Chemistry in the JohnsHopkins University.

Containsoriginal articles by Americanand foreign chemists; reviews of works relating to chemical science; reports on progressin the variousde.partmentsof Chemistry; and items of general interestto Chemists.

Publishedin numbersof from 64 to 80 pages six numbersforming a volume of from 400 to 500 pages.Price for the volume $3.00; single numbers50 cents.Subscriptionsand communicationsshould be addressedto the Editor.

CONTENTS FOR FEBRUARY 1880 VoL I. No. VI.ON A METHOD FOR THE PROXIMATE ANALYSIS OF PLANTS, by H. B. Parsons. ON THE OXIDATION OF SURSTITUTION PRODUCTS OF AROMATIC HYDROCARBONS:

ON THE ESTIMATION OF PHOSPHORIC ACID AS MAGNESIC PYRO-PHOSPMATE, IV. ON THE OXIDATION OF ORTHOTOLUENESULFHAMIDE, by Ira RemSenby F. A. Gooch.

LABORATORY NOTES, by A. Michael. and C. Fahlberg.I. ON MONETMYL-PHTHALATE. ON AN UNUSUAL CASE OF ELECTROLYSIS, by J. W. Mallet.

II. ON A NEW FORMATION OF ETHYL-MUSTARD OIL. REPORTS, NOTES, &c., by J. W. Mallet, the Editor, and others.III. ON THE PREPARATION OF METFIYL.ALDEHYDE.IV. ON THE “MIGRATION OF ATOMS IN THE MOLECULE,” AND REIMER’S ,

CHLOROFORM ALDEHYDE REACTION.

STUDIES FROM THE BIOLOGICAL LABORATORY.Edited by H. NEWELL MARTIN, Professorof Biology in the Johns Hopkins University.

CONTENTS OF No. 2, 1880.I. Onthe respiratoryfunctionof theinternalintercostalmuscles. By H. NEWELL IF. On the So-calledheat dySpucea. By CHRISTIAN SIBLER.

MARTIN and EDWARD MUSSET HARTWELL. V. A self-feeding chronographpen. By H. NEWELL MARTIN.

II. Observationson thephysiology of the spinal cord. By ISAAC OTT. VI. Observationsupon the early Stages in the developmentof the fresh waterIII. On the effect of two succeedingstimuli upon muscular contraction. By pulmonates. By W. K. BROOKS.

HENRY SEWALL. ‘111. The developmentof amblystomapunctetum. By S. F. CLARKE.

Price per number $1.00. No. I, 1879, (91 pp, 4 plates) can still be furnished. All communicationsshould be addressedto the Editor.

AMERICAN JOURNAL OF PHILOLOGY.Edited, with the co-operationof leading scholars,by B. L. GILDERSLEEVE, Professorof Greek in the Johns Hopkins University.

This Journal will be open to original communicationsin all departmentsof Philology, classical,comparative,oriental and modern; yet a large por.tion of the space will be given up to condensedreports of current philological work, and arrangementshavebeenmadeto presentregularly summariesofthe chief articles in the leadingphilological journals of Europe,while a close watch will be kept over the fragmentaryand occasionalliterature to which theisolatedAmericanscholarseldomhasfull access. The reviews of bookswill be intrustedas far as possibleto specialists; and it is hopedthat the Journal willmeeta want that has long been acknowledgedamong Americanscholars,and serveas a meansof inter-communicationandasan organofindependentcriticism.

TheJournal wili be in the ordinary review form, four numbersto constitute a volume, of from 400 to 500 pages,one volume to appeareachyear.Thesubscription pricewill be threedollars a year, payableupon the receipt of the first number.Vol. I. No. I. is now ready and contains original articles by GooDWIN of Harvard, CARTER and PACKARD of Yale, LANMAN of the Johns Hop-

kins University, MERRIAM of Columbia College, T. DAVIDsoN of Boston, and the EDITOR, besidesreviews of booksand notices of journals by well-knownspecialists. Articles have been promised for early numbersby SHORT of Columbia, GARNEYT of Annapolis, F. D. ALLEN of Yale, MORRIS, BRANDY andELLIorT of the JohnsHopkins University.

All communicationsshouldbeaddressedto the Editor.

Coj5ies of the7ohnsLloj5kins U;ziversity Circulars maybe obtained,as soonaspublished,of Messrs.CUS/JiNGS&‘ BAILE Y, No.262 WestBa/timore Street,Baltimore. Price 5 centseach.