JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Optics of Searchlight Illumination

E. 0. HULBURTNaval Research Laboratory, Washington, D. C.

April 15, 1946

INTRODUCTION

IN this paper the optical features of searchlightillumination are analyzed in considerable

detail. Experimental measurements and calcula-tions are given which led to quantitative answersto the questions, how does the range at which anobject can be seen in the searchlight illuminationvary with, (a) the portion of the searchlight beamused to illuminate the object, (b) the distance ofthe observer from the searchlight, (c) the candle-power of the searchlight, and (d) the haze in theatmosphere.

The results given here depend entirely onexperimental facts. Pertinent numerical facts ofvision, attenuation and scattering of light byhaze, geometry of a searchlight beam, and thedistribution of light in the beam were broughttogether and from these the answers to the abovequestions were worked by calculation for theNavy 36-inch searchlight and the Army 60-inchsearchlight. In addition, a few direct observationswere made of the brightness of searchlight beamswhich were found to be in fair agreement with thecalculations.

Since the searchlight is a visible light apparatusdesigned to be employed by observers using theireyes, the range at which an object can be seen inthe searchlight illumination is essentially a prob-lem in vision. The optical properties of search-

SEARCHLIGHT

A 4' ==1

1,

_ B B - AXIS+

_ _ _ -

I - - t

D S __REROBSERVER -

(A)

+

(B)

FIG. 1. Geometry of searchlight beam.

lights and of atmospheric haze have been knownfor some years, but the necessary facts of visionhave not been known, and have become availableonly recently. These facts, however, are for smallobjects which subtend less than 5 minutes of arcat the observer. Therefore the present conclu-sions refer only to such small objects. Largerobjects can be considered when suitable visiondata concerning them are forthcoming.

SUMMARY OF RESULTS

The general results are summarized below,although there is some risk of over-simplificationin such brief statements. The results apply to theNavy 36-inch and the Army 60-inch searchlights.x is the maximum visual range of an objectilluminated by a searchlight at night viewed byan observer alongside the searchlight and at adistance d from it. A homogeneous atmosphereand a small object are assumed. It was found that,

(a) The range x of the object illuminated by the "near"side of the beam (the portion of the beam near theobserver) is about 20 percent greater than when theobject is illuminated by the "far" side of the beam, fora clear atmosphere. With increase of haze the differencedecreases. (See Fig. 9.)

(b) For a clear atmosphere the range x increases about 25percent as the observer moves from d=30 feet to 100feet from the searchlight, and about 50 and 75 percentwhen he moves to d=200 and 500 feet, respectively.The percentage increases in x remain approximatelyconstant with increasing haze. (See Fig. 10.)

(c) The range x increases with the fourth root of the areaand reflectivity of the illuminated object and with theeighth root of the candlepower of the searchlight, for aclear atmosphere. With increase of haze the increasesof x are even less rapid. (See Fig. 11.)

The general conclusion was reached that bymeans of the present detailed manner of calcula-tion the effectiveness of a searchlight in revealingsmall objects can be calculated completely fromthe distribution curve of light in the searchlightbeam.

BRIGHTNESS OF SEARCHLIGHT BEAM

Referring to Fig. 1A, let AB be the axis of thebeam of the searchlight A. At point P in the beam

483

VOLUME 36, NUMBER 8 AUGUST, 1946

E. 0. HULBURT

let s/ be the angle between AP and AB. Assumethe beam to be a circular cone with light distri-bution across the beam given by Fig. 1B; - issymmetrical with ,6 and is 1 for ' 0. Let AP bexi, and assume x1 so great (more than, say, 100times the diameter of the searchlight mirror) thatthe , V, curve is independent of xi. Let c be themaximum beam candlepower, and i the illumi-nation at P.

Theni=c)7xf2 exp (-fix), (1)

where /3 is the attenuation coefficient of theatmosphere for collimated light. Equation (1) isthe definition of A.

Let the line of sight DB of an observer at Dpass through P. Let DE be parallel to AB;AD=d; DP=x 2 ; and angle PDE be . Let theconventions of the signs of 1' and be thoseshown in Fig. 1A. Let all lines be in the sameplane BAD.

-q is a function of ,6 and hence of x2 . To dc-termine the relation we note from the geometryof Fig. 1A that

and(sin y)/d = [sin (90°-V)]/x 2.

Whence, eliminating -y, I

tan A/ = (d/x2) sec 4)- tan 4).

The brightness Ab of an element of the beam atP as seen by the observer at D is

Ab = bi exp (- 3x2)dx, (3)

where crb is the coefficient of scattering by theatmosphere backward toward D.

Assuming that /3 and b are constant through-

TABLE I. Atmospheric attenuation and transmission.

Visual Transmis-Wcather, range v, Attenuation sion a per

amount of haze sea miles 8 sea mile-' sea mile

Exceptionally clear 37.3 0.105 0.914.4 0.273 0.8

Clear 11.0 0.356 0.77.67 0.511 0.65.65 0.693 0.5

4.28 0.916 0.4Light haze 3.25 1.204 0.3

2.44 1.608 0.21.70 2.303 0.1

Thin fog 1.31 2.997 0.05

A.

FIG. 2. Scattering of light by haze.

out the region of the atmosphere under considera-tion, the brightness b of the beam seen by theobserver in the direction of P is

b= f rbi exp (-/3x2)dx.0

Substituting (1) into (4) gives

b C= cf nx1F2 exp [-a3(xl+x2)]dx.0

(4)

(5)

Since in all cases considered here a and aresmall, i.e., not greater than 3 and usually lessthan 1, we have to a close approximationx1 =x 2 =x. (2) and (5) reduce, respectively, to

,P=d/x-0, (6)

b = cJbc fx-2e-2#xdx.0

(7)

The brightness b was determined from (6) and (7)by graphical integration for stated values of/3, d, 4), I, and c. No examples of the graphicalintegrations are given; they are elementary andtedious.-

484

(2)

SE7,ARC1LIGHT ILLUIMINATION

ments in this connection other than those alreadyreferred to.

It may be clarifying to give the details of thedetermination of K = 3.72 X 10-2. Referring toFig. 2 a beam of incident light i the directionshown is scattered by an element of the atmos-phere at P. o- is the fraction of the incident lightscattered per unit solid angle at angle 0 with thedirection of the incident light. The curve is a plotof the values of uo,2 derived from the measure-ments of the brightness of a searchlight beam for0 from 200 to 160°. The strong forward scatteringis clearly shown in Fig. 2. 0-b is the back scatteredlight. Since the lower atmosphere reduces thebeam by scattering only, with no absorption,

The attenuation d and the back scattering -

were known from earlier work' on atmospherichaze. The attenuation 1 is listed in the thirdcolumn of Table I for various visual ranges andweather given in the first two columns whichwere taken from the International Daylight Visi-bility Table. The visual range v is the maximumdistance that a large black object can be seenagainst the horizon sky in daylight. It has beenshown' that 13v = 3.92. It is convenient here to usethe transmission per sea mile a, where

a = e-$. (8)

The values of a are in the fourth column ofTable I.

It is known that the attenuation of visible lightin the lower atmosphere is almost entirely causedby scattering. Therefore the scattering andattenuation are proportioned. Hence

OCb = K. (9)

From observations' of the brightness of a search-light beam at night for two types of atmosphere,very clear a=0. 8 and light haze a=0. 3 , K wasfound to be the same value 3.72X10-2 in eachcase. Then

0-b = 3.72 X 10 2. (10)

We assume that (10) is true for all the values of 13of Table I. This can only be an approximateassumption, for it seems very probable that Kchanges as the weatheri changes from very clearto thick fog. However, there are no measure-

' E. 0. Hulburt, J. Opt. Soc. Am. 31, 467-476 (1941).

0= J ao27r sin dO,

=27rurbf (a,0/0b) sin Odd.0

(11)

From a graphical integration of (11), with ogiven by the curve of Fig. 2, one found 1326.90,or K = 1/26.9 = 3.72 X 10-2 .

Light distribution curves, in the present nota-tion the -q, 4A curves, are given in Fig. 3 for theArmy 60-inch and the Navy 36-inch searchlights.Data of these searchlights are in Table II. Thevalues of the maximum beam candlepower arelower than values sometimes stated, but areprobably fairly representative of the searchlightsin actual use.

Figures 4 and 5 are photographs of the beam ofthe Army 60-inch searchlight. The beam wasdirected at the sky about 5° above the horizon,the camera being 5 feet from the searchlight inthe case of Fig. 4 and 40 feet in the case of Fig. 5.The night was normally clear; a was estimated tobe about 0.7. The times of exposure were 30seconds; the light streaks in the beam werecaused by insects and moths fluttering in the

TABLE II. Searchlight data.

Max. beamAm- Kilo- candlepower Lumensperes Volts watts without shutter per watt

Army-60 inch 150 78 11.7 400,000,000 6.2Navy-36 inch 195 90 17.5 340,000,000 7.2

2 Reference 1, Fig. 4.

FIG. 3.

485

E. 0. HULI3URT

FIG. 4. Army 60-inch searchlight beam, camera FIG. 5. Army 60-inch searchlight beam, camera5 feet from searchlight. 40 feet from searchlight.

light. A scale of is marked in each picture. Itwill be realized that the most useful part of thesearchlight beam is the small circular area at theend of the beam of radius about 10 or less, for thisis the place where distant objects are illuminatedby the searchlight.

From the foregoing equations and data thebrightness b of the searchlight beam was calcu-lated for a number of cases and is plotted inFigs. 6 and 7. All values of b were for the axialplane of the searchlight which passes through theeyes of the observer, i.e., plane BAD, Fig. 1.Each value of b was calculated from Eqs. (6) and(7) by graphical integration. Figure 6 gives thevariation of b with for d = 7.5 feet and for theatmospheric transmission a = 0.3 and 0.7. Figure 7gives the variation of b with d, for = 0, forseveral values of a. The circumstance that theb, curves of Fig. 6 fall rather sharply to zero ata certain value of provides the explanation ofthe familiar observation that the beam comes toa definite end when viewed by an observer nearthe searchlight. The finite end of the beam isclearly shown in the photographs of Figs. 4 and 5.As the observer moves away fron the searchlightthe end of the beam becomes less distinct, andwhen he is several miles away the beam fades outimperceptibly in the distance, if the atmosphereis homogeneous.

In general the b curves of Figs. 6 and 7 were ofno great interest in themselves, for their trendsare about what one would expect from simpleconsideration. Their importance was in their use

in the calculation of ranges of objects. A point ofminor interest was the approximate constancy ofb with for greater than about 1, shown inFig. 6. The relation can be stated as a theorem inphysical optics; the theorem can be proved andthe conditions under which it is exact and underwhich it becomes inexact can be laid down. Itappears to be a new theorem. However, it is notused here, and we leave its elucidation to thestudent.

FIG. 6.

486

SEARCHLIGHT ILLUMINATION

Two sets of experimental observations of thebrightness of a searchlight beam were made inwhich b was measured for k = 0 for several valuesof d. One set was made with a 60-inch Armysearchlight and the other with a 24-inch Navysearchlight. The observations are plotted ascrosses in Fig. 8, the upper four referring to the60-inch and the lower three to the 24-inch search-light. b was measured with a calibrated Macbethilluminometer with a blue filter over the illumi-nometer lamp to obtain a color match with thebeam. The illuminometer had an objective lens of12 inches focal length which made the centralfield about 1 in diameter. The instrument wasused to measure the brightness b of the beam atthe point 0=00, as shown in the photographs ofFigs. 4 and 5. The use of the illuminometer of 10field to measure b at the end of the beam where bfell from a maximum value to zero in about 10could only. be expected to give an average valueof b.

In the case of the 24-inch Navy searchlight themaximum beam candle power c and the atmos-

10 .. ...._ _ _ _ _ _ .. .... ........ ....... ..... ...... .

I0

bCAN[SO

10

I0

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if:f ,fflf f liffliffl _n T 4 1 ~~~~~F f i _

~~~~~~~~~~~~~~i ar L4. 4 .

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W~~~~~~~~~~~~~~~Ifi fM M, Hi

10 20 30d40 50 60 FEET

.�llll�Iillflllllillfll llllllflhlll.lflfll�lliulhflll�llilnil ii Hill�u qu tu CU lULlZU 4U bu u TUU

d FEET

FIG. 7. Brightness of beam at various distances.

FIG. 8. Observed and calculated brightness of beam.

pheric transmission were measured at the sametime that b was observed. c was 50.3 X 106 candlesand a was 0.70. a was measured by means of atelephotometer and a known light at a knowndistance. The a, 41 curve of the distribution oflight in the beam was not known for the 24-inchsearchlight. However, since the searchlight waswell designed, its qj, A curve was assumed to beapproximately that of the Navy 36-inch search-light of Fig. 3. On this assumption the b, d curvesfor = 0 and + 1 were calculated and areplotted in the dotted curves of Fig. 8. One wouldexpect the observed points, the crosses, to lie onthe =O' curve or perhaps between the two curves. They do this tolerably well, indicatingfair agreement between the direct measurementof b and the values obtained by calculations frommeasurements of haze and data of the searchlight.

In the case of the 60-inch Army searchlight theatmospheric transmission was not measured.However, the night seemed normal (it was thesame evening that the photographs of Figs. 4 and5 were taken) and a was estimated to be 0.7. On

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487

IDU <:UU

E. 0. HULBURT

this basis with c=4X 108 and the , ,6 curve ofFig. 3, the calculated b, d curves of Fig. 8 weredetermined for 4) = 00 and 1. They agree about asexpected with the four observed points shown bythe crosses.

In comparing the observed and calculatedvalues of the brightness of the Army searchlightit was assumed that the brightness was caused byatmospheric haze and not to the insects flyingaround in the beam which are so noticeable in theforeground of the photograph of Fig. 4. Theassumption was probably correct because theregion at the end of the beam where the bright-ness was measured was several hundred feetabove the ground where there were few insects.

RANGES OF OBJECTS IN SEARCHLIGHTILLUMINATION

An object illuminated by a searchlight appearsto an observer who is not too far from the search-light to be surrounded or immersed in the lumi-nous beam of the searchlight. Usually the objectappears brighter than the surrounding field oflight; in fact, under the supposition of thisreport, namely, that the beam is caused by anoptically homogeneous atmosphere throughoutthe length of the beam, an object, even if paintedwith ordinary black paint, is always brighter thanthe searchlight beam surrounding it. It is as-sumed that the object is so small and so far awaythat its longest linear dimension subtends anangle less than about 5 minutes of arc at theobserver. Thus the illuminated target is approxi-mately a point source of light surrounded by aluminous field. In this case the threshold illumi-nation of the point source at the eye is knownfrom an earlier investigation' and the maximumranges at which the object can be seen can becalculated.

A plane object is assumed of area A square feetand of diffuse reflectivity R. It is assumed thatthe plane of the object is normal to the axis ofthe searchlight beam, and that the observer is sonear the searchlight and the object so far fromthe searchlight that the line of sight of theobserver is also approximately normal to theplane of the object. It is assumed that the

' E. A. Knoll, R. Fotsey, and E. 0. Hulburt, "Visualthresholds of steady point sources of light in fields ofbrightness from dark to daylight," preceding paper, thisissue, J. Opt. Soc. Am. 36, 480 (19461).

illumination i on the object is mainly caused bythe searchlight and that the illumination on theobject from other sources, as night sky light,stars, aurorae, moon, etc., are relatively weak.Then, if x is the distance from the searchlight tothe object, i is given by (1), or

i = CqX-2e-f. (12)

The illuminated object is a source of light ofcandlepower iAR/1r in the direction of the ob-server, i being in foot candles. Since the object isassumed to appear to the observer approximatelyas a point source, the illumination j which itproduces at the observer is

j = iA Rr-X- 2e-x. (13)

The earlier experiments 3 showed that the illu-mination j at the visual threshold, for youngobservers with good vision, from a point sourcein a field of brightness bf was given approximately(within a factor of 3) by

i= 10-10(1+3.38X 106bf)-, (14)

where j is in footcandles and b is in candles persquare foot. (14) was found to hold for b rangingfrom zero to about 1500 c/ft.- 2 We shall use (14)in the present searchlight case. There is a possibleerror in doing this. (14) referred to the case of auniform field of diameter about 25 minutes of arcor greater surrounding the point source. The fieldof the searchlight beam around the illuminatedobject is in general not uniform, as shown by theb, curves of Fig. 6. It was considered that theerror due to the nonuniformity was not serious.

Substituting (12) and (13) into (14) leads to

(x-2e-:$)= 1010(1 ±3.38 X 106bf) 7(7r/ARc-), (15)

where x is the maximum visual range of theobject, or simply the "range" of the object. Inthe case of the searchlight the field brightness bfis the sum of the brightness b of the beam and thebrightness b of the night sky. Then (15) is

(x-1e-fX) 2 = 0-10

X [1+3.38X 106(b+b8 )]'(7r/ARcqj). (16)

From (16) the range x was calculated for variousconditions of haze, positions of target and ob-server, and types of searchlight, using the valuesof the beam brightness b from Figs. 6 and 7.

(16) is of the form x2etx=n which cannot be

488

SEARCHLIGHT ILLUMINATION

yield only moderate increases in the visual rangesof illuminated objects.

In the following numerical calculations we shallassume throughout an object for which AR - 100and whose angular diameter at the observer isnot greater than about 5 minutes of arc. Since weshall be concerned with ranges greater than 1 seamile such a target is, for example,

Length10 feet2025

Width10 feet5

20

Reflectivity

1.001.000.20

FIG. 9.

solved explicitly for x. A nomograph of thisfunction was prepared to facilitate numericalsolution.

The brightness of the horizon sky on clear,moonless nights is about 3 X 10-5 cu ft.- 2 , and is

less than this if there is much haze, fog, or clouds.It is seen from Figs. 6 and 7 that the values of b.are usually much greater than 3 X 10-5 unlessthere is considerable haze (a <0.3) and theobserver is at a considerable distance from thesearchlight (d>200 feet). Therefore b8 is usuallyless than b.

For an object on the axis of the searchlight=1. Approximately b8 and the number 1 on the

right-hand side of (16) are usually negligible.Therefore (16) may be written approximately

(x-e-f)2 I- b(ARc)-. (17)

From (7) approximately for ,3 small b - c. Then(17) becomes

(x-2e-Ox)2 c (AR)-'c-l,or

xeI 2 c (AR)ic08. (18)

From (18) it is seen that for a small the range xincreases approximately with the fourth root ofthe size and reflectivity of the object and with theeighth root of the candlepower of the searchlight;with increasing haze, i.e., increase of j3, theincrease of x is even less. This explains why greatincreases in the candlepower of the searchlight

It is also assumed throughout that bs=3X10-5candle per square foot.

RANGE OF OBJECT IN VARIOUS PARTSOF THE BEAM

We take d = 7.5 feet, which means that theobserver is 7.5 feet from the axis of the search-light. The range at which he can see the targetwas calculated from (16) for various values of with the values of b from Fig. 6. The results aregiven in Fig. 9 for the Navy 36-inch searchlightfor a clear (a=0. 7 ) and a hazy (a=0.3) atmos-phere and for the Army 60-inch searchlight fora=0. 7 . It is seen from the curves of Fig. 9 thatwhen the object is illuminated by the portion ofthe beam on the side of the axis nearest to theobserver, i.e., 4 is negative, the ranges are greaterthan when the object is illuminated by theportion of the beam on the side far from the ob-server, i.e., 4 is positive. The reason, of course, isthat in the "near" case the portion of the beamis less bright than in the "far" case, as seen fromthe curves of Fig. 6. The fact is familiar tooperators of searchlights who know from ex-perience that they can see objects somewhatbetter in the near side than in the far side of thesearchlight beam. The difference, however, be-comes less as the haze increases.

An important simplifying result appears fromthe curves of Fig. 9, namely, the range is rela-tively constant for 4 from about -0.1° to +0.3°.This means that we may make subsequent rangecalculations for =00 with the realization thatthe ranges obtained are not sensitive to the exactpositioning of the axis of the beam on the object,as long as the object is within = -0.1 to+0.30.

489

E. 0. HULBURT

homogeneous atmosphere, and the improvementin range occasioned by the observer movingaway from the searchlight follows a curve

. ------ __._.__.._.__..|||!|different from those of Fig. 10. For example, bmay be very bright due to haze in the first fewthousan eet, an en wi increasing is ancemay fall to low values. In consequence, as theobserver moves away from the searchlight hemay obtain at first only a small improvement inrange; then, as he continues to move away hemay suddenly find the range much increasedbecause of the fact that he has reached a position

ME ;min which his line of sight to the object passesalongside of, and not through, the bright sectionof the beam.

RANGES FOR SEARCHLIGHTS OF

VARIOUS CANDLEPOWERS

In this case x was calculated from (16) as a0 function of c for various amounts of haze, for

0=00, and for two positions of the observerWi40(~4ttiit4Sit[tg]tt d=20 and 100 feet. The , V/ curve of the Navy

36-inch searchlight was used. The x, c curves are

FIG. 10. in Fig. 11, and illustrate the relatively slowincrease of range with increase of candlepower.

RANGE OF OBJECT FOR THE OBSERVER The slow increase is indeed obvious from (16)IN VARIOUS POSITIONS or (18).

In this case x was calculated from (16) as afunction of d for various amounts of haze, for anight sky brightness b= 3 X 10- cu ft.- 2 , and for

= 0, using the values of b of Fig. 7. The resultsare in Fig. 10. It is seen that there is an increasein range as the observer moves away from thesearchlight, the increase being, for a clear atmos-phere, about 25 percent as the observer movesfrom 30 feet to 100 feet from the searchlight, and ....about 50 percent when he moves to 200 feet. Thevalue of x given in Fig. 10 for no beam were ofacademic interest, and were obtained by puttingb=0 in (16).----

The curves of Fig. 10 are true only for ahomogeneous atmosphere. In the case of asearchlight turned upward to view objects in the ----sky the atmosphere is usually non-homogeneous,and often the non-homogeneity consists in rela-tively heavy haze in the first few thousand feet E 1above sea level, and a relatively clear atmosphereabove. In such case the b, d curve is quitedlifferent from the b, d curves of Fig. 7 for a FIG. 1l.

490

LETTERS TO THE EDITOR

Although this report is not primarily concernedwith the design of searchlights it is of interest toremark on the effect of width of beam broughtout by the calculations of the Army 60-inch andthe Navy 36-inch searchlights, the 60 inch havinga beam width of about 7/10 of that of the 36 inch,as seen from Fig. 3. We have ascribed to theArmy searchlight a maximum beam candlepowerc of 400 million and to the Navy searchlight 340million. Assume that c for the Navy searchlightwere 400 million; the values of the ranges of theNavy searchlight of Fig. 9 would be increased byabout 4 percent for ao=0.7. We see then fromFig. 9 that the widths of the flat maxima of thex, curves are roughly in proportion to 7/10 andhence to the beam widths given by the q, , curvesof Fig. 3 for the two searchlights. In other wordsthe angular width of the most effective portion ofthe searchlight beam as judged by seeing objectsat maximum ranges is roughly proportional to theangular width of the beam as determined by thelight distribution curve , 4,. It has sometimesbeen surmised that narrowing the beam mightgive greater increase in range than might beexpected from the increased light intensity occa-

sioned by the greater concentration of light. Itappears that the surmise is not correct for thetwo searchlights under consideration.

In conclusion it is well to emphasize again thatthe ranges of Figs. 9-11 refer to objects that aresmall enough to appear approximately as pointsources. The ranges of larger objects cannot yetbe worked out because visual thresholds of largerobjects are not available. Also, it may be men-tioned again that the present results are restrictedto the axial plane of the 'searchlight BAD, Fig. 1.The case of the searchlight tipped upward ordownward so that it illuminates the object in aportion of the beam above or below the axialplane has not been worked out. The case mayreadily be calculated by the present methods, butit appeared that no important new facts were tobe learned from its consideration at this time.

It is a pleasure to acknowledge the cooperationof the Army Engineer Board, Fort Belvoir,Virginia. The Board, through Major 0. P.Cleaver, Lieutenant F. J. Millican, and Mr. C. F.Cashell, operated the 60-inch searchlight for thepurpose of the photographs of Figs. 4 and 5 andthe measurements of Fig. 8.

Letters to the Editor

The Basic Sensation Curves of the Three-Color Theory

W. S. STILESDepartment of Scientific and Industrial Research, National Physical

Laboratory, Teddington, Middlesex, EnglandMay 31, 1946

M R. HL. DE VRIES has described determinations ofi the "basic sensation curves of the three-color theory"

based on observations of the visibility of a small teststimulus of one color viewed foveally against an adaptingfield, generally, of another color.' As Mr. de Vries claims hismethod to be a new one, may I point out that closelysimilar measurements were used to derive the spectralsensitivity curves of the three-cone mechanisms in a paperpreviously published under the title "The directionalsensitivity of the retina and the spectral sensitivities of therods and cones."' The derivation of the spectral sensitivitycurves was only a part of a much wider investigation, andit may have escaped the attention of Mr. de Vries on thisaccount.

A comparison of Mr. Vries' results with my own may beof interest. In Fig. 1 the broken-line curves are thoseobtained by de Vries for a color normal subject G.W.N.

(Curves z, 1 and 3 in his Fig. 3), except that here log (sensi-tivity) instead of sensitivity has been plotted. The full-linecurves are taken from Fig. 41 of my 1939 paper, and havebeen reduced to the value 1 (log value=0) at their re-

.3 5

'3 -

4 O | 1 71 0 ~400 00 600 706

.3 /~~~~~~~

B.,---0074 6 ~oo

WooO7.000T0 WAVGGTh1 (T

FIG. i. Log (spectral sensitivity) curves for the three mechanisms offoveal cone vision.

491