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rubbed with a little vaseline so that it ^noves easily through thecork.

Care should be taken that the bottle and tubes are as dry as

possible before putting the apparatus together. It is advisable toset up the apparatus and let it stand for some time with a chlorideof calcium tube attached to the L-tube.

When the experiment is to be performed, the bulb is pusheddown nearly to the bottom of the bottle and the bit of rubber tubingover the L-tube is closed with a pinch cock so that the kerosenestands at the same level in both branches of the TJ-tube. Thebulb is crushed by pushing it down suddenly against the bottomof the bottle, and then raised so that as much of it projects abovethe cork as at first. As the water vaporizes, the kerosene movesin the manometer so tliat in a few seconds or so a difference oflevel amounting to more than 10 cms. is observable.

Of course, other liquids besides water may be taken. Etherhas such a high vapor tension at ordinary temperatures that mer-curv instead of kerosene should be used in the manometer.

ELEMENTARY EXPERIMENTSIN

OBSERVATIONAL ASTRONOMY.

BY GEORGE W. MYERS.

(Continued from Rage 40.}

EXPERIMENT XXXI.Find the length of earth’s radius by Wallace’s method.

Let A, B, C of the figure be the tops of three posts of sameheight, above water-level set up along the shore of Lake Michi-gan or by the side of a straight canal. Sighting from A over Bthe line of sight will cut the vertical post at C at a point D aboveC. The points A, B, and C.will be on a circumference concentricwith the circumference a. b. c of the earth^s surface. Let CD.

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B D, and A D be measured. Suppose the vertical D c meets thecircumference A, B, C at d.

Then by elementary geometry, since B A d == B C D, arid

Wallace’s Method.Fig. 28.

B D C is common to the triangles BCD and D A. 4, these twotriangles are similar, and

-^^-^or.^-^-X^.AD CD CD

But dD=2r (nearly) ; r denoting the radius of the earth.Hence

^-^h^-EXPERIMENT XXXII.

To find the radius of the earth.

After the latitude and longtitude of points on the earth^s surfaceare found, it is possible to determine the radius of the earth inmiles. The geographical coordinates of the Observatory of Ber-Hn are given in the Jahrbuch as Longitude + o h. o m. o. s. andLatitude 4- 520 3°" -^ an(! t01" Cape Town, South Africa, Longi-

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tude �o h. 20.3 m. and Latitude � 33° 56’. Supposing the earthto be a sphere, and that the two stations, as B and C, lie on thesame meridian (which is roughly true for Berlin and Cape Town,and the discrepancy can be allowed for), compute the radius of

Earth.V\g. 29.

the earth, B E, and the chord extending from Berlin, B, to CapeTown Observatory, C, assuming the measured length of the greatcircle arc, C Q B, to be 6,495.6 miles.

Using the i&" terrestrial globe and scale of both miles anddegrees, determine the radius of the earth /from measures of arcsof great circles between various places.

Hipparchus found that on March 31 st at noon the sun shonevertically into a deep well at the city of Syene, 500 miles south ofAlexandria, while at the latter place the gnomon showed that atnoon of the same day the sun was south of the zenith by ~^\ of.a circle (=7°.2). What would these data indicate the circum-ference and radius of the earth to be ?

[NOTE : The arc Berlin-Cape Town is not the one actually usedbut it will suffice to illustrate the method as well as the one actuallyused, and these stations are needed in the next experiment.]

EXPERIMENT XXXIII.To find the distance to the moon.

The stations used above, Berlin and Cape Town, will exem-plify the present problem. The observer at Berlin, B, measures

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the altitude, Nl B M, or senith distance, Zi B M, of the moon,by means of the most accurate instruments available, constructedon the principles crudely represented in our hand quadrant, orTycho’s quadrant. So also does the observer at the Cape Oh-

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servatory, C, measure the zenith distance, Z2 CM, or the altitude,N2 C M, at the same time as does the observer at B. The timeis set by previous agreement. The former experiment gave usBE (= E C) and B C. The sum of the latitudes being B EC(= 96°26’.2), one-half the difference between 180° and B ECgives E B C, or E C B. Having measured Zi B M and Z2 C M,the former added to E B C and the sum deducted from 180° willleave M B C in degrees, and the latter added to E C B and thesum .subtracted from 180° will leave B C M. Knowing B C M,C B M, and B C, we solve the triangle by geometry, or better, bytrigonometry, and obtain B M and C M, and finally E M, thedesired distance from the moon to the earth.

Supposing the Berlin observer finds the zenith distance,Zi B M, of the moon to be 53° i5’.i, at the instant that the CapeTown astronomer finds the zenith distance, Z2 CM, to be 34° 28’How far is the moon from the earth; i. e., how long is E M, if theradius of the earth i? 3.963 miles?

(To be continued.}