418 



KNOWLEDGE • 



[Nov. 24, 1882. 



TRANSITS OF VENUS. 



By Richard A. Proctor. 



FOR some inscrutaMo reasons, any statement in which 

 Venus, the sun, and the earth are introduced seems 

 by many to l>e re^rded as, of its very nature, too perplex- 

 ing for' any one but the astronomer even to attempt to 

 understand. My talk in the next few paragraphs shall be 

 a' out a dove, a dovecot, and a window, whereby, perhaps, 

 some may W tempted to master the essential points of 

 the astronominal (juestion who would be driven out of 

 hearing if I spoke a)>out planets and orbits, ascending nodes 

 and descending no<les, ingress and egress, and contacts 

 internal and external. 



Fig. 1. 



Suppose I), Fig. 1, to be a dove flying between the 

 window, A H, and the dovecot, C c, and let us suppose that 

 a person looking at the dove just over the bar, A, sees her 

 apparently cross the cot at the level, a, at the foot of one 

 row of openings, while another person, looking at the dove 

 just over the bar H, sees her cross the cot apparently at the 

 level, />, at the foot of the row of openings next above the 

 row a. Now suppose that the observer docs not know the 

 distance or size of the cot, but that he does know in some 

 ■way that the dove Ricsjiisl midway between the window 

 and the cot ; then it is perfectly clear that the distance, a h, 

 between the two rows of openings, is exactly the same as 

 the distance, A B, Wtween tlie two window-bars ; so that 

 our observers need only measure A B with a foot-rule to 

 know the scile on which the dovecot is made. If A B is 

 one foot, for instance, then '/ /< is also one foot ; and if tlie 

 doT«-cot has three e<|iial divisions, as .shown at the side, then 

 C »■ i» exactly one yard in height. 



Thus we have here a ca.s«! where two observers, without 

 leaving their window, can tell the size of a distant object. 



And it is quite clear that wherever the dove may pass 

 l»twt-en the window and the house, the observers will be 

 "|U«lly able to determine the size of the cot, if only they 

 know the relative distances of the dove and dovecot. 



Thus, if D (I is twice us gnat as D .\, as in Fig. 2, then 

 n 6 is twice as gri-at as A 15, the b-ngth which the observers 

 know ; and if D n is only e.jual to half D A, as in 

 Fig. .3, then n A is only e<juul t« half the known length, 

 A IV In every fiossible case the length of a li is known. 

 Take one other cas*- in which the proportion is not quite so 

 kimple : — Suppose that I> " is greater than D A in the pro- 

 portion of 18 to 7, u in Fig. 4 ; then A a is greater than 



A B in the same proportion ; so that, for instance, if A B 

 is a length of 7 in., 6 a is a length of 18 in. 



Fig. 3. 



W'e see from these simple cases how the actual size of a 

 distant object can bo learned by two observers who do not 

 leave the room, so long only as they know the relative dis- 

 tances of that object nnd of another which conies between 

 it and them. We need not specially concern ourselves by 

 inquiring /into they could determine this last point; it is 

 enough that it might become known to them in many ways. 

 To mention only one. Suppose the sun was shining so as 

 to throw the sliadow of the dove on a uniformly-paved 

 court between the house and the dovecote, then it is easy 

 to conceive how the position of the shadow on the uni- 

 form paving would enable the observers to determine (by 

 counting rows) the relative distances of dove and dovecot. 



Fig. 4. 



Now, Venus comes between tho earth and sun precisely 

 as the dove in Fig. 4 comes between the window, A B, and 

 the dovecot, li ti. The relative distances are known exactly, 

 and have been known for hundreds of years. They were 

 first learned by direct obsc-rvation ; afterwards by the 

 application of the laws of Kepler as interpreted and cor- 

 rected by Newtonian astronomy. The distance of the 

 earth from the sun has been found to bear to that of Venus 

 very nearly that of lOO to 72 ; so that, when Venus is on a 

 line between the earth and sun, her distances from these 

 two bodies are as 28 to 72, or as 7 to 18. 



These distances are proportioned, then, as D A to D a in 

 Fig. 4 ; and the very same reasoning which was true in 

 the case of dove and dovecot is true when for the dove and 

 dovecot we substitute Venus and the sun respectively, 

 while for the two observers looking out from a window vn- 

 substitute two observers stationed at two difFerent parts of 

 the earth. It makes no dillerence in the essential princi- 

 ples of the problem that in one case we have to deal with 

 inches, and in the other with thousands of miles; just as 

 in speaking of Fig. 4 we reasoned that if A IJ, tho distance 

 between the eye-level of the two observers, is 7 in., then 



Fi»,'. 



1) n is 18 in., so we say that if two stations, A and B, Fig. 

 on the earth, E, are 7,000 miles apart (measuring the dis- 

 tance in a straight line), and an observer at A sees Venus' 

 centre on the sun';! disc at n, while an observer at B sees 

 her centre on the sun's disc at h, then h a (measured in a 

 straight line, and regarded as part of the upright diameter 

 of the sun) is equal to )H,000 miles. So that if two ob- 

 servers, so placed, could observe Venus at the same instant^ 

 and note exactly where her centre seemed to fall, then since 



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