288 



SUN S DISTANCE. 



firms 



Fig. 4. 

 Disk rt i ersed 



-'.'''•" 



- ^iTicrress 



In figure 4 is represented by a black 

 line the path which Venus will appear 

 to describe across the Sun's disk in the 

 transit of 1882, (reversed in regard of 

 right and left, for the convenience of 

 subsequent investigations) as seen from 

 the centre of the Earth. For the 

 present let us lay aside the considera- 

 tion of the Earth's rotation. An ob- 

 server in the northern portion of the 

 Earth will see Venus describe, not the 

 black line, but the fainter line below 

 the black line and parallel to it. An 

 observer in the southern portion of the Earth will see Venus describe 

 the fainter line above the black line. The path seen by the southern 

 observer is longer than that seen by the northern observer, and there- 

 fore occupies a longer time. Consequently the mere observation of 

 the duration of the transit at these two stations would give informa- 

 tion on the lengths of the two chords, and therefore would give 

 means of computing the amount of separation of the two chords: and 

 this apparent separation corresponds to the angle S AS' in figure 3. 

 We have therefore all the means of computing the angle A S' B, and 

 of inferring from it the Sun's distance; although, as may be imagined, 

 the intervening calculations are sufficiently complicated. 



But this is on the supposition that the Earth has no motion of rota- 

 tion. Let us introduce the consideration of rotation, and see how it 

 modifies the result. 



Let us place ourselves over a globe with its south pole elevated to 

 represent the illuminated portion of the Earth on the day of transit. 

 By bringing the meridian of 135° E. to the vertical, we shall see the 

 portion of the Earth turned toward the Sun at the ingress of Venus 

 on the Sun's disk; by bringing the meridian of 75° E. to the vertical, 

 we see that portion turned toward the Sun at the egress. The re- 

 versed form given to the solar disk in the cut (fig. 4) enables us to 

 refer lines on the globe and on the diagram to corresponding geomet- 

 rical directions, when we imagine ourselves to be looking through 

 the diagram upon the globe.* 



Now, fixing our attention on a northern station, in the United States 

 of America for instance, it will be seen that the translation of this 

 place by the movement of rotation carries it to meet the motion of 

 Venus. Consequently it tends to shorten the duration of the transit. 

 But by virtue of the northerly position of that station, the duration 

 of transit is already shortened. Consequently, by combination of 

 these two effects, the duration of the transit at the northern station 

 is very much shortened. 



Now, can we select a southern station such that the same rotation 



- On account of the unavoidable omission of the diagrams representing the illuminated 

 portions of the Earth at the times of ingress and of egress of the two transits, a few pas- 

 sages have been omitted, and equivalent ones introduced, using the globe as a means of il- 

 lustration. — J. H. 



