64 ROUGH WAYS MADE SMOOTH. 



feet apart. Suppose they note that the two tracks along 

 which, as seen from these two points, the bird seems to cross 

 the face of the distant globe, lie at a distance from each 

 other equal to one-third of the globe's apparent diameter. 

 Now, the bird being twice as far from the globe as from the 

 window, the two tracks on the globe necessarily lie twice as 

 far apart as the two points from which they are seen or they 

 lie 6 feet apart. The globe's diameter therefore is 18 feet. 

 Knowing thus how large it is, and knowing also how large 

 it looks, the observers know how far from them it lies. So, 

 in the Halleyan method of determining the sun's distance 

 by observing Venus in transit, astronomers are stationed far 

 north and far south on the sunlit half of the earth, corres- 

 ponding to the window of the imaginary experiment. Venus 

 corresponds to the bird. The observers note along what 

 track she travels across the sun's face. (That they partially 

 determine this by noting how long she is in crossing, in no 

 sense affects the principle of the method.) They thus learn 

 that such and such a portion of the sun's diameter equals 

 the distance separating them, some six or seven thousand 

 miles perhaps, whence the sun's diameter is known. And 

 as we know how large he looks, his distance from the earth 

 is determined. 



A peculiarity distinguishing this method from the former 

 is that the observers must have a station whence the whole 

 transit can be seen ; for practically the place of Venus's 

 track can only be ascertained satisfactorily by timing her 

 passage across the sun's disc, so that the beginning and end 

 must be observed and very carefully timed. This is to some 

 degree a disadvantage ; for during a transit lasting several 

 hours the earth turns considerably on her axis, and the face 

 turned sunwards at the beginning is thus very different from 

 the face turned sunwards at the end of transit. It is 

 often exceedingly difficult to find suitable northern and 

 southern stations belonging to both these faces of the earth. 

 On the other hand, the other method has its peculiar dis- 

 advantage. To apply it effectively, the observer must know 



