THE 



AMERICAN JOURNAL OF SCIENCE 



[THIRD SERIES. 1 



Aet. XXXI. — Distance of the Stars by Doppler's Principle ; 

 by Gr. ¥. Colles, Jr. 



Among the many interesting and important applications of 

 Doppler's principle for finding the velocity of a body in the 

 line of sight or sound, is one which has been apparently little 

 noticed, namely, that to the determination of distance. It is 

 true, however, that this is easily accounted for by the fact that 

 the principle itself is not yet far enough advanced for the 

 application of such a problem. I believe the first mention of 

 it is that made by Fox Talbot, in a paper read before the 

 Rritish Association in 1871, in which he showed how Dop- 

 pler's principle might be applied to finding the distance of a 

 binary system. Supposing the orbit of each star to be ac- 

 curately known, in shape and position, let their relative veloci- 

 ties be taken by the spectroscope when the two stars are moving 

 as nearly as possible in the line of sight. Now, since we know 

 the shape of the orbit, we know the proportionate velocities of 

 the stars at any point of it ; hence, knowing also the absolute 

 velocities at one point of the orbit, we can deduce them for the 

 point where each star is moving only across the line of sight. 

 Then, finding the angular velocity at this point, and dividing 

 the computed linear velocity by it, we have the distance of the 

 system. Or otherwise, knowing the actual period of the sys- 

 tem, the absolute velocity at any point gives us the true size, 

 or diameter, of the orbit ; and dividing this by the angular 

 diameter, we have, as before, the distance of the system. 



Talbot's idea was taken up in 1886 by Prof. A. A. Rambaut, 

 now Astronomer Royal of Ireland, and he has quite elaborately 



Am. Jour. Sci.— Third Series, Vol. XLV, No. 268.— April, 1893. 

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