April 7, 1916] 



SCIENCE 



477 



anew by such men as Copernicus and Tycho 

 Brahe. 



With the announcement by Kepler, early 

 in the seventeenth century, of his laws of 

 planetary motion, it became possible to de- 

 duce from the periodic times of revolution 

 of the planets around the sun their relative 

 distances from that body, and thus to 

 determine the distance of the sun from the 

 earth, by determining the distance or par- 

 allax of one of the planets. 



From observations of Mars, Kepler ob- 

 tained the distance of the sun from the 

 earth as about three times that accepted up 

 to his time. His value, however, was but 

 one seventh of the true distance. About 

 fifty years later Plamsteed and Cassini 

 working independently, and using the same 

 method as that employed by Kepler, ob- 

 tained for the first time approximately the 

 correct value of the distance of the sun 

 from the earth. In a letter, dated Novem- 

 ber 16, 1672, to the publisher of the Philo- 

 sophical Transactions, Flamsteed says : 



September last I went to Townley. The first 

 week that I intended to have observed c? there 

 with Mr. Townley, I twice observ'd him, but could 

 not make two Observations, as I intended, in one 

 night. The first night after my return, I had the 

 good hap to measure his distances from two Stars 

 the same night; whereby I find, that the Parallax 

 was very small; certainly not 30 seconds: So that 

 I believe the Sun's Parallax is not more than 10 

 seconds. Of this Observation I intend to write a 

 small Tract, when I shall gain leisure; in which 1 

 shall demonstrate both the Diameter and Distances 

 of all the Planets by Observations; for which I 

 am now pretty well fitted. 



During the two and a half centuries since 

 Flamsteed 's determination there have been 

 more than a hundred determinations of the 

 solar parallax by various methods. In the 

 method used by Flamsteed, the rotation of 

 the earth is depended upon to change the 

 relative position of the observer, the center 

 of the earth, and Mars. ( Diagram shown.) 

 Another method is to establish two stations 



widely separated in latitude, and in ap- 

 proximately the same longitude. At one 

 station, the zenith distance of Mars will 

 be determined as it crosses the meridian 

 north of the zenith; at the other station, 

 the zenith distance will be determined as 

 it crosses the meridian south of the zenith. 

 The sum of the two zenith distances minus 

 the difference in latitude between the two 

 stations will give the displacement of Mars 

 due to parallax. These two methods have 

 been successfully applied to several of the 

 asteroids whose distances from the sun are 

 very near that of Mars. 



The nearest approach of Venus to the 

 earth is during her transit across the face 

 of the sun, and these occasions, four during 

 the last two centuries, have been utilized to 

 determine the solar parallax. Here as in 

 the case of Mars two different methods may 

 be used, either by combining observations 

 at two stations widely separated in lati- 

 tude, or at two stations widely separated in 

 longitude. (Diagrams shown.) 



The methods just described for obtaining 

 the solar parallax, the geometrical meth- 

 ods, were made available, as has been said, 

 by the discovery of Kepler 's laws of plane- 

 tary motion. Newton's discovery of the 

 law of gravitation gave rise to another 

 group of methods, designated as gravita- 

 tional methods. The best of these is prob- 

 ably that in which the distance of the sun 

 from the earth is determined from the mass 

 of the earth, which, in turn, is determined 

 from the perturbative effect of the earth 

 upon Venus and Mars. This method is 

 long and laborious, but its importance lies 

 in the fact that the accuracy of the result 

 increases with the time. Professor C. A. 

 Young says: 



This is the "method of the future," and two or 

 three hundred years hence will have superseded all 

 the others — unless indeed it should appear that 

 bodies at present unknown are interfering with 

 the movements of our neighboring planets, or un- 



