SIMON NEWCOMB 375 



directly measure distance, its direction from us, must be deter- 

 mined as precisely as possible from time to time. Its course has 

 been mapped out for it in advance by tables which are published 

 in the Astronomical Ephemeris, and we may express its position by 

 its deviation from these tables. Then comes in the mathematical 

 problem how it ought to move under the attraction of all other 

 heavenly bodies that can influence its motion. The results must 

 then be compared, in order to see to what conclusion we may be 

 led." 



It is not easy to understand the obstacles that had to be over- 

 come in a series of investigations in which in the solution of so 

 complex a problem as that Newcomb undertook. The general 

 treatment is indicated by Bostwick * in the following statement: 



"If the universe consisted of but two bodies say, the sun and 

 a planet the motion would be simplicity itself; the planet would 

 describe an exact ellipse about the sun, and this orbit would never 

 change in form, size, or position. With the addition of only one 

 more body, the problem at once becomes so much more difficult 

 as to be practically insoluble; indeed, the 'problem of the three 

 bodies' has been attacked by astronomers for years without the 

 discovery of any general formula to express the resulting motions. 

 For the actually existing system of many planets with their satel- 

 lites and countless asteroids, only an approximation is possible. 

 The actual motions as observed and measured from year to year 

 are most complex. Can these be completely accounted for by the 

 mutual attractions of the bodies, according to the law of gravita- 

 tion ? Its two elements are, of course, the mapping out of the lines 

 in which the bodies concerned actually do move and the calcula- 

 tions of the orbits in which they ought to move, if the accepted laws 

 of planetary motion are true. The first involves the study of 

 thousands of observations made during long years by different men 

 in far distant lands, the discussion of their probable errors, and 

 their reduction to a common standard. The latter requires the 

 use of the most refined methods of mathematical analysis; it is as 

 Newcomb says, 'of a complexity beyond the powers of ordinary 

 conception.' " 



The practical impossibility of ever completing this remarkable 

 series of studies is almost obvious, for in magnitude that task is 



1 A. E. Bostwick, American Review of Reviews, August, 1909. 



