igis-] SEE— THE EULER-LAPLACE THEOREM. 340 



be subtracted from tbc distance from the aphelion to the sun, which 

 would develop in the same time, and found to be equal to 



I - r ^^(i - 1? ' 



it will give for the distance of the foci after l revolutions 



2^.? 2i7r<:gg(3 - rr) 



I - 1^ c(i - ^^y • 



The initial transverse axis was 2g/(i — ^t,) , and if we divide this into 

 the last expression, we get for the eccentricity of the orbit at this 

 time : C — • ^t^^Q/c, terms in C' being neglected as insensible. 



In Euler's paper the factor 3 in the last term is inadvertently 

 omitted. He remarks that the original eccentricity was ^, whereas 

 after i revolutions it is decreased by the negative term shown above, 

 and thus is subject to a secular diminution, owing to the secular 

 action of the resisting medium. 



After this discussion Euler reaches the conclusion : " A re- 

 sistentia ergo excentricitas continuo minuitur, orbitaeque planetarum 

 propius ad figuram circularem reducuntur " (p. 271). 



He therefore recognized clearly that the effect of a resisting 

 medium is to decrease the eccentricity incessantly, and to render 

 the orbit more and more circular ; and had reached this important 

 conclusion some fifty-six years (1746) before the corresponding 

 theorem was established by Laplace in 1802. 



Accordingly as Euler's reasoning is essentially rigorous, though 

 not the same as that of Laplace, it is evident that he was the first 

 discoverer of the theorem which is of such fundamental importance 

 in the theories of cosmogony. 



It is remarkable that although Laplace had this theorem clearly 

 before his mind for a quarter of a century at the close of his life 

 (1802-1827) he did not once suspect that the planets and satellites 

 had originated in the distance and through the action of a resisting 

 medium had neared the centers about which they now revolve, and 

 thus acquired the wonderful circularity of their orbits. 



It is well known that Laplace continually refers to these bodies 

 as detached by rotation, in the form of zones of vapor, as first 



