39II-] 



LXCREASE OF THE SUX'S MASS. 



271 



The last of these papers is the most important, since it supple- 

 ments and extends the results of the earlier investigators. Professor 

 Stromgren's method is one of great generality and appears to be the 

 most satisfactory yet devised; and we shall base our brief discussion 

 ■chiefly on this paper. 



If cr be a very small quantity, and (pit) some function of the 

 time, the original unit of mass becomes i -|-o-<^(n. and the differ- 

 ■ential equations of motion become 



d^y 



dt 



r,+k\\ + o-(^(o] ';3 = o ; 



(I) 



where k- is the gravitation constant, and the mass is unity at the 

 initial epoch ^ = o. 



The new constant of areas becomes 



dv 



dx 



Other formulas of interest are: 



la = i\(T<^{t) — 2d\<j I 0'(/) jit , 

 - = - [i + 2I/. [ie] cos i{e + ;// — tt)] 



(3) 



(4) 

 (5) 



And finally after a careful investigation of all effects due to 

 errors of the first order of the disturbing force, (T(f>(t), Stromgren 

 iinds : 



8a 



8e = 



= — aa\ 



/ + 2 - (sin E — sin E 



41 



I — r 



(T (sin E — sin E^ , 



s/\ — e^ 



CTT = a(cos £ — COS E) . 



en ^ 



(6) 



