20 Prof. R. Clausius on the Relations between the 



least an approximative determination of that function. I have 

 therefore developed the function Jj in a series, and calculated 

 some of the terms of that series. 



From the above-mentioned differential equation 



tfr _ 1 



m -r-7- = — kr n + mc 2 -*} 



dr r 3 



we obtain by the first integration : — 



wherein E, as before, denotes the energy of the motion. This 

 gives, for the determination of the time, the differential equation 



dt= dr 



V m r* mn-\- 1 



or, multiplying both numerator and denominator by r, 



^ (r2) . . (39) 



Into this we will introduce the constants p and q instead of 

 E and c, putting, according to equations (22) and (33), 



\A*+ 



E = *- " + 8 1X p» +1 and c 2 = — oV" 

 2(w+l) m 



We then get 



i#3 



dt= 



\/~^9Y 



m n-\- 1/ ' m ft + 1 



If we take away the factor — p n+3 from the root-sign, we 

 obtain 



or, otherwise written, 



+ 3 



-\yf*r* tM . (40) 



V k r / ■ n + 3/rV 2 /r\" +3 



