[ 132 ] 

 XXIII. Proceedings of Learned Societies, 



ROYAL SOCIETY. 

 [Continued from p. 66. "} 

 Nov. 25/ I TIE following papers were read : — 



1852. A 1. "New solution of Kepler's Problem." By Pro- 

 fessor P. A. Hansen. 



It is well known how much labour has been bestowed by geometers 

 on the solution of Kepler's Problem, and what complicated results 

 have been obtained for the coefficients in the expression for the 

 Equation of the Center. I have lately found a new solution of this 

 problem, which differs strikingly from former solutions in this respect, 

 that it leads to an unexpectedly simple law of coefficients. It is as 

 follows : — 



Let g be the mean anomaly ; 



be the angle of excentricity ; 

 • be any positive integer number. 



Put /3 = tan |., ju = i cos2 ^, 



&c. 

 Then the Equation of the Center 



= (1 -/5«)2;;^J P, . ft+P.+i . Q, . /3«+2 + p,^,. Q^ . /3'+4+ &c.|sin t>. 



The analysis which has led me to this, and the form of this result, 

 are by no means peculiar to the Equation of the Center only, but apply 

 to all functions which it is necessary to develope in series proceeding 

 by sin ig or cos ig. 



2. "An Experimental Inquiry undertaken with the view of ascer- 

 taining whether any, and what signs of Current Force are manifested 

 during the organic process of Absorption (Lacteal) in living ani- 

 mals."— Part II. By H. F. Baxter, Esq. 



In the experiments related in this paper, it is shown that when the 

 electrodes of a galvanometer are brought into contact, one with the 

 mucous membrane of the intestine, and the other with the chyle 

 flowing from the lacteal of the same point, an effect upon the needle 

 occurs indicating the chyle to be positive. The effects may be partly 

 due to the changes which take place during secretion, the mesentery 

 acting as a conducting body; this supposition however will not 

 negative the conclusion that the effects may be attributed, in some 

 measure at least, to the changes which occur during lacteal ab- 

 sorption. 



3. "An Experimental Inquiry undertaken with the view of ascer- 



