Astronomy. — "The longitude of Hyperions pericentre and the 

 mass of Titan'. Bj Dr. J. WoltjkrJr. (Communicated by 

 Prof. W. DE Sitter). 



(Communicated in the meeting of December 28, J 918). 



1. In my dissertation '), published in the course of this year, I 

 commenced the determination of the action of Titan on the motion of 

 Hyperion. The developments include tiie libration in the critical 

 argument, in the semi-axis major and in the eccentricity, together 

 with a determination of the mean motion of the argument of the 

 libration; further the large inequality of the critical argument, propor- 

 tional to the first power of Titan's eccentricity. As I intend to carry 

 on these computations, the first thing to be done is to determine the 

 libration in the longitude of pericentre and the mean motion of this 

 element. The results are contained in this paper, which forms a conti- 

 nuation of the memoir already cited. 



To this end the development of the perturbative function 

 ("Investigations" Chapter I) has to be continued by the compu- 

 tation of the derivative with respect to e, the eccentricity of 

 Hyperion. The determination of the derivative with respect to a, 

 the semi-axis major, being closely related to this computation, we 

 also shall derive this function, though not required for the purpose 

 of this paper. 



To check the special values of the perturbative function used for 

 these developments, an independent computation of the same values 

 has been carried out, starting from the goniometric development of 

 the square of the mutual distance of the two satellites. Tiie greater 

 part of the numerical computations involved has been performed by 

 Mr. D. Gaijkema, computer at the Leiden Observatory. 



2. The determination of the derivative of the perturbative function 

 with respect to e consists of the computation of the function 



ö/([l]) 



1) "Investigations in the theory of Hyperion"; hereafter to be cited as "investi- 

 gations". 



