Royal Society. 223 



contained in the capsules of Cordylophora are true ova, and not 

 gemmae ; he has demonstrated in them a distinct germinal vesicle, 

 and has witnessed the phenomenon of yelk- cleavage ; and the paper 

 details the development of the embryo to the period of its escape 

 from the capsule in the form of a free- swimming ciliated animacule, 

 and traces its subsequent progress into the condition of the adult 

 zoophyte. 



2. " On the Secular Variation of the Moon's Mean Motion." By 

 J. C. Adams, Esq., M.A., F.R.S. &c. 



The author remarks, that in treating a great problem of approxi- 

 mation, such as that presented to us by the investigation of the 

 moon's motion, experience shows that nothing is more easy than to 

 neglect, on account of their apparent insignificance, considerations 

 which ultimately prove to be of the greatest importance. One in- 

 stance of this occurs with reference to the secular acceleration of the 

 moon's mean motion. Although this acceleration and the diminu- 

 tion of the eccentricity of the earth's orbit, on which it depends, 

 had been made known by observation as separate facts, yet many of 

 the first geometers altogether failed to trace any connexion between 

 them, and it was not until he had made repeated attempts to explain 

 the phenomenon by other means, that Laplace himself succeeded in 

 referring it to its true cause. 



The accurate determination of the amount of the acceleration is a 

 matter of very great importance. The effect on the moon's place, 

 of an error in any of the periodic inequalities, is always confined 

 within certain limits, and takes place alternately in opposite direc- 

 tions within very moderate intervals of time, whereas the effect of 

 an error in the acceleration goes on increasing for an almost inde- 

 finite period, so as to render it impossible to connect observations 

 made at very distant times. 



In the ' Mecanique Celeste,' the approximation to the value of 

 the acceleration is confined to the principal term, but in the theories 

 of Damoiseau and Plana, the developments are carried to an im- 

 mense extent, particularly in the latter, where the multiplier of the 

 change in the square of the eccentricity of the earth's orbit, which 

 occurs in the expression of the secular acceleration, is given to terms 

 of the seventh order. 



As these theories agree in principle, and only differ slightly in the 

 numerical value which they assign to the acceleration, and as they 

 passed under the examination of Laplace, with especial reference 

 to this subject, it might be supposed that only some small numerical 

 rectifications would be required in order to obtain a very exact 

 determination of this value. 



It has not been, therefore, without surprise, which he has no 

 doubt will be shared by the Society, that the author has lately found 

 that Laplace's explanation of the phenomenon in question is essen- 

 tially incomplete, and that the numerical results of Damoiseau's and 

 Plana's theories, with reference to it, consequently require to be very 

 sensibly altered. 



Laplace's explanation may be briefly stated as follows. He shows 



