218 Reviews, and Notices respecting New Booh. 



cilia at the stigma, and seven round, and one at the apex ; legs and belly 

 dull silvery. 



3. costalis Curt. 

 3 lines : pale ochreous shining ; superior wings variegated fuscous, with a 

 dot on the disc, the costal cilia long and black, with a long pale space at 

 the centre. 



Jan. 1st, 1834. 



XXXVIII. Reviews, and Notices respecting New Books. 

 Mathematical Tracts. By J. W. Lubbock, Esq., F.R.S. 



THIS volume, which forms an important addition to the libraries 

 of the astronomer and the analyst, consists of three tracts, the 

 objects of which we proceed to state, seriatim. 

 1. On the Theory of the Moon, and on the Perturbations of the 

 Planets. 



Mr. Lubbock's object in this memoir is to give a connected but 

 brief sketch of, and to improve, a portion of his researches in phy- 

 sical astronomy, printed in the Philosophical Transactions. Laplace 

 adopted the analytical investigation of the theory of the moon 

 proposed and employed by Clairaut, but carrying the approxima- 

 tion much further : " it has since been pushed to an almost incre- 

 dible extent by M. Damoiseau, without any alteration, however, in 

 the method employed. 



" Laplace," Mr. Lubbock states in his Preface, " insists particu- 

 larly upon the necessity of having recourse to the equations in 

 which the true longitude is the independent variable ; but notwith- 

 standing the respect whicb is due to so great authority, I am con- 

 vinced, after much reflection, that the method which I have sub- 

 mitted to the Royal Society, and which forms the groundwork of 

 this essay, is on many accounts to be preferred. According to this 

 method, the expressions for the parallax, and the true longitude 

 obtained by the reversion of series in the method of Clairaut, are 

 arrived at directly." 



It being desirable to introduce into the science of physical astro- 

 nomy a uniform system, by employing, if possible, methods which 

 embrace the motions of all the heavenly bodies*, Mr. Lubbock has 

 shown howthe perturbations of the planetsand those of the satellites 

 of Jupiter may be obtained from the equations employed in his theory 

 of the moon ; and how also the table of the arguments which occur 

 in the theory of the moon may be used in the planetary theory The 

 resulting expressions for the planetary perturbations differ in form 

 from those of the Mecanique Celeste, Mr. L. obtaining the inequali- 

 ties of the reciprocal of the radius vector, by the method of inde- 

 terminate coefficients, directly from an equation, without the inter- 

 vention of an auxiliary variable, while he obtains those of longitude 

 from an equation differing from that employed in the Mecanique 

 Celeste, and other works in which the same methods are adopted. 



* On this subject see also our Report of the Proceedings of the Royal 

 Society, in the present Number, p. 216—217- 



