454 Notices respecting New Books. 



to the few who possess the requisite technical knowledge. Many 

 attempts have been made to give elementary explanations of the 

 inequalities of the celestial motions, but seldom with much success : 

 indeed, if we except Maclaurin's Account of Newton's Discoveries, 

 Mr. Airy's Treatise on Gravitation, and the work now under 

 review, it would be difficult to point out one from which a student 

 about to enter on the works of Newton and Laplace would derive 

 any considerable aid ; and even in respect of these master-pieces it 

 may perhaps be said, that their merit will hardly be appreciated ex- 

 cepting by those who have proceeded to some extent in the technical 

 examination. But Sir John Herschel has not confined himself merely 

 to the illustration of methods already known. In discussing certain 

 effects of perturbation he has struck out an entirely new path, and 

 presented the subject in a light which certainly renders it much 

 easier of comprehension ; and on this account the work must be re- 

 garded as an important contribution to physical astronomy. To these 

 new views he thus alludes in his preface : — 



" In delivering a rational as distinguished from a technical expo- 

 sition of this subject, the course pursued by Newton in the section 

 of the Principia alluded to has by no means been servilely followed. 

 As regards the perturbations of the nodes and inclinations, indeed, 

 nothing equally luminous can be substituted for his explanation ; 

 but as respects the other disturbances, the point of view chosen by 

 Newton has been abandoned for another which it is somewhat diffi- 

 cult to perceive why he did not, himself, select. By a diflferent re- 

 solution of the disturbing forces from that adopted by him, and by 

 the aid of a few obvious conclusions from the laws of elliptic motion, 

 which would have found their place, naturally and consecutively, as 

 corollaries of the seventeenth proposition of his first book (a propo- 

 sition which seems almost to have been prepared with a special view 

 to this application), the momentary change of place of the upper 

 focus of the disturbed ellipse is brought distinctly under inspection ; 

 and a clearness of conception introduced into the perturbations of 

 the eccentricities, perihelia and epochs which the author does not 

 think it presumptuous to believe can be obtained by no other method, 

 and which certainly is not obtained by that from which it is a de- 

 parture The reader will find one class of the lunar and 



planetary perturbations handled in a very difi^erent manner from that 

 in which their explanation is usually presented. It comprehends 

 those which are characterized as incident on the epoch, the principal 

 among them being the annual and secular equations of the moon, 

 and that very delicate and obscure part of the perturbational theory 

 (so little satisfactory in the manner in which it emerges from the 

 analytical treatment of the subject), the constant or permanent efl^ect 

 of the disturbing force in altering the disturbed orbit. I will venture 

 to hope that what is here stated will tend to remove some rather 

 generally diflfused misapprehensions as to the true bearings of New- 

 ton's explanation of the annual equation." 



The third Part relates to Sidereal Astronomy. If the former is 

 that which is likely to have the fewest readers, this undoubtedly is 



