SOLIDS ON si hi \(ES. 



perties of the Segnerian axes. This was firs! effected b\ 

 Lagrange 33 in the Memoirs of the Academy of Berlin f<>i 

 177*. In the course of this solution, which is repeated with 

 an improved notation in the Mtcanique Jbtalytiqtte, the well 

 known values of the resolved angular velocities in terms of 

 the coordinates and resolved velocities of the body's poles, are 

 given firsl as mere analytical abridgments, and made after- 

 wards to exhibit their geometrical signification; a method 

 which this author has followed on various other occasions. 

 Nine years before this, however. Lagrange had considered 

 another highly interesting case of planetary oscillation, the 

 librations of the moon. His memoir on this subject was 

 crowned by the Academy of Sciences in 1764 and will ever 

 be memorable in the annals of Demonstrative Mechanics a* 

 containing the application of the beautiful principle of vir- 

 tual velocities in all its simplicity and power to the most ge- 

 neral speculations of Dynamical Philosophy 11 . Combined 

 with the great theorem of D'Alembert, this principle dis- 

 penses altogether with the slow and enforced aids of Geome- 

 try, and leads the analyst at once frojn the definition of 

 velocity and force safely and rapidly to the most recondite 

 - terets and the most elevated regions of the Science. In the 

 Berlin .Memoirs for L780, Lagrange resumed the whole sub- 

 ject, and in an admirable dissertation regarded by himself as 

 the mosl finished of his productions, he terminates in formulas 

 which delineate, in all their intricate variety, the motions of 

 our satellite, lor ages withoul number past and to come. 

 These expressions are the results of a skilful transformation ol 

 the genera] equations in the case of rotation round a body- 

 axis which forms with its mean direction a very small but 

 variable angle, taking into account the figure which the moon 



ilution fhi Probleme 'In Moovemeot dc Rotation d'un Corps. 

 . .M''m. Berl. I 

 '* Recherches sur U libration de la Lune. Hist. Acad. Par. Prix. Tome IX 



