276 HISTORY OF SCIENCE. 



ing of the lunar sphere, the movement has received the name of the 

 librarian, from a Latin word, libratio^ a balancing. This is due to seve- 

 ral distinct causes : the moon's axial velocity being sensibly uniform, 

 while its orbital velocity varies in different parts of its course round 

 the earth, sometimes a little more of the eastern or western edge is 

 visible at one time than another ; again, the moon's axis is not quite 

 perpendicular to its orbit, and sometimes we see now a little of one 

 polar region, now a little of the other ; lastly, we view the moon from 

 different points, at its rising and at its setting. The combined effect 

 of all these librations is that the part of the lunar surface visible at 

 one time or another, is fVoths of the whole, the remainder, or the 

 portion never seen, is T^Vhs. The portion of the moon's surface now 

 visible is the same that our most remote ancestors looked upon, and 

 mankind will never behold the opposite hemisphere of our satellite. 

 It might be supposed that the secular acceleration (p. 216) would in 

 time prevail over the axial rotation; but the periodic inequalities 

 which affect the orbital movements of the moon equally affect its axial 

 rotation. The law of gravitation explained so much that it would 

 be strange if it failed to explain the isochronism of the moon's rota- 

 tions. The question was still in an unsettled state when Lagrange's 

 investigation led him to conclude that it depended on the circum- 

 stance of our satellite possessing a certain figure, which could not be 

 discovered by observation. He supposed that, the moon being origi- 

 nally a fluid body, it assumed, when it solidified, a less regular figure, 

 in consequence of the earth's attraction, than if that attraction had 

 not existed. The moon's equator, by virtue of this attractive action, 

 assumed the form of an ellipse instead of a circle, with the longer axis 



of the ellipse directed towards the earth. 

 The lunar equatorial regions may of 

 course have the bulging due to the 

 -*^. moon's original axial rotation, but the 

 \ bulging at the parts a and b (Fig. 130) 

 * would be greater than at c and d. If the 

 moon were at any time so placed that the 

 line a b was not directed towards the 

 earth's centre, the effect of the latter's 

 attraction would be to bring it into this 

 position. Lagrange's theory has the merit 

 of accounting for the otherwise inexpli- 

 cable additional coincidence of the nodes 

 FlG - T 3- of the moon's equator with the nodes of 



its orbit. 



In mechanical science the principle of virtual velocities was recog- 

 nized throughout the eighteenth century as the great principle of statics. 

 Lagrange extended this formula in a more general manner than his 

 predecessors, and showed that it is applicable to any system whatever 



