170

THE MOON S CHANGES

M t to M 2 , fig. 55, and A C forcibly kept in the positionindicated, there would be the change of face we havedescribed, yet that in the nature of things if a bodywere set without rotation travelling round a centralglobe, it would as it went round turn itself also,as if upon an axis, and so keep always the sameface directed towards the central globe. For ex-ample, if a rod extending from B and rigidly attachedto M x , carried that globe round E in the mannerindicated, then the face A would remain constantlyturned towards B : may it not be, it might be asked,that as the globe moved under gravity round E thesame thing would happen ? If the globe M u initiallyat rest, were propelled by a blow directed exactly onthe line B M x with precisely the velocity correspondingto the circular orbit under gravity, might

not the result of the attractions exerted by E be tocause the globe M x not only to go round E, but toturn itself always so as to have the same face directedtowards E ?

Now it is mathematically demonstrable that theattraction of E can have no effect whatever in causingthe direction of the line A M to change as the body(supposed to be spherical *) circles around E. Butthe considerations on which such a demonstrationwould be based are by no means so obvious as is com-

* If the body be not spherical, forces tending to produce arotation come into play ; but if the body has even only a roughlyglobular form, such forces are altogether too small to produce anyappreciable amount of rotation during a single revolution.