515 



ceived to begin at c, and to end at a ; and if we conceive an 

 unit-mass at b to attract two other masses, regarded as col- 

 lected into points, and as situated respectively at c and at a ; 

 this attraction of b will disturb the relative motion of a about 

 c, if a be supposed to be nearer than b is to c, by producing 

 a series of groups of smaller and smaller forces, of which 

 groups it may be sufficient here to consider the two following. 

 The first and principal group consists of the two disturb- 

 ing forces ^10 and ^o i, and of these the first is purely ablati- 

 tious, or is directed along the prolongation of the side of the 

 triangle abc, which is drawn from c to a, and it has its inten-- 

 sity denoted by the expression lba~'^, since we have for this 

 force, and for its tensor and versor, the expressions 



0i,o = i/3(-a^H; T0,,o = i6«-'; u^,,oi:u/3. (29) 

 The second disturbing force, of this first group, has for ex- 

 pression 



^o,i = |aj3a-'(-a^)-^ = |ai3a-^«-='; (30) 



its intensity is exactly triple of that of the former force, being 

 represented by ^ba~^; and its direction is the same as that of 

 a straight line drawn from c to a', if a' be a point such that . 

 the line aa' is perpendicularly bisected by the line bc (pro- 

 longed through c if necessary). These two principal disturb- 

 ing forces evidently correspond to those which were considered 

 for the case of our own satellite in a communication above al- 

 luded to ; the second force being the one which was described 

 in that former communication as being directed to what was 

 there called the " fictitious moon," and was conceived to be 

 as far from the sun in the heavens on one side, as the actual 

 moon is on the other side, but in the same great circle. 



If we now extend that mode of speaking so far as to con- 

 ceive a similar reflexion of the sun with respect to the moon, 

 and to call the point in the heavens so found the " fictitious 

 sun," the moon being thus imagined to be seen midway among 

 the stars between the actual and the fictitious sun : and if we 



