THE MOON’S MOTIONS.

79

Now, let us make a separate figure to indicate tieactual state of tiings in such a case as we have con-sidered. There is the sun at S (fig. 18, Plate Y.)pulling at the moon with a force which we have repre-sented by M S ; and he is pulling at the earth with aforce which we represent on the same scale by S H.This last force, so far as the moon’s place with respectto the earth is concerned, is clearly a force tending tokeep the moon and earth together. It may be repre-sented then, in this sense, by the line S H, or as a forcetending to thrust the moon from the sun (almost asstrongly and directly as the direct action on M tendsto draw the moon towards the sun).* Thus the moonis virtually acted on by the two forces represented byMS and SH,*and therefore, by the well-known pro-position called the triangle of forces, we have as theresultant perturbing action on the moon, a force re-presented by the line MH.f

* Of course the sun’s action on the earth does not really amountto a force thrusting or repelling the moon from the sun. But indetermining the sun’s perturbing action on the moon, we have ineffect to take the excess or defect of the sun’s full action on themoon, as compared with his full action on the earth, so that thelatter action necessarily comes to be viewed in a sense contrary toits real nature, precisely as in ordinary arithmetic a sum which ispositive in itself comes to be viewed as negative when it is to besubtracted.

t If the student is more familiar with the parallelogram of forcesthan with the same property under the form called the triangle offorces, he should draw a line from M parallel and equal to S H ; hewill find that MH is the diagonal of a parallelogram having thisline and M S as adjacent sides.