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at A.* And let this be noted as to the present con-dition of the body. It has increased its distance fromS, and has thus far asserted, in a sense, the powerinherent in it when at A, by virtue of its high velocitythere ; it has also increased its angular rate of escape,the angle S B Z exceeding the angle SAY. But ineffecting this it has sacrificed a portion of its velocity,the influence of the orb at S having acted retardinglythroughout the whole of this portion of the body’scourse; and, as a matter of fact, the velocity at B isless than the velocity at A, in the proportion that A Sis less than B 0.
As the body passes onwards from B, the sun’saction continually reduces the angle corresponding toS P T, S B Z, continually reducing also the velocity ofthe body so long as this angle remains obtuse. This•process is in this respect the reverse of the processpassed through as the body moved from A to B, andends in the restoration of the rectangular thwartmotion when the body has arrived at «, directly oppo-site to A. Yet the part Bp a of the body’s course isdescribed under circumstances wholly different fromthose operating while the body was moving from Ato B. The time from A to B is much less than thetime from B to a ,—in the same proportion, in fact,
* It will be remembered that in the above paragraph explana-tion of what actually happens, and not a proof that it must hap-pen, is attempted. To show that when the angle corresponding toS P T ceases to increase, the body must be travelling on a courseat right angles to A Y, is impossible without introducing mathe-matical considerations much more fully than is proper in this place.