PLANETARY MOTIONS 51 



to that of an arc as compared with its tangent. That the 

 two forces mentioned do not act cumulatively, but in 

 opposition to each other, resulting in a logical diminution 

 of speed, clearly appears from the direction of the line 

 psZt, which depicts the mean direction of the action of the 

 central force, and which visibly intersects the tangent at 

 an acute angle. This loss of velocity, be it noted, is not in 

 any sense attributable to the presence of a resisting 

 medium, but is the inevitable and logical outcome of the 

 principle of central attraction, and calls for the assign- 

 ment of a substantial counteracting centrifugal force. 



Suppose, for the sake of argument, that the moon 

 really did fall acceleratively as Newcomb describes, then 

 at the end of the first quadrant she will have gained a 

 velocity equal to 3350 feet per second in addition to the 

 "persistent" momentum with which she started out. 

 Would not this constitute quite an embarrassment of 

 riches ? Furthermore, what shall be said of the contradic- 

 tory statements: that the moon only falls two miles dur- 

 ing the entire month; that she doesn't fall at all, since she 

 perennially preserves her mean altitude; that she falls 

 out to apogee and in to perigee 31,000 miles alternately; 

 and, finally, that she falls not uniformly but accelera- 

 tively? 



Suppose that you were called upon to run a hundred 

 yards against time, starting from scratch and thence to 

 and around a goal post and return ; do you think you could 

 make as good a showing and with no greater expenditure 

 of energy as in a straightaway course of the same length! 

 Of course you couldn't ; and you could not find a sane boy 

 old enough to know what it means to run such a race who 

 would say you could. Astronomers, however, tell us that 

 the moon can! Every month she starts from perigee, 

 runs her way out to aphelion, makes a wide detour, and 

 returns to the starting point. At all points in her orbit 

 180 degrees apart, her compass direction is exactly re- 

 versed, showing that she must arrest all her motion east- 

 ward or westward, as the case may be, before she can 

 acquire a new motion westward or eastward ; yet month 

 after month she has been doing this throughout the cen- 



