55 



cisely the same period oi time, how would they be able to perform 

 so marvellous a feat ? Suppose the eight circles (fig. 7) to re- 

 present a globe revolving in a orbit round E. Suppose tne cen- 

 tre of the revolving globe to be precisely 240,000 miles from the 

 centre E ; and its own diameter to be just 2000 miles. Its cen- 

 tre, therefore, will describe an orbit of 1,440,000 miles in cir- 

 cumference ; but the corresponding orbits of the points A and 

 B, whichare each 1000 miles from C, will be respectively 1,434,000 

 and 1 ,446,000 miles. To get through these orbits, inthe same time ^ 

 A would have to travel with a less, and B with a greater velocity 

 than C ; or, if they did not, it would happen that when C com- 

 pleted its revolution, A would be 6000 miles in advance, and B 

 6000 behind it ; but cohesion of the parts prevents them ever 

 getting farther away from C than 1000 miles; and, therefore, 

 they must proceed in some other way than by orbits concentric 

 with C's. In each octant of the supposed case, the difi'erence in 

 the lengths of the three octants is 750 miles ; A's octant being so 

 much shorter than C's, and C's so much shorter than B's. Sup- 

 pose their revolution to be effected by means of a force acting 

 in the direction of the centre C, or in such other way as that all 

 the three points shall travel with precisely the same degree of ve- 

 locity. When the revolving mass finishes its first octant and reach- 

 es the position No. 2, A will have run through its own proper 

 octant, and 750 miles more, for which it finds room by running 

 to that distance outside of its orbit ; while, on the other hand, B 

 saves a like distance by falling 750 miles within its orbit ; so that 

 all the three points have travelled precisely the same distance in 

 the same time, each 180,000 miles. The points a and z now 

 come into play, as the outer and inner points of circumference: 

 when the mass completes its second octant, a is found, like A, to 

 have run another 750 miles outside of its orbit, while z has fal- 

 len within its orbit to the same extent The points h and y now 

 come into play, and repeat the operation, and so on, through 

 the remaining octants, so that when the revolution is completed, 

 A has made up its deficiency of 6000 miles by revolving or ro- 

 tating round C, whose external circumference, containing the 

 points A and B, is exactly of that dimension ; while, on the other 

 hand, B has saved 6000 miles, by constantly falling back in the 

 opposite direction ; and the general result of the process is that 

 the three points have travelled precisely the same number of miles; 

 C along the mean orbit of the mass ; but A and B along two 

 new orbits, each of precisely the same dimensions as C's, but 

 drawn round different centres, corresponding to their respective 

 diametric distances from C. Their orbits are indicated in the dia- 

 gram by the two dotted circles. In no other way could the 

 feat have been accomplished, than by A and its successors a, ^, 



