OP ASPECT, ROTATION, LIBEATION, ETC. 109

Thus let us suppose that the globe M 4 (fig. 55,Plate XIII.) circuits round the globe E withoutany change of position. Then when the movingglobe has completed one-fourth of a revolution,A B C D, and is at M 2 , the points A, B, C, Dwill be in the position shown, B instead of A beingtowards E. When the moving globe is at M s , C willbe towards E; when the globe is at M 4 , D will betowards E ; and lastly, when a complete revolutionhas been effected, A will again be turned towards E.Obviously, to keep A always directed towards E, theline M 2 A should be shifted through a quarter-revo-lution to the position M 2 B ; M s A should be shiftedthrough half a revolution to the position M s C ; andM 4 A through three-quarters of a revolution to theposition M 4 D,—all these shiftings being made inthe same direction, viz. in the direction ABCD,which is the same as that in which the body itself ismoving.

This is shown again in fig. 56, Plate XIII., wherewe see that if the middle point of the disc of themoving globe is the same real point on this globe, asit travels through the positions M u M 2 , M s , M 4 .... toM 8 , this globe must have turned in the manner showniu fig. 56 a, the radii in which to the points 1, 2, 3, 4,&c., are respectively parallel to the radii to M 4 , M 2 ,M 3 , M 4 , &c., all of which are directed upon the centralorb E.

But it may occur to some readers that althoughundoubtedly if a globe were carried from the position