Chap. V.] GRAVITATION AND INERTION. 71 



' Let A F B (Plate XII.) represent the surface of the 

 earth, c its centre, v d, v e, v f, the curve lines which 

 a body would describe, if projected in a horizontal 

 direction from the top of a high mountain successively 

 with more and more velocity ; and, because the celes- 

 tial motions are scarcely retarded by the little or no 

 resistance of the spaces in which they are performed, 

 to keep up the parity of cases, let us suppose either 

 that there is no air about the earth, or at least that it 

 is endowed with little or no power of resisting : and 

 for the same reason that the body projected with a 

 less velocity describes the lesser arc v d, and with a 

 greater velocity the greater arc v e, and, augmenting 

 the velocity, it goes farther and farther to f and g ; 

 if the velocity was still more and more augmented, it 

 would reach at last quite beyond the circumference 

 of the earth, and return to the mountain from which 

 it was projected. 



The body is supposed to be projected with a hori- 

 zontal force from v sufficient to carry it as far as d ; 

 then with a force sufficiently increased to carry it as 

 far as E ; then as far as f, and so on to g. Now, 

 even admitting that each increase in the projecting 

 force will carry the body still farther round the earth 



Dr. Playfair tells us that but for the discovery of the motion of 

 the earth, that law might have remained for ever unknown.^ 



I have shown that in the heavens that law is no longer required 

 for the purpose for which it was invented. Idem, p. 245. 



' Encyclopedia Britannica, 8th Edition. Fourth Dissertation. 



