76 OF SIMPLE ACCELERATING FORCES. 



absolutely inconsiderable in comparison with the whole 

 velocity ; so that the element of space becomes a true 

 measure of the temporary velocity, in the same manner as 

 any larger portion of space may be the measure of a uni- 

 forixi velocity. 



Scholium 2. In this country it has been usual, at 

 least till very lately, to preserve the geometrical accuracy 

 introduced by the great inventor of the method effluxions, 

 and to call ** any finite quantities, in the ratio of the velo- 

 cities of increase and decrease of two or more magni- 

 tudes," the fluxions of these magnitudes (46). Thus, if 

 we call the increments of x and y, x andj', we have, for 

 the fluxions, any magnitudes x and y, so assumed, that 

 X :y shall be equal to x : j when these increments become 

 evanescent. On the continent, it has been more common 

 to write dx and dy for x aud y, considered as actually 

 evanescent. It has been observed by Euler, at the be- 

 ginning of his Integral Calculus, that the language of the 

 English is the more correct, but that the continental nota- 

 tion is the more convenient. His words are these : 

 ** Quas enim nos quantitates variabiles vocamus, eas An- 

 gli, nomine magis idoneo, quantitates fluentes vocant, et 

 earum incrementa infinite parva seu evanescentia fluxiones 

 nominant, ita ut fluxiones ipsis idem sint, quod nobis dif- 

 ferentialia. Haec diversitas loquendi ita jam usu inva- 

 luit, ut conciliatio vix unquam sit expectanda : equidem 

 Anglos in formulis loquendi lubenter imitarer, sed signa, 

 quibus nos utimur, illorum signis longe anteferenda viden- 

 tur." Art. 6. In fact, however, the English do not call 

 the evanescent increments fluxions, any more than a mile 

 is an evanescent quantity, when we speak of a velocity of a 

 mile an hour. There are certamly some cases in which 



