OF SIMPLE ACCELERATING FORCES. 77 



the fluxiooal notation is inconvenient; thus, when we have 

 occasion to write d^x^rSdr, it would be impossible to ex- 

 press this equation without deviating from that method ; we 

 might, indeed, write (^x)'z^^Xf but we still introduce a 

 heterogeneous character. It is, however, a great inele- 

 gance, to say the least, not to distinguish a characteristic 

 from a multiplying quantity by a difference of type ; for dx 

 means, according to all analogy, the product of d and x : 

 and it is much more intelligible to write dx, as Lacroix 

 and many others have done, instead of dx, as it is generally 

 printed in the works of Laplace. It must always be un- 

 derstood, then, that dx, as well as *•, denotes a finite quan- 

 tity proportional to an evanescent element : but when we 

 use other characteristics of variation, such as S or A, it 

 is not always necessary to limit their signification so pre- 

 cisely : and it will sometimes be convenient to employ the 

 mark d for an element of matter, considered as evanescent, 

 and AX for an evanescent increment of x, corresponding 

 to the fluxion dor. 



Scholium 3. Now, a uniform force is a force that 

 uniformly increases the velocity of a moving body. For 

 example, if the velocities, at the beginning of any two 

 separate seconds, be such that the body would describe 

 one foot and ten feet in the respective seconds, and the 

 spaces actually described become two feet and eleven feet, 

 each being increased one foot, the accelerating force must 

 be denominated uniform : it must also be uniform, in the 

 still stricter sense of the definition, if the velocities, at the 

 end of the second, have been so increased, that the body 

 would describe two and eleven feet respectively in another 

 second, if they continued their motion unaltered. 



Scholium 4. The power of gravitation, acting at or 

 near the earth's surface, may, without sensible error, be 



