MACLAURIN'S TREATISE, 1742 185 



The term velocity had been under dispute, par- 

 ticularly in the controversy between Berkeley and 

 Walton. Maclaurin evidently perceived the diffi- 

 culty in arguing that variable velocity is a physical 

 fact ; he says (p. 55), "the velocity of a variable 

 motion at any given term of time is not to be 

 measured by the space that is actually described 

 after that term in a given time, but by the space 

 that would have been described if the motion had 

 continued uniformly from that term. If the action 

 of a variable power, or the velocity of a variable 

 motion, may not be measured in this manner, they 

 must not be susceptible of any mensuration at ali " — 

 an argument not lii<ely to convince or silence hostile 

 critics. He quotes Barrow's definition of velocity — 

 *'the power by which a certain space may be 

 described in a certain time." In discussing * 'power" 

 Maclaurin brings in the consideration of * ' cause " 

 and ''efìfect" in a way that sounds odd in a work 

 laying the foundations to the abstract doctrine of 

 fluxions. Maclaurin uses the word ** limit," without 

 giving it a formai definition. Theorem XII reads : 

 '*The velocity of a motion that is accelerated or 

 retarded perpetually, is, at any term of the time, 

 to the velocity of an uniform motion, in a ratio that 

 is always a limit between the ratio of the spaces 

 described by these motions in any equal times 

 before that term, and the ratio of the spaces de- 

 scribed by them in any equal times after it. " 



168. In the Pliilosophical Trans acttons^ voi. xlii, 

 for the years 1742-43, London, 1744, Maclaurin 



