wtT. it] DISSERTATION SECOND. 59 



to the question concerning the force of the moving body, you 

 add that it is to be employed in putting in motion another 

 body, which is itself free to move, no doubt remains that the 

 force is as the velocity multiplied into the quantity of matter. 

 So also, if the force of the moving body is to be opposed by 

 a resistance like that of gravity, the length of time that the 

 motion mav continue is one of its measurable effects, and 

 that effect is, like the former, proportional to the ve'locity. 

 There is a third effect to be considered, and one which al- 

 ways occurs in such an experiment as the last, — the height 

 to which the moving body will ascend. This limitation 

 gives to the force a definite character, and it is now measur- 

 ed by the square of the velocity. In fact, therefore, it is not 

 a precise question to ask, What is the measure of the force 

 of a moving body ? You must, in addition, say, How is the 

 moving body to be employed, or in which of its different ca- 

 pacities is it that you would measure its effect ? In this state 

 of the question there is no ambiguity, nor any answer to be 

 given but one. Hence it was that the mathematicians and 

 philosophers who differed so much about the general ques- 

 tion of the force of moving bodies, never differed about the 

 particular applications of that force. It was because the con- 

 dition necessary for limiting the vagueness and ambiguity of 

 the data, in all such cases, was fully supplied. 



In the argument, therefore, so strenuously maintained on 

 the force of moving bodies, both sides were partly in the 

 right and both partly in the wrong. Each produced a mea- 

 sure of force which was just in certain circumstances, and 

 thus far had truth on his side : but each argued that his was 

 the only true measure, so that all others ought to be reject- 

 ed ; and here each of them was in error. Hence, also, it is 

 not an accurate account of the controversy to say that it was 

 about words merely; the disputants did indeed misunder- 

 stand one another, but their error lay in ascribing generality 



