On the Resistance of Fluids. 363 



this sum must, as above shown, be expressed by BV+Su-f- he. 

 that is, it is proportional to the velocity simply. But if we consider 

 the effect of the force, not with relation to the sum of the obstacles, 

 but to their number, this number, as will appear further on, will be 

 represented by ^Bv^ , and will be proportional to the square of the 

 velocity when all the obstacles are equal. Hence this famous ques- 

 tion is only a dispute about words ; and as such we need dwell no 

 longer upon it." 



Now who does not see that a sum of equal obstacles is as their 

 number 1 If therefore their sum is as the velocity, their number 

 surely cannot be as the square of the velocity. " Hence this famous 

 question" was not settled by Gregory, notwithstanding he seemed 

 to dispose of it so easily. Nor has this " unaccountable" dispute 

 been accounted for to my satisfaction by Prof. K. ; for I have not 

 been able to discover any element which when assumed by one par- 

 ty to be constant and by the other to be variable, will account for 

 the different results at which the parties arrived. The real differ- 

 ence between the Newtonians and Leibnitzians was simply this: 

 they attached different ideas to the term force. One party by the 

 force of moving bodies meant the power inherent in them by means 

 of their mass and motion, to effect changes of motion in other bod- 

 ies ; in this sense their force is as their velocity. The other party 

 by the same term meant the power to penetrate or make impressions 

 on other bodies ; in this sense the force is as the square of the velo- 

 city. When I affirmed, in my article on the Resistance of Fluids, 

 that the force of a particle on the plane at any instant of its action is 

 as the square of the velocity, I neither concurred with nor dissented 

 from the views of either of these disputants, for the simple reason 

 that I attached a different idea to the term force from that attached 

 to it by either of them. The term was used by me in its elementa- 

 ry: sense, and confined to that sense by my definition. In this sense 

 it is a magnitude whose nature is independent of the nature of the 

 effect which it may be concerned in producing ; and in this sense it 

 enters as an element and only as an element into mechanical agency 

 in every other aspect in which it can be contemplated. The dis- 

 pute between the Newtonians and the Leibnitzians is another apt 

 illustration of the necessity of confining the term force and other 

 similar terms to some one fixed meaning. The two meanings at- 

 tached to it by these disputants are only two out of perhaps a dozen 

 that might be pointed out ; and their dispute is only one out of a 

 thousand that have arisen from this loose manner of using the term. 



