302 Mr DE morgan, ON THE GENERAL PRINCIPLES OF WHICH THE 



The four postulates give the diagonal law: but the diagonal law gives the four postulates; 

 grant the law, and the postulates all follow. Actual experiment, then, should be applied to 

 the finished law: which would be proved with far greater ease than the indifference to order 

 of successive aggregations. 



6. Dynamical pressure. A misuse of terms prevails in this part of the subject. Writers 

 distinguish two kinds of force; accelerating force and moving force. Accelerating force, which 

 any one would suppose to be the force which accelerates, is no such thing: it is the effect pro- 

 duced, the very acceleration itself. I dwell upon this in memory of the confusion which it 



d~ "v 

 created in my own mind when I was a student. The symbol is a purely mathematical 



notion: and it means the acceleration which the velocity of ,v is receiving at the end of the 

 time t. This acceleration depends upon the pressure applied at the particle directly and the 

 mass of the particle inversely: but it is made to take its name from one only of the two deter- 

 minants. It is as if a man were held to be one speaking man or another, accordhig as he made 

 one speech or another. The confusion may have arisen in this way. Just as in statics we 

 are held to exclude the idea of motion, so in dynamics we are held to exclude the idea of equi- 

 libration, and of forces as equilibrating. Accordingly, supposing ourselves only to know force 

 by motion produced, we make motion produced a measure of the force. In so doing we are 

 simply wrong: the momentum produced is a measure of the force. By substituting the simple 

 term acceleration for accelerating force, we gain truth and clearness at one step. 



Again, the so called moving force, designated by m -— , represents the pressure which 



produces acceleration: or only differs from it by our choice of units. Let the pressure be 

 measured by that unit which, applied to a unit of mass, creates a unit of velocity in a unit of 

 time, and the above expression represents the number of units of pressure. In writings on 

 dynamics, the moving force is a mysterious effect of the pressure which is not the pressure, but 

 as the pressure. If momentum were more definitely introduced, and as a magnitude per se, 

 instead of a convenient name for a formula, the rate of alteration in momentum would claim 

 its name and introduction; and the dependence of this rate on the pressure applied would be 

 a great law of mechanics. But as the matter often stands, the rate at which momentum varies 

 is not introduced in connexion with momentum, and momentum itself is not presented as a 

 real thing, but as a product of two symbols. The differential coefficient of momentum, 

 detached from its primitive function, is presented under a name which just confounds it with 

 its cause, without deducing it from its cause. 



One of the principles in operation in the preceding confusion is this, that causes are in 

 quantity as their effects. The celebrated disputes about the measure of force have arisen in 

 great part from this assumption, which holds good only so long as we know nothing about the 

 cause except its effect. In this case, cause is but another name for the effect, for every pur- 

 pose of calculation, and for every purpose of thought, except the craving for the idea of cause, 



