342 ScientifiG Proceedings, Royal Dublin Society. 



Persons can say this respecting force who would not dream of 

 saying that the area of a plane curve is the total amount of the 

 ordinates within given limits ; which would be a precisely analo- 

 gous statement. 



(There is a quite similar progression as to energy. Energy is 

 said to be " force acting through space," then the " space-integral 

 of force," then the " sum of the tensions.") 



(6.) The following way in which the statical pressure of a weight 

 is regarded by one of our foremost dynamicists illustrates very 

 strikingly the tendency of which we are now complaining. 



It is conceived that when a weight is lying on a table, the 

 downward gravity of the weight and the upward resistance of 

 the table are each producing in each second of time a certain 

 quantity of momentum. Observe there is no reference in this to 

 molecular kinetics as the ground of molar pressure ; indeed none 

 such would be here of any use. This mode of conception would 

 be quite allowable, as a mathematical artifice, if anything 

 were to be gained by having recourse to it. But it is intended to 

 be what may be called an ontological, or at least a dynamical, 

 fact. The objection to it is that it is a departure from the notion 

 of pressure, which is derived independently of phenomena and 

 relations of phenomena belonging essentially to motion; it is 

 arbitrarily adding to the contents of the notion of pressure nearly 

 all that is wanting to make it into impulse. The two momenta 

 cannot coexist in reality, any more than two equal and opposite 

 velocities in the same point, though it is often a very useful and 

 perfectly justifiable artifice to conceive of these doing so. 



We cannot leave the present point without some reference 

 to D'Alembert's principle, which is described' as reducing kinetics 

 to statics. Of course nothing that we have said really conflicts 

 therewith. We shall merely observe that it is only by a fiction, 

 though an entirely legitimate one, which constitutes a most 

 useful and perfectly valid method, that the " impressed forces," 

 the " efiective forces," and the " forces of constraint," can all be 

 regarded as, in modern language, impulses, which are respectively 

 proportional to their own forces proper. It is only the " efiective 

 forces " which are really and literally impulses. 



(7.) It is said, as in the above quoted definition of force, by many 

 who perhaps would readily agree to what we have just now 

 said, that statical force "tends" to produce motion, and that 



