April 8, 1910] 



SCIENCE 



527 



it survive through the entire history of 

 physics. 



The paradosy of this dominant idea of 

 modern physics being a mere picture 

 created by the human mind, disappears 

 when we consider how the same method is 

 employed in subjects other than physics. 



In history, for example, we have impor- 

 tant culminating events which we ascribe 

 to ' ' certain influences, ' ' awhile as a matter 

 of fact the most that we actually know and 

 observe in history is a series of individual 

 acts, prompted, we suppose, by certain pur- 

 poses. 



The Franco-Prussian war came when the 

 German Kaiser decided to send the tele- 

 gram from Ems, when Prince Bismarck 

 decided to publish certain parts of this tele- 

 gram, when Von Moltke decided that the 

 army was ready, when Napoleon III. de- 

 cided to emulate the military career of 

 his uncle, when the Congress of Vienna de- 

 cided, in 1815, to give Prussia additional 

 Rhenish territory, when in 868 the father 

 of Lothar gave to his son the middle king- 

 dom, the modern Lorraine, between Prance 

 and Germany. 



In practise we find it more convenient to 

 say that "certain influences" had been at 

 work for a full thousand years which cul- 

 minated in the victory of Prussia over 

 France. In physics, we give to the corre- 

 sponding "influences" the name forces. 

 That's the whole story ! We measure these 

 influences by the mass-acceleration of the 

 body under consideration. 



The extension which this idea of force 

 has received in later times is known to us 

 all. Huygens was the first to show that 

 Galileo's fundamental variable, linear mo- 

 mentum, might change in two ways, 

 namely, in direction and amount; and he 

 gives us for the first time a. method of 

 computing the force when the momentum 

 varies in direction only— a force which we 



now call ' ' centrifugal. ' ' Later, in the case 

 of rigid bodies the conception of "angular 

 momentum" was introduced; its time vari- 

 ation we now call either "torque" or 

 "processional couple" according as the 

 angular momentum varies in amount only 

 or direction only. 



This definition is identical in form and 

 meaning with that of Galileo. 



The essential step made by Lagrange, in 

 his treatment of the simplest possible case, 

 namely, a single particle, is to derive both 

 the time variation of momentum and the 

 rate of directional change of momentum, 

 each by differentiation of a single function. 



Momentum for him is the velocity-varia- 

 tion of kinetic energy, a quantity whose 

 time-variation is the tangential force; and 

 centrifugal force is the space-variation of 

 kinetic energy: but each of these is still a 

 time-variation of momentum, agreeing per- 

 fectly with Galileo's original definition. 



The space-variation of potential energy 

 is the measure of stress'— or more properly 

 a stress integral — which we do not under- 

 stand — but which nevertheless can be eval- 

 uated in terms of force. 



I shall detain you for only one more il- 

 lustration. 



Faraday had discovered a quantity— the 

 "electrotonic state," he called it— electro- 

 kinetic momentum, we call it — whose varia- 

 tions through any closed circuit, were 

 always accompanied by an electric current 

 in that circuit. Not knowing the cause of 

 this current, physicists agreed to say that 

 an "electromotive force" was at work 

 whenever the electro-kinetic momentum 

 changed, and to define this electromotive 

 force as the time rate of change of electro- 

 kinetic momentum (Neumann). Here 

 again we have a generalized force intro- 

 duced as a synonym for an unknown 

 cause; exactly as was done by Galileo in 

 the first instance. 



