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SCIENCE 



[N. S. Vol. XXVIII. No. 710 



portional to acceleration would evade detection 

 by methods of this kind, since it influences the 

 motion of a body just like a mass measured 

 numerically by the proportional factor. Con- 

 sidered as mass-term or force-term, the sign 

 is reversed as required, and accurate balance 

 vs^ith other impressed forces is never brought 

 about. The acceleration that would be pro- 

 duced otherwise is reduced, but steady condi- 

 tions enter at a finite value of actual accelera- 

 tion. Supposing, however, that the density of 

 the body falls off, and the "ballast" of real 

 mass is thus diminished, equation (3) ap- 

 proaches a limit X — ij = 0. And if the 

 proportional factor m^ of equation (2) be now 

 increased, the acceleration corresponding to 

 equality of X and R will grow less. Equilib- 

 rium of the body m can be approached asymp- 

 totically, therefore, somewhat as in the case 

 of resistance (proportional to speed) due to 

 eddy currents set up by motion in a magnetic 

 field. For the hydrodynamic problem, the 

 limiting condition Z — B = would corre- 

 spond to a rigid massless shell forced through 

 the liquid. The energy supplied would go 

 directly into the latter, the shell transmitting 

 the force Z applied to it, undiminished by 

 any distribution throughout its own volume. 

 It is interesting to compare this with the ap- 

 plication of the "equilibrium theory" to 

 problems in acoustics. 



Every essential aspect of the ideas con- 

 nected with the equation of motion and the 

 forms derived from it by transposition of 

 terms is found repeated in the parallel elec- 

 trical statement. The more fundamental 

 form, for a circuit with impressed electro- 

 motive force, resistance, capacity and self- 

 induction, is, with obvious notation. 



E — Eo — IR = L dl/dt. 



(5) 



Equation (5) is immediately consistent with 

 the scheme devised by Newton and d'Alembert 

 for the dual measure of forces, in terms of the 

 favoring and hindering agencies themselves 

 on the one hand, and their net result on the 

 other. The former arise externally to the 

 system moved, and the latter affords a mode 

 of calculation in which no exciting stimulus 

 appears directly. The recognition of the co- 



efficient L as " electric inertia " is well rooted ; 

 and the proper sense in which the terms of the 

 first member are all " external " is seen readily 

 enough, even in its application to IB, though 

 obscured here, to a certain extent, by the 

 habitual elementary expression of Ohm's law 

 in the form E<=IR, without explicit recog- 

 nition of it as involving terminal velocity and 

 equilibrium. It is further apparent how the 

 equation 



[E — Ec — /iJ] — [L dl/dt] = 



(6) 



presents the idea of d'Alembert's principle, 

 with considerations parallel in detail to those 

 governing its use elsewhere. The proper es- 

 tablishment of these particular analogies is 

 far-reaching enough to excuse their discussion 

 with so much elaboration of emphasis on ex- 

 ceedingly simple conceptions. But there are 

 some indications that original meanings here 

 have become a little incrusted with the for- 

 malism of mathematics. A deliberate effort 

 to restore them is not superfluous, if there is 

 any habit of indifference toward fictitious 

 forms of statement to be checked. However 

 harmless such habits may be on familiar 

 ground, they must tend to magnify the diffi- 

 culties inseparable from attempts to explore 

 and subdue new territory; and, on the other 

 hand, the slightest improvement in giving nat- 

 ural and direct expression to essential phe- 

 nomena is likely to find quick reward in more 

 rapid advance or deeper insight. At this 

 junction-point of the older mechanics with 

 the modem dynamical treatment of electricity, 

 the transfer of methods from one line of 

 thought to the other calls especially for all 

 precision of ideas that is possible, in view of 

 the inevitable margin of vagueness associated 

 with equations that have been generalized and 

 extended so far beyond their first application. 

 With the introduction of electrons, an added 

 element of definiteness is infused into electric 

 inertia, and the new suggestion reacts also 

 upon the finality of previous conceptions re- 

 garding all mass. We are asked to entertain 

 the possibility that mass is everywhere ex- 

 pressible quantitatively in electromagnetic 

 terms; and to acknowledge as an illusion any 

 former conviction that mass is necessarily 



