On Resistance and Conductance Operators. 479 



then say that the stream n x a. lies between 



6 ax 



2 dn 2 v* 



HdxB 



18. The value of the stream which we have found at C must 

 be the same at every point in the tube. This depends on -7- 

 being constant. Now from equation (1) we deduce 



If 

 3B 



dn 2 ~ —; 



and n x oL is constant. In the case we are now treating, all 

 molecules having the same mass and diameter, the relation 

 between ex! and a is the same at all points of the tube. There- 

 fore n{oi—ot!) is constant, and -~ is constant. 



19. It would appear from this investigation that if the 

 molecules of gas I. could be so guided as never to collide with 

 each other, but only with the common enemy, the molecules 

 of the other gas (the motion being in other respects unaltered), 



2 dn vfi 

 then the stream-velocity would assume ^ —~ ^ as its limiting 



value. We might, on the other hand, keep continually changing 

 the directions, so as to make and maintain a the same for all 

 classes without changing its mean value a, or in other respects 

 altering the motion. In this case the stream- velocity would 



assume the limiting value ~ -~ ^/B. 



LXII. On Resistance and Conductance Operators, and their 

 Derivatives, Inductance and Permittance, especially in con- 

 nexion with Electric and Magnetic Energy. By Oliver 

 Heavislde*. 



1. TF we regard for a moment Ohm's law merely from a 

 JL mathematical point of view, we see that the quantity R, 

 which expresses the resistance, in the equation V = RC, when 

 the current is steady, is the operator that turns the current 

 C into the electromotive force V. It seems, therefore, appro- 

 priate that the operator which takes the place of R when the 

 current varies should be termed the resistance-operator. To 

 formally define it, let any self-contained * electrostatic and 



* Communicated by the Author. 



