124 Prof. S. P. Thompson on the Graphic Representation 



v + Av, the quantity of motion here communicated to the sur- 

 face-element in the unit of time is 2n(v + Au); therefore the 

 force which becomes effective is 2nAv; that is, proportional 

 to the heat-motion given up to the gas by the surface-element. 



As to the reversed motion at higher pressure, this is, no 

 doubt, produced by the air-currents arising on the warmer side, 

 which become weaker and weaker as the rarefaction increases, 

 until at last, at the neutral point, they exactly counterbalance 

 the contrary force of the air-molecules. Since these air- 

 currents differ in strength and direction according to the form 

 of the surface at which they arise, the conductivity of the 

 warm substance, the shape of the vessel, &c, the dependence 

 of the position of the neutral point on all these is thus 

 accounted for. 



The complicated phenomena in the so-called electrical radio- 

 meters cannot, so far as they take place in the highest rare- 

 factions, well be regarded as analogous heat-effects upon the 

 air-molecules, but are much rather conditioned by the laws of 

 electrical phenomena in highly rarefied-air spaces, so that 

 their investigation, though of importance for the explanation 

 of those laws, is not so for that of radiometer-motion. 



2£VIII. On the Graphic Representation of the Law of Efficiency 

 of an Electric Motor. By Professor Silvanus P. Thompson*. 



(1) "TTABIOUS graphic constructions have been given at 

 ▼ different times to represent the work performed by 

 an electric motor and the electric energy expended upon it. The 

 main defect of those hitherto given has been that they present 

 these quantities in such a manner that a comparison of the 

 two, which would show the efficiency of working of the motor, 

 is not immediately evident. Moreover it has not been possible 

 hitherto to show on one construction both the law of maximum 

 rate of working and the law of efficiency. The following con- 

 struction makes them evident to the eye. Fig. 1. 



Let the vertical line AB (fig. 1) repre- 

 sent the electromotive force, E, of the 

 electric supply when the motor is at rest. 

 On A B construct a square A B C D, of 

 which the diagonal B D may be drawn. 

 Now measure out from the point B, along 

 the line BA, the counter electromotive 

 force of the motor e; this quantity will in- 

 crease as the velocity of the motor increases. 

 Let e attain the value B F. Let us inquire what the actual 

 * Communicated by the Physical Society. 



A 



< 



F 





/ 



/I 



c 



B 





c 



