THE FORMS OF ENERGY. 123 



system of electric units, took as the primary unit of resistance that in 

 which unit rate of working would maintain unit current, and a committee 

 of the Association prepared resistances determined in terms of this unit. 

 Now, in this electro-magnetic system the unit rate of working is 1 erg per 

 second, and the current, 0, is measured in terms of dynes on unit pole at 

 1 cm. distance by 1 cm. length, i.e. the resistance, R, is really measured in 

 mechanical units, and when we put for any circuit 



Rate of working = C 2 R, 



the product C 2 R is in mechanical units, if and R are in terms of the 

 above units. 



But Joule showed that the heat developed in any resistance is 

 proportional to C 2 R, which leads us to suppose that the work required 

 to maintain C in R is all transformed to heat in the wire having that 

 resistance. If, then, we measure the heat in calories, the current in 

 electro-magnetic measure, and the resistance in terms of the new unit, 

 we shall have on the one hand the heat, and on the other its mechanical 

 equivalent in C 2 R. As soon as the new resistance standards were fixed, 

 Joule himself made an experiment to obtain the mechanical equivalent 

 by this method (Scientific Papers, i. p. 542). Converting to foot-lbs. 

 and degrees Fahrenheit, the result was 782 instead of 772, so different a 

 result that Joule was induced to undertake a repetition of his water- 

 friction experiment to find whether the error lay in his work or in that 

 of the committee. The result of his second great experiment was 

 published in the Phil. Trans., 1878, pt. ii. 



The method adopted generally resembled that of his earlier experi- 

 ment, but he employed a different contrivance for doing work, one which 

 had already been used by Him. The set of paddles was rotated at a 

 uniform speed by a handle. If the calorimeter had been free to move 

 round the axis of the paddles, it would have spun with them, but it was 

 kept fixed by applying a couple which could be measured. This couple 

 was equal and opposite to that which was exerted on the water and 

 calorimeter by the paddles, and equal to the couple applied to the 

 handle since the rotation was steady. Now, the total work done by a 

 couple G in n revolutions is 



so that the value of the mechanical energy was known at once from n 

 and G. For other details the original paper may be consulted (Scientific 

 Papers, i. 632). Joule's final result was that 772'55 Ibs., falling 1 foot 

 at the sea level in the latitude of Greenwich, would acquire kinetic 

 energy which, transformed to heat, would raise 1 Ib. of water from 

 60 to 61. This confirmed in a remarka,ble manner the accuracy of the 

 earlier work, and showed that the determination of the electric standard 

 of resistance was faulty. But the fault had been made plain from other ex- 

 periments, and a redetermination showed an error of more than 1 per cent. 

 It will be convenient to express Joule's value of the mechanical equiva- 

 lent here in various units, for the sake of comparison with later results. 

 These later results are all somewhat larger than Joule's, chiefly through 

 the adoption of the nitrogen or hydrogen scale of temperature, with slightly 

 larger degrees about 15, than those of the mercury-in-glass scale used 

 by Joule. 



