J= — — j where R is the resistance of the calorimeter-coil as 



in Terms of the Mechanical Equivalent of Heat. 13 



half the weight of the other. The remaining experiments are 

 satisfactory in this respect, the loss being a few tenths of a 

 gram, due principally to the removal of the thermometer. 



The result of the experiment is J = 42,039,000 0, where 

 is the value of one tenth of the 10-ohm coil in earth-quadrants 

 per second. Reduced to the new value for the constant of the 

 sine-galvanometer, it becomes J =42,055,000 O. 



I have also calculated the experiment from the formula 

 cV&t 

 h 



measured in the ordinary manner, corrected to the mean tem- 

 perature of the water, and further corrected for superheating. 

 I estimated the superheating from observations of the main 

 and derived currents when the strength of the former was 



c'Bf 



varied. The expression should give the true resistance 



of the coil at any instant. When the currents are smaller, the 



c'W 



superheating is less, and the comparison of the value of — - 



c 



for a zero-current, obtained by graphical extrapolation, with 

 its value for the full current, should give the superheating. 

 The method is not very accurate, as the observations with 

 the smaller currents are uncertain. I find the increase of 

 resistance due to superheating to be about 1 part in 700, cor- 

 responding to a difference of temperature of 2° C. When 

 this correction is applied, the second method of calculation 

 gives J = 42,156,000 0. 



This result depends upon the square of the main current ; 

 and as the temperature of the coil changed 6° or 8° during the 

 experiment, its mean resistance is somew^hat uncertain. Hence 

 this result has not the weight of the former. 



The discovery of this discrepancy has greatly delayed the 

 publication of this paper. It may be due to conduction 

 to the water, which was guarded against by varnishing the 

 wire and using distilled water, but was not proved to exist. 

 For let E be the difference of potential of the ends of the 

 coil, e the E.M.F. of polarization, R and r the resistances 

 of coil and water respectively. Then the current in the coil is 



E . E— e 



C= ™ and the current in the water is c = - . 



K r 



The energy converted into heat is 



In the first method of calculation above the energy is com- 



