Determination of the Mechanical Equivalent of Heat. 161 



the average value of the P.D. between the terminals of the 

 resistance. 



It is evident that if the loss of heat during the experiment 

 is to be small enough to be neglected in comparison with the 

 quantity of heat generated, either the rise of temperature 

 must be small, or must take pl?ce in a very short time, or 

 the ratio of the cooling' surface to the mass of the water 

 heated must be small. As it is impracticable to reduce either 

 the rise of temperature or the time to very small limits, and 

 also to measure them with ease and accuracy, it is clear that 

 the result is best obtained by using a large quantity of water, 

 for the ratio of the surface area to the mass can then be made 

 small enough to bring the error due to cooling within the 

 required limits. But a large quantity of water necessarily 

 involves the use of a large amount of electrical energy ; and 

 we thus arrive at the result that the accuracy attainable 

 depends upon the amount of power at our disposal, and will 

 be greater the greater the electric power that can be supplied. 



In designing such an apparatus, then, the first thing to 

 determine is the amount of electric power that can be used, 

 and the details should then be arranged so as to get the least 

 error in the result. In those cases in which an increased 

 accuracy in one measurement involves a diminished accuracy 

 in another, it is best to make the errors due to the two causes 

 equal. For example, suppose that the time during which the 

 electric energy is supplied is such that we can only measure 

 it to one per cent., while the error due to cooling during the 

 experiment is only J per cent. We can clearly increase the 

 accuracy of the result if we increase the time until the pro- 

 bable error in reading it is equal to the error due to cooling 

 during that time, say | per cent. If we were still further to 

 increase the time, the error due to cooling would increase 

 and exceed J per cent., and our result would therefore be less 

 accurate. This equality of course does not apply to errors 

 that are not interdependent, such as errors in reading volts 

 and amperes : each of these errors should independently be 

 be made as small as possible. 



The measurements to be made are as follows : — 



(a) The value of the constant current passed through the 

 resistance. 



(b) The average value of the P.D. between its terminals. 



(c) The mass of water heated, to which must be added the 

 water-equivalent of the containing vessel, resistance-coil, and 

 stirrer. 



(d) The rise of temperature of the water. 



(e) The time during which the current is passed. 

 Phil. Mag. S. 5. Vol. 39. No. 237. Feb. 1895. M 



