THE MECHANICAL EQUIVALENT OF HEAT. 
415 
Section IX.— The Measurement of Mass. 
Eowland, in the paper to which reference has already been made, takes objection 
to Weber’s determination of “ J,” on the ground that he used only 250 grms. of 
water. Also M. Arnoux in the discussion which followed D’Arsonval’s paper 
said, “ Its determination has always been carried out in diminutive apparatus ... in 
which the losses by radiation attained a high figure. With large apparatus the loss 
by radiation becomes negligible since the volume increases as the cube and its 
radiating surface as the square only of the linear dimensions. With appliances 
capable of transforming into heat a few hundred kilogrammetres per second, we ought 
to succeed in determining the mechanical equivalent to three or four (sic) places.”* 
Now as the quantity of water used by us was small, it will be well to point out the 
considerations by which we were influenced. 
Besides the mass of water, which is used in the calorimeter, account must be taken 
of what is usually termed the “ water equivalent” of the calorimeter. [We take this 
opportunity of remarking that when we, in subsequent statements, use the word 
“ equivalent ” we refer to the water equivalent of our calorimeter, and do not use the 
word in the sense in which it occurs in Bowland’s paper as meaning “ the mechanical 
equivalent;” this we have designated by the letter “ J.”] Now it is the very 
difficulty of satisfactorily determining this equivalent, rather than the estimation of 
loss by radiation, which has led experimenters to prefer a large mass of water, when 
practicable, in order to make any error in the equivalent one of the second order. 
Up to the time of writing, only twm methods seem to have been generally adopted 
for determining the equivalent, (1) the method of mixtures, (2) the method by calcula¬ 
tions from the specific heats and masses of the component parts of the calorimeter. 
Of the first of these we need say but little, for Joule himself obtained values which 
varied amongst themselves by 12 per cent.t We did not, however, dismiss this 
method without trial, for having applied it, with every conceivable precaution, to one 
of our calorimeters, we obtained numbers whose differences were so great as to render 
them useless for the purposes of this investigation. 
The second method is attractive on account of its simplicity, but since the specific 
heats have probably been determined by the application of the first method,j the 
accuracy is not of a superior order. Of greater weight is the consideration that a 
calorimeter has no definite limits, it being impossible to foretell to what extent and in 
what manner the necessary supports, connections, and surrounding envelopes have to 
be introduced. The method which we have adopted of making the experiments 
* Rowland’s calorimeter, when full, weighed over 12 kilos.. Joule’s about 6 kilos. 
t See Table, p. 639, ‘Joule’s Scientific Papers,’ vol. 1. 
X We may quote from Prof. Eyeeett's ‘Units and Physical Constants,’ “Specific Heat of Liquids.” 
“ We have omitted decimal figures after the fourth, as even the second figure is different with different 
observers.” To this we may add that the specific heat of solids will bear no closer scrutiny. 
