CONTINUOUS ELECTRIC CALORIMETRY. 
127 
The last line contains the values of D calculated on the elementary theory, 
neglecting the variation of the gradient, assuming the same two values (1) and 
(2, 3, 4), and taking the heat-loss per degree constant. This assumption gives 
h — ‘07145 for the heat-loss, and J scl = — ‘00207 joule per gramme degree for the 
defect of the specific heat from 4‘200. 
Comparing the observed and calculated values of D on the two assumptions, we 
see that the relatively large discrepancy of ‘00060 on the elementary theory in the 
value calculated for the small flow (5), is exactly accounted for by the correction for 
variation of the gradient in the flow-tube. 
The effect of applying the correction in this particular case is to increase the value 
of the specific heat from 4 1793 to 4'1 810, i.e., by 4 parts in 10,000. This correction 
is very small, but it cannot be neglected, because it is systematic. Besides, it is 
much larger than the errors of observation, which rarely amount to so much as 
1 in 10,000 on a single flow with a rise of 8°. 
In the discussion of these observations, Dr. Barnes (§ 5, p. 226) concludes, from 
the close agreement of the observed and calculated values of the heat-loss for the 
larger flows, that the elementary theory is valid and requires no correction, provided 
that the flow exceeds a certain limit, about ‘35 gm./sec. But the agreement for 
the larger flows results merely from his method of calculation, and is no evidence 
that the correction is negligible. The need for the correction could not arise per 
salturn below a certain limit, as he suggests. 
The existence of the correction is obviously required by theory, and it is a 
remarkable verification of the accuracy of his observations that the small apparent dis¬ 
crepancy on the smaller flows, which he was prepared to attribute to some unknown 
source of error, should be so nearly accounted for by the variation of temperature 
distribution with flow, which is a necessary consequence of the method adopted. 
In going through the summary of observations (Barnes, Table XVIII.), it may be 
noticed that there is generally a small systematic error of this nature in the results, 
as calculated on the elementary theory, tending to make the value of the specific 
heat smaller, the smaller the flows from which it is calculated. It would not, 
however, be worth while to recalculate the whole in detail as above illustrated, 
because the correction is so small that it may reasonably be applied to the observa¬ 
tions as a whole. 
In any particular case, for a pair of flows, the correction can most easily be applied 
by means of the numerical formulae (15) already given. This will not give the best 
results, if more than two flows are available, but the residual errors will then be 
accidental, so far as this particular correction is concerned. A few examples of this 
method of correction, taken from the first few experiments at 29°‘10 C. with 
calorimeter C, are given in the following table. The heat-loss in this calorimeter 
was much smaller than in calorimeter D, owing to a better vacuum and a smaller 
flow-tube. The correction is consequently smaller, and its effect is more obscured by 
