DETERMINATION OF THE SPECIFIC HEAT OF WATER. 447 
and the rate at which heat is given up at the time ¢ is 
dH /dt = pkT/c. 
If the cooling correction is applied in the usual way, the rate at which heat is lost 
would, during the period of heating, be taken as half that corresponding to the final 
period, or in other words we should take loss of heat as Sa T during the period of 
: AT ; 
heating, and as — (¢ — T) from the time that the temperature of the calorimeter has 
become steady. It is seen that in this way of calculating, the term 4 (pest) is 
neglected. This term represents the amount of heat which is necessary to raise 
a thickness 3 of the material through which the heat is conducted to the final 
temperature of the calorimeter. 
We see from this investigation that a certain amount of the air surrounding the 
calorimeter should be added to the water-equivalent. For air a? is about 0°26, and 
in our experiments the walls of the enclosure were 3°8 centims. from the calorimeter. 
We may, without sensible error, neglect the error due to the curvature of the sides 
of the calorimeter and substitute 3°8 for c. The value of f? then becomes 
0:2672/(3°8)? = 0°18. 
As several minutes always intervened between the time at which the temperature 
of the calorimeter had become constant and the observations for the cooling 
correction, 6?(t — T) was always greater than 10 and e~®“—” was therefore quite 
negligible. We may in this case then simply calculate the water-equivalent of a 
quantity of air surrounding the calorimeter, and having a thickness of ¢/3 or 
1°3centims. ‘The total effective surface of the calorimeter being 724 sq. centims., the 
quantity to be added to the water-equivalent becomes. 0°28. 
2. Correction for Thermometer.—In taking the water-equivalent of the thermo- 
meter, it is usual to consider only that part which is plunged into the water, but this 
requires justitication, as it is clear that those parts of the thermometer which are close 
to, but not actually in contact with the water, must be heated also. The following 
calculation will give an estimate of the error which may be thus introduced. We 
may assume, in the first instance, that the thermometer which is surrounded by air 
rising from the calorimeter will not give up any appreciable heat to the outside, so 
that we may apply the same differential equation for the flow of heat as that used in 
the former problem. We may treat the thermometer as a glass rod of indefinite 
extent, having the temperature of its surface in contact with the water raised at a 
uniform rate pt until t = T when it is kept constant at the temperature pT. 
The solution of the equation applied to this case gives us :— 
