THE MECHANICAL EQUIVALENT OF HEAT. 
307 
Section I. —General Description. 
Let R be the resistance of a conductor at a certain standard temperature d, then 
if the ends of the conductor be kept at a constant ditference of potential E 
dt J.E.^ 
where Q, is the quantity of heat generated by the current, t is time, and J the 
mechanical equivalent of heat. 
If the wire is immersed in water, and if the capacity for heat of the water and the 
calorimeter at the standard temperature 6 is M, then 
dQ 
dt 
It is necessary to distribute the heat generated in the wire throughout the whole 
calorimeter as quickly as possible, otherwise we cannot accurately observe cWjdt, 
hence, since work must be done when stirring, we have to deal with a mechanical as 
well as with an electrical supply. Let the rise in temperature per second due to the 
mechanical supply be cr, and let ^ denote the quantity of heat generated by both 
electrical and mechanical sources. Then 
dQe, o- 
dt 
y ~ “h crlVI — IM 
O . ll 
dt 
(3). 
It is certain that some heat will be gained or lost by radiation, conduction, and 
convection. Let p be the rise or fall per second in temperature due to radiation, &c., 
when the difference between the external and internal temperatures is 1° C. Denote 
the temperature of the surrounding envelope by 9q, and the temperature of the calori¬ 
meter at any time by 6 ^; also suppose that M becomes M' and R becomes R' when 
0 becomes 6^ 
We now have 
dQ., I 
dt 
= + <rW - pW {6, - e,)* = M 
dt 
( 4 ). 
where ^ denotes the gain of heat due to all causes, hence 
E2 
J.E'. M 
7 + {or - p{d^ — 6>o)} 
dt 
* It E shown in Section Xll. that we are justified in assuming that Newton’s law of cooling holds 
true over our range of temperature. 
