Conduction of Heat in Liquids. 



37 



This equation cannot be exactly solved, but an approximate solution 

 of sufficient accuracy can be obtained. This gives t as a function of 

 a, p, c, and k ; but t is determined from the galvanometer reading's, 

 and x, />, and c can be otherwise determined, thus h is at once 

 obtainable. 



With the smaller apparatus, when the dish remained unemptied, 

 the value of t, when water was in the tub, exceeded ten minutes, and 

 for nearly all other liquids it is greater. The integral can be 

 replaced by the summation — 



2 ( t _ x) - 9 / 2e -«V/«*-x){|(i- x ) S -3^(i- x )+(^J}QT = 0, 



.... (7) 



where Qt is proportional to the heat transmitted to the liquid daring 

 the interval t, and t — % is the time between the middle of this 

 interval and the epoch of swiftest rise of temperature. It is not 

 necessary to take t the same throughout ; thus at the beginning of 

 the experiment when/(£) varies rapidly, t must be taken smaller 

 than subsequently. The terms in the summation answering to the 

 last few minutes of the experiment are always very small. 



When the water was siphoned from the dish, any gain or loss of 

 heat through the dish subsequent to the operation was very small 

 compared to that given up to the liquid previously. Thus no serious 

 error will be introduced by supposing f(t) = after the siphoning. 



It will be observed that what the galvanometer readings give is 

 the time when the platinum wire is heating fastest, while the equa- 

 tion gives this epoch for the liquid at the same depth as the wire. 

 Since the temperatures of the media are changing very slowly, it is 

 scarcely conceivable that they could differ by a finite quantity, or 

 that their rates of change should not be practically alike. The 

 assumption made in the present method is of a totally different order 

 from that made by previous observers dealing with thin layers of 

 liquid. Their assumptions would be equalled only by supposing 

 the dish and the liquid touching it to be always identical in 

 temperature. 



Theoretically the absolute quantity of heat initially given to the 

 dish is of no importance, except in so far as it modifies the rate at 

 which heat is subsequently communicated to the liquid. Experi- 

 mentally it was found that both the quantity and the temperature of 

 the water poured into the dish could be varied to a considerable 

 extent without sensibly altering the epoch of quickest rise of tempe- 

 rature. When the water was siphoned the initial quantity of heat 

 was of still less importance. With most liquids, however, the water 

 was heated to a fixed temperature, viz., 75° C, and a measured 



