Heat by the Method of Mixtures. 271 



Then if we take the algebraic sum of these variations we 

 obtain 2A0 as the total correction for the observed tempera- 

 ture 6 n at the end of the experiment, which added to this 

 observed temperature gives the correct value of 6 to use in 

 formula (2). This method requires us to know both the tem- 

 perature of the externa] air and the quantity A. The first is 

 known from observation ; the second can be determined from 

 the formula for loss of heat by radiation, which is given on p. 

 91, vol. i (Jamin's Physique), as 



Q = loss of heat per sec = k${0—fZ) 



hence A6= « temp. « = — ffi*~ff 

 F 4000 (M + W)c 



where 



S_. is the surface of the calorimeter. 



k-. " value of a (small) calorie. 

 Hence 



A = -° 0025 M^r* (•) 



c being taken as unity. 



Method of Regnault.^ — To render the observation of the ex- 

 ternal temperature (a temperature always hard to determine 

 with accuracy) unnecessary, the readings are taken at intervals 

 as before, but commenced before and extended after the time 

 during which equalization is taking place. The whole opera- 

 tion comprises three periods, the first a short period just before 

 the introduction of the body ; the second beginning with the 

 introduction of the body into the calorimeter and ending with 

 the maximum temperature ; the third, during which a few 

 additional observations are made on the rate of cooling. Let 

 x be the interval between successive readings, a, n, and b the 

 number of readings in the three periods respectively, and # , V 

 2 . . . to m the readings of the thermometer during the second 

 period, the body being introduced at the beginning of the 

 &+lnth interval, (0 = 6 ). Also let t 19 t 3 equal the mean tem- 

 peratures during the first and third periods, and A x , A 3 the 

 mean loss of temperature for these periods for the time, x, and 



B A- f) 4- /9 



let # m ,= ^— ± 9 d m ,, = -±—*, etc., and A 2 ', A 2 ", etc., be the mean 



temperatures and corresponding losses of temperature due to 

 radiation during the successive intervals of the middle period. 



* The value of the constant term in this formula will of course depend on the 

 nature of the radiating surface of the calorimeter. 



f This method of correction is essentially that described in Professor Holman's 

 paper, in which a somewhat different method of reduction is adopted. 



