1. z = 

 and 2. z 



278 Methods of calculating and determining 



z= its specific heat, 

 e=- the equivalent of the thermometer. 



Then, as the temperature of the water, the air, and the iron, are 

 supposed to be the same in both cases, we shall have by the two 

 expressions, 



T^'tde _ T:{w-[-e-\-gx) tde 



it it 



H'w't de i:'{w-\-e+g'x)tde . 

 if ~ It' ' 



jfrom which we derive 



3. -. = J, • Hence 



4. i:t'{w-\-e)-\-i:t'gxtdef=.T't{w-\-e)-ir"T'tg'xttde, and by- 

 transposition, 



5. i:t'gx-T'tg'x={T't-'Yt') .{w-{-e)t{tit') .de, and by 

 division, 



n:'t-i:t').{w-\-e)t{tp')de , .^ 



6. x= ~' Yfio- — 'V't ' ' which, if there be no cor- 



to O 



rection for thermometric variation, will be reduced to the simpler form, 



r£'t-Tt').{w-\-e) 



7. x= Fp / __'Y/f(f> — ' C^)' And as the value of a; is now 



found, we may substitute it in either the first or second equation, to 

 enable us to find the value of z. The first would give, (omitting 

 the correction tde^ 



^ _ i{i:'t-i:t').(w-^e\ 



8. z=- ^^ ^tg-ltg /^ Had we taken the 



ti 

 second equation in which to substitute the value of a;', the value of z 



X r.. lC^'t-'Yt').(w^e)\ 



would have been = 1— ^ 2 § L . From 



t'l 



either of these we may obtain 



TTXff-g-0.(^. +e) 



^' ^~ i{i:t'g-i:'tg') ^^'> 



The necessity of applying the correction ±de, arises fi-om the lia- 

 bility of the warm current of liquid ascending from the hot metal 

 to elevate the temperature of the thermometer above that which 

 ought to be exhibited by the liquid when the maximum effect of the 

 solid has been attained. By taking the thermometer out of the 



