276 Methods of determining and calculating 



perature ; if the expansion of the vessel could be made to measure 

 its own increase or diminution of temperature we should have the 

 simplest of all possible cases ; for calling 

 w= the weight of water in grains, 



T= the degrees of change in temperature which it undergoes, 

 g= the weight in grains of the containing vessel, 

 t= the change of its temperature by the experiment, and 

 x= the specific heat of the material of which the vessel is com- 

 posed, that of water being unity, we shall have TW =gtx or x= 



TW . .^ , 



— — (1). This supposes the experiment to be made with such re- 



gard to the thermometric and hygrometric state of the air as to re- 

 quire no correction on that account. 



2. If we introduce a mercurial thermometer, with a brass scale, 

 to measure the change of temperature, putting 



b= the weight of brass immersed, 



m= the weight of mercury, 



c= the weight of the glass bulb and that part of the stem which 



sinks into the water, we have, for the equivalent of the thermometer 



ingrains of water, the following expression, .11276 & + . 0327TO-f- 



.18511c, and as by suspending the thermometer or otherwise fixing 



it in a certain position for many experiments, we can always use the 



same part of its length, we may substitute for this complex term the 



simple expression e for the thermometrical equivalent in grains of 



T(W4-e) 

 water; then the formula (1) will become x= (2). It was 



by this method of trial and calculation that the three experiments 

 before mentioned, gave .17854 for the specific heat of glass, though 

 in the expression for the thermometer I have chosen to use the mean 

 of six other determinations until I can repeat and vary the experi- 

 ment, so as to be satisfied which is nearest to the truth. 



3. The specific heat of the containing vessel being known, we 

 proceed to that of any other solid, wrought iron for example, putting 

 its weight in grains =^, and its specific heat =z. T will now rep- 

 resent the change of temperature not only of the water and ther- 

 mometer but also of the containing vessel, and t the change of the 

 solid, i,g, X and e being the same as above, then will itz=T(w-{- 



T{w-\-gx-^e) 

 gx-^-e) and z= j: (3), or the formula may be simphfied 



