COMPARISON OF I'l.. \TINIM \\l> c.\S TIIF.I.'Mi >\IKTi:i 79 



whence, by certain simplifications, we get finally 



This formula was used first to calculate the coefficient a between the known 

 temperatures 0and 100, the value found being afterwards utilised for the calculation 

 of the temperatures observed in the comparisons. 



XXXII. CORRECTIONS RELATING TO THE " DEAD SPACE." 



The corrections, which must be applied to the observed pressures, to reduce them 

 to what they would have been had the whole of the " dead space " been at 

 throughout, are easily deduced from the laws of BOYLE and GAY-LussAC. 



( 1 ) Let us first supj>o.se that the " dead space " is composed of different parts 



v v, + v, + r, + . . . 

 whose temperatures are 



'l> ^2> ^1) 



If now we reduce to these gaseous volumes without changing the pressure p to 

 which they are subjected, we have as total variation of volume 



The temperatures f,, <,, t t . . . , being generally positive, Ar is negative. 



(2) To find the correction sought, it is necessary to transfer from the reservoir, 

 where the temperature is T 3 , and the pressure p, a quantity of gas occupying at 

 the volume Av, or what comes to the same thing, the volume of the reservoir V must 

 be increased by a quantity equal to Aw (1 -\- T). It is evident that this increase in 

 volume involves a variation of pressure 



. 



which can also be written 



and which represents the correction sought. 



For the application of these corrections we constructed two tables. The first gives 

 for every degree the values of 



' etc - 



and enables the values of Av to be rapidly calculated. 



