from Orifices at different Temperatures. 287 



Then, in consequence of the expansion of the metal, the ratio 



D 2 



of the areas -=g becomes 



(l + <yr) 2 D 2 



(l + e b ry d» 



and the true difference of the square roots of the heads is 



The formula of flow, allowing for the alteration of the dimen- 

 sions by rise of temperature, is therefore 



(1 + e r) 2 . D 2 _ _ 



Let e c = -000006, 



* 4 = -00001, 



t= 190°- 60°= 130; 



(l + <vr) 2 , /I-00078\" , 



(T+^^ 1 + ^-(t001f) ^1-00078 = 0-999355. 



Hence it is obvious that the effect of the expansion of the 

 reservoir and orifice is very small for the range of temperature 

 in these experiments. Allowing for that expansion, we get 

 for the experiments at 190°, 



•99935 D 2 t _ ,_ 

 c = ^2 {n/Ai-VA 2 }, 



or slightly smaller values of the coefficient than those given 

 above. 



It is rather curious that it is stated in Mr. Isherwood's paper 

 that the results are corrected for the variation of the size of 

 the orifice as the temperature varied, but no mention is made 

 of a correction for the size of the reservoir or the expansion of 

 the vessel to which the index-marks denoting the initial and 

 final heads were attached. If these latter corrections have 

 been omitted, though this is difficult to believe, Mr. Isher- 

 wood's results should be divided by 



where e c is the coefficient of expansion of the material of the 

 reservoir, whatever that was. This would sensibly diminish 

 the apparent increase of discharge at high temperatures given 

 in his experiments. 



