ON THE MECHANICAL EQUIVALENT OF HEAT 381 



of little importance where a difference of temperature is to be meas- 

 ured; and T is the temperature on the air thermometer. 



On the mercurial thermometer, using the and 100 points as fixed, 

 we have the following by comparison with No. 6167: 



Thermometer No. 6163; = -057400 V t ; 

 Thermometer No. 6165; = -46265 V 1 ; 

 Thermometer No. 6166; = -075281 V 1 . 



The Kew Standard 



The Kew standard must be treated separately from the above, as the 

 glass is not the same. This thermometer has been treated as if its 

 scale was arbitrary. 



In order to have variety, I have merely plotted all the results with 

 this thermometer, including those given in the Appendix, and drawn 

 a curve through them. Owing to the thermometer being only divided 

 to -J F., the readings could not be taken with great accuracy, and so 

 the results are not very accordant; but I have done the best I could, 

 and the result probably represents the correction to at least 0-02 or 

 0-03 at every point. 



(d) Reduction to the Absolute Scale 



The correction to the air thermometer to reduce to the absolute 

 scale has been given by Joule and Thomson, in the Philosophical 

 Transactions for 1854; but as the formula there used is not correct, 

 I have recalculated a table from the new formula used by them in their 

 paper of 1862. 



That equation, which originated with Rankine, can be placed in the form 



where p, v, and /j. are the pressure, volume, and absolute temperature 

 of a given weight of the air; D is its density referred to air at C. 

 and 760 mm. pressure; fa is the absolute temperature of the freezing 

 point; and m is a constant which for air is 0-33 C. 

 For the air thermometer with constant volume 



T = 100 P'~P 



or, since D = 1, 



tt - /,, = T- -00088 T 



from which I have calculated the following table of corrections: 



