OF ARTS AND SCIENCES. 113 



Thermometer No. 6166: 

 2 1 =.(i7l7L'Or'"—V" — -00018 T(T— 40) (l — .003 (T+ 40)) ; 



where V, V", and V" are the volumes of the tube obtained by 

 calibration ; / ', t ", and t '" are constants depending on the zero point, 

 and of* little importance where a difference of temperature is to be 

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



On the mercurial thermometer, using the 0° and 100° points as fixed, 

 we have the following by comparison with No. 6167 : — 



Thermometer No. 6163 ; t = .057400 V— t ; 

 Thermometer No. 6165 ; t = .46265 V— t ; 

 Thermometer No. 6166 ; t = .075281 V— t . 



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 \° 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 



p -? = C (1 — m & D) ; 



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

 of a given weight of the air ; D is its density referred to air at 0° C. 

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

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

 vol. xv. (n. s. vii ) 8 



