APPENDIX TO THE MECHANICAL EQUIVALENT OF HEAT 471 



6 to 12, so that the mean shall be nearly 14 and 16 -5, I find the 

 following for the ratios : 



1-0044 1-0042 



1-0042 1-0042 



1-0049 1-0040 



1-0047 1-0030 



1-0047 1-0035 



1-0052 1-0035 



Mean, 1-0047 1-0037 



So that we have the following for Joule's old and new values : 



Old. New. 



423-9 423-9 



Correction for thermometer 2-0 1-6 



Correction for latitude -5 -5 

 Correction for sp. ht. of copper -7 



427-1 426-0 



My value 427-7 427-1 



Difference -6 1-1 



or 1 in 700 and 1 in 390, respectively. 



But the correction found in this way is subject to local irregulari- 

 ties, and it is perhaps better in many respects to get the equation giving 

 the temperature of Joule's thermometer on the air thermometer. Let 

 T be the temperature by Joule's thermometer, and t that by the air 

 thermometer. Then I have found 



t = 0-002 + 1-00125 T -00013 \ 100 T\ \ 1 -003 (100 -f T) \ 



The factor 1-00125 enters in the formula, probably because the ther- 

 mometer which Joule used to get the value of the divisions of his ther- 

 mometer was not of the same kind of glass as his standard. The rela- 

 tive error at any point due to using the mercurial rather than the air 

 thermometer will then be 



E = 1 $** = 00125 + -00000039 \ 23300 666 t + 3 f\ 

 dT * 



