a new Air-thermometer. 301 



Let z = the increment of the column B C due to the change 

 of temperature ; then 



Volume of mercury in A B C before expansion 



Volume of this mercury after its expansion 



= (P+p)b(l+l). ...... (8) 



Section of the tube after its expansion 



Volume of mercury in A B C after its expansion 



^(P+p+z)b(l+~). ... (4) 

 Therefore, by equating (3) and (4), we get 



p+*= 



but 



H 



Pl (i + i)=p + * ; 



p v + vJ, . 3 p : . i 



1+ f P 1+ « 



-('>'fX'-f-|('-i)' 



On the supposition that the marks corresponding to the tem- 

 peratures t and t l are made upon the glass, V being the volume 

 of the air at t temperature ; then we have 



V 1= v(l + I) + L (l _ ( x«(l + !). 



Let —f and —, be put for the expansions for one degree, then 



P 



Substituting the values of ^~ and V t in equation (1), and solv- 



