300 Mr. T. Tate on the Construction of 



L/ ( _f= change of the column of mercury D corresponding 

 to t x —t difference of temperature. 



-, — = the expansion of mercury and glass respectively 

 a p 



per unit of volume, for t l —t degrees change of 



temperature. 



Then we have 



When the expansion of the mercury and glass are neglected, 

 P,=P, and in this case equation (1) becomes 



V-V-gJ^fc-Ol 

 but 



••• L '.-'=^+7)^-')« • • • • • » 



which shows in this case that lit x -t is proportional to t l — 1 } and 

 consequently that the graduations on the scale EF must be 

 uniform. 



From equation (2), we have 



V 1 



Length of 1 degree on the scale = - • ^ , 



and 



V T 

 Range for T degrees . . . = - • jgg^ 



If V=l, a = -006, *=50,andT=54; then we find the length 

 of one degree on the scale to be about one-third of an inch, and 

 the range or length of the whole scale E F to be about 18 inches. 



It will be observed that the glass ball G need not greatly ex- 

 ceed the size of the bulbs of some of our ordinary thermometers ; 

 and the whole length of the instrument may be 5 or 6 inches 

 less than that of a barometer. 



These formulae are sufficiently exact for determining the pro- 

 portion of the different parts of the instrument ; but it is neces- 

 sary that we should determine the amount of the disturbances 

 arising from the expansion of the mercury and glass. 



Throughout the following investigation, all terms are neglected 



which contain as a factor the product of - and -, or the square 

 of either of them. 



