AEROSTATICS. 231 



not appear to observe the same law with the varia- 

 tions of temperature ; and it is found, that, for equal 

 variations of temperature, the variations of the bulk 

 of the mercury constitute a series, of which the dif- 

 ferences are in arithmetical progression, or in which 

 the second differences are constant. Hence the rela- 

 tion between the temperature and the expansion of 

 mercury, may be expressed by a quadratic equation, 

 or by the abscissae and ordinates of a line of -the se- 

 cond order. 



323. If D be any number of degrees reckoned 

 from the freezing point of water in FAHRENHEIT'S 

 thermometer, the real temperature corresponding 



to D is 207 ( 1 + v 



72 



This formula is derived from D ALTON'S experiments. 

 See his System of Chemical Philosophy, Part i. 

 p. 14. 



If D = 72, which is known to mark the degree 

 according to FAHRENHEIT'S thermometer, at which 

 mercury congeals; the temperature, as deduced 

 from this rule, is 207, which, therefore, is the real 

 distance between the freezing of mercury and the 

 freezing of water. Hence the degrees on the mer- 

 curial thermometer, reckoned from the degree which 

 marks the congelation of mercury, are as the square 

 of the real temperatures, reckoned from the same 

 point of congelation. 



The 



