and on its Measurement by Thermometer's. 455 



a priori ; and indeed water is known to form a remarkable devia- 

 tion from such a law, having a maximum density at 39°*1. 



The next consideration of consequence is the true law for the 

 expansion of gases ; and the generally received law of equal 

 increments leads, as before stated, to inadmissible consequences ; 

 so that, taking the mercurial thermometer as our standard, we 

 should examine the applicability of the law of uniform expansion 

 to them, or Dalton's law. Now the formula V=V e a *° gives, 

 by putting t°= 1 for the temperature between the freezing and 

 boiling of water for atmospheric air, and Vj the corresponding 

 volume, 



V 



— l=6 a =l-375, according to Gay-Lussac. 



= 1-3726, „ Dalton. 

 = 1*3645, „ Rudberg. 



= 1*3665, „ Regnault. 



Taking Rudberg's determination, we have 



a=log e (1-3645) = -310788 



and the volume V of atmospheric air is found from the formula 



y = y , e *°x '310788 



where V is the volume at any temperature, and f are the + 



degrees above or below it respectively, measured in terms of the 



interval between the freezing- and boiling-points of water taken 



f 



as unity. If f be measured on Fahrenheit's scale, we have ■?—. 



J 180 



in place of t°, and 



y_y > e *°x -0017266 



t° 



If the t° are on the Centigrade scale, we have r^ in place of t°, 



and y = y o>e ^x -00310788 



Eor mercury, from the above, we have for degrees on Fahren- 

 heit's scale, 



y_y m e t°x -00009921 



and for degrees on the Centigrade scale, 



y __ y i ^ x -000178576 



With these formulae it is easy to compare the scales of the air 

 and mercurial thermometers when formed on the rules of equal 

 increments and uniform expansion. 



The expansion of mercury being less than one-twentieth that 

 of air, the differences of the two scales for the mercurial thermo- 

 meter are very much less than those of the two scales for the air 



