416 On the Ratio of Expansion of Gases, [Dec. 



To put the error in another hght; it is proved that 480 C. I. 

 at 32'' become 508 if elevated to 60°. The volume I set out 

 with increases one cubic inch for every additional degree. Now 

 suppose the temperature raised to 61°, the volume will then be 

 609 C. I. or it will have increased one inch ; but 1 is not the f-^ 

 of 608 ; therefore gas does not increase -^-^ of its volume for 

 each degree, at any point of the scale, except 32°, as the works 

 I have referred to inform us : 100 volumes at 50° do not become 

 102-08 if raised to 60°, neither do 100 at 70° become reduced 

 to 97*92 if lowered to 60°, as the examples there given seem to 

 show. 



Taking the fact that 480 volumes at 32° increase one volume 

 for every additional degree as a foundation, we may easily form 

 a rule by which to ascertain what space any volume at any tem- 

 perature will occupy at any other temperature between 32° and 

 212°. 



Add the number of degrees which the gas is above 32°, to 480 ; 

 this will be the first number. 



Add the number of degrees which the required temperature 

 is above 32°, to 480 for the second number. 



The volume on which the calculation is made will be the third, 

 and the fourth will be the volume required. 



For example, I have 100 C. I. of gas at 70°, and I wish to 

 know what their volume would be' at 60°, 



480 + 38 = 518 first number, 

 480 + 28 = 608 second number ; 

 then 518 : 508 :: 100:98-069 



rsuppose the 100 C. 1. to be at 50°, what will they be at 60° ? 



480 + 18 = 498, 

 480 + 28 = 508; 

 then 498 : 508 :: 100 : 102-008 



I will now give an extreme case, worked both ways, to show 

 the great inaccuracy of the old method, and the correctness of 

 mine. 



Raise 100 C. I. from 32° to 212*». 



100 -f- 480 = -208333 ; -208333 x 180 = 37-4999 ; 37-4999 -h 



100 = 137^4999 



480 : 660 : : 100 : 137-5. 



Reduce 137-5 C. I. from 212° to 32°. 



137-6 -f. 480 = -286458 x 180 = 51-5624; 137-5 - 51-5624 



= 85-9376 



660 : 480 :: 137-6 : 100. 



Thus the error, by the old rule, amounts to more than 14 cubic 

 inches. I am, Sir, yours, &c. 



