Mr. Meikle's Uepty to Mr. Ivory. 5l^ 



inculcate, af6 full of extravagant inconsistency, and run 

 counter to universal experience. But having produced these 

 extracts, Mr. Ivory consoles himself that all my objections to 

 his doctrines are derived from extreme cases. That this pitiful 

 excuse is groundless, may be seen from some of the examples 

 I formerly adduced ; where the errors alone are extreme, and 

 scorn all bounds, while the cases are taken within moderate 

 limits. Let us take, for instance, Mr. Ivory's own example, 

 to which, of course, he cannot object, PhiL Mag, for Feb- 

 ruary, 1827, page 94, where the density is to be doubted, and 

 the initial temperature of the air is 32" F. By putting, there- 

 fore, /j'=I, /?=2 and t= 32° in the general formula — 



8 V / p 



it becomes equal to 90° for the rise of temperature due to 

 doubling the density ; making the resulting temperature 122". 

 Now, if Mr. Ivory's rule were correct, the same air, by having 

 its acquired density halved, should just have its temperature 

 lowered 90°, or from 122" back again to 32° ; being in every 

 respect restored to its original condition, for its quantity of heat 

 is supposed to have all the while undergone no change. But 

 if, in the same formula, we put p'=:2,'f)=l, and r=122^ the 

 depression of temperature, in place of 90", is no less than 

 213°.75 ; furnishing the extreme error of 123°.75, in Mr. 

 Ivory's own mean case. 



But, lest all these instances may not satisfy Mr. Ivory, it 

 may be worth while to prove the universal inconsistency of 

 his rule, be the case what it may. For this purpose, I resume 

 the general expression 



!(«» -^ ') X '-r- 



First, let the density suffer a sudden increase, or let p exceed 

 p't which makes the last expression a rise of temperature. Next 

 suppose the same mass of air, which has acquired this rise of 



* This, it will be recollected, is the general and analytical expression 

 for Mr. Ivory's new law. In it, ^' and r denote the density and Fahren- 

 heit temperature of the air, at the beginning of any sudden change of its 

 volume, and ^ the density at the end ; Uie formula itself being the cor- 

 responding change of temperature. 



OCT.— DEC. 1828. o-.^^ v^ 2 



