Astronomical and Nautical Collections. 373 



compensated, in the approximation that has been adopted, by the 

 alteration of the other coefficients. 



Mr. Ivory, observing with some truth that Dr. Young's inverse 

 series was not in all cases so convergent as could be desired, or 

 even as the author appeared to believe it, has still more lately 

 applied the powerful machinery of his analytical investigations to 

 the construction of some tables upon a hypothesis which seems in 

 most respects to represent the constitution of the atmosphere with 

 sufficient accuracy, and which agrees also extremely well with the 

 most approved observations. Mr. Ivory adopts the opinion of 

 Schmidt, and of some later experimental philosophers, that a dimi- 

 nution of temperature diminishes the actual bulk of a given portion 

 of air by an equal quantity of space for each degree of the ther- 

 mometer, and infers that, at the temperature of about — 500° of 

 Fahrenheit, the air would cease to occupy any space whatever as 

 such, or in the form of a gas. He seems, however, to have ima- 

 gined in some of his earlier papers, that the diminution of tempe- 

 rature might still be equable in ascending to all possible heights ; 

 and even in his essay, printed in the Transactions for 1823, he 

 says, " there is no ground in experience for attributing to the gra- 

 dation of heat in the atmosphere any other law than that of an 

 equable decrease as the altitude increases . . . : it therefore seems 

 to be the assumption most likely to guide us aright in approximat- 

 ing to the true constitution of the atmosphere." From this hypo- 

 thesis he derives the very convenient conclusion that the pressure 

 must vary at a certain power of the density, or that y = z", n 



5 

 being nearly — : but finding it impossible to suppose the atmo- 

 sphere so little elevated as this hypothesis would require, he modi- 

 fies it by the addition of another term to the value of y, though 

 ivithout very clearly relinquishing in words the original supposi- 

 tion, and ultimately adopts an expression equivalent to that 

 which has already been mentioned in this paper, or y = .75z 

 + .25z\ 



Mr. Ivory first expands the well known expression for the re- 

 fraction into a series by means of the binomial theorem, and finds 



