Mr. Ivory on the Theory of the Astronomical llefractions. 351 



in determining the constants of the formula. The refractive 

 power of the an- was obtained by Delambre from a great 

 number of astronomical observations ; the same quantity was 

 deduced by MM. Biot and Arago from experiments on the 

 gases with the prism ; and the results of two methods, so en- 

 tirely different, agree so nearly, that there seems no ground 

 for preferring one to the other. The remaining part of the 

 French table, for altitudes less than 16°, is computed by a 

 method of Laplace, which the author has explained, with- 

 out disguising its defects, in the fourth volume of the Mec. 

 Celeste. The two atmospheres with densities decreasing in 

 arithmetical and geometrical progression, which it now ap- 

 pears were imagined by Newton, and which have been dis- 

 cussed by Thomas Simpson and other geometers, are found, 

 when the same elements are employed, to bring out hori- 

 zontal refractions on opposite sides of the observed quantity. 

 Laplace conjectured that an intermediate atmosphere which 

 should partake of the nature of both, and should agree with 

 observation in the horizontal refraction, would approach 

 nearly to the true atmosphere. It must be allowed, that these 

 conditions, which may be verified by innumerable instances 

 between the two limits, are vaguely defined ; and in order to 

 ascertain the real meaning of the author, recourse must be 

 had to the algebraic expressions. When this is done, it will be 

 found that the atmosphere intended is one of which the den- 

 sity is the product of two terms, one taken from an arithme- 

 tical, and the other from a geometrical progression ; the ef- 

 fect of which combination is to introduce a supernumerary 

 constant, by means of which the horizontal refraction is made 

 to agree with the true quantity. No one will deny the merit 

 and the ingenuity of Laplace's procedure; but though very 

 skilful, and guided in some degree by fact, it is liable to all 

 the uncertainty of other arbitrary suppositions, as indeed the 

 author allows. Dr. Brinkley has given the character of the 

 French table fairly when he says, that it is only a little less 

 empirical than the other tables. On divesting Laplace's hy- 

 pothesis of vagueness in the language, and expressing it in 

 the unequivocal symbols of algebra, it does not appear to 

 possess any superiority over other supposed constitutions of 

 the atmosphere in leading to a better and less exceptionable 

 theory ; at least the Mec. Celeste has been many years before 

 the public, during which time not a few geometers have la- 

 boured on the subject of the refractions ; but no improvement 

 originating in the speculations peculiar to Laplace has oc- 

 curred to any of them. 



