362 Astronomical and Nautical Collections. 



thought it justifiable to have recourse to the very arbitrary and in- 

 correct supposition that the curve maybe considered as nearly agree- 

 ing with a hyperbola, having for its equation t = Cj/"*"'. The refrac- 

 tion is indeed easily computed upon this hypothesis ; but it be- 

 comes, as Kramp has shown, at the horizon, 42', instead of 36' 26", 

 as it ought to be in the supposed state of the atmosphere, and at 

 45°, no less than 2|' instead of about 57". In short, the failure 

 could not possibly have been more total, if the essay had been the 

 work of the idlest schoolboy, instead of one of the four or five 

 greatest mathematicians that have ever existed : for in the same 

 rank with Archimedes and Newton, and Euler and Laplace, it is 

 difficult to say what fifth philosopher has any right to be classed : 

 perhaps Leibnitz, and possibly Lagrange ; but this question will 

 long remain undecided, i^it requires to be determined by a jury of 

 their peers. 



Methods q/" Mayer and Lambert. Kramp, v. 41,47. 

 The formula of Mayer was published without demonstration in 

 his Lunar Tables, and appears to have been only an empirical mo- 

 dification of those of Euler and Bradley, approaching so nearly 

 to Bradley's results as scarcely to require any distinct consi- 

 deration. 



Lambert published in 1759, at the Hague, a separate essay, en- 

 titled Les ■proprieties remarquahles de la route de la Lumi^re par les 

 airs; and he resumed the subject in the Berlin Almanac for 1779. 

 He has adopted in this research a supposition respecting the 

 asymptote of the curve which Mr. Kramp has shewn to be inadmis- 

 sible ; and his method of computation exhibits an error at the 

 horizon amounting to 87". But " Lambert might have concluded" 

 says Kramp, " from his own geometrical investigations, the approxi- 

 mate result which Mayer had already obtained in part, that is, that 

 for the same absolute elasticity" as expressed by the height of the 

 barometer, " the horizontal refraction must be reciprocally propor- 

 tional to the square root of the cube of the specific elasticity," de- 

 pending on the temperature ; and he contradicted himself when he 

 objected to what Mayer had said on this subject." 



