Astronomical and Nautical Collections. 361 



which has often been remarked in practical astronomers, Dr. 

 Bradley chose to begin by supposing the approximate refraction 

 known, and to correct it so as to make it exactly proportional to 

 the tangent of the zenith distance diminished by three times the 

 refraction. Leaving the horizontal refraction 33' 0", as assigned in 

 Simpson's Table, he makes it 51" at 45°, instead of 53". Dr. 

 Bradley has, however, the merit of having first introduced an ac- 

 curate mode of allowing for the effect of the actual temperature of 

 the atmosphere at the place of observation, which he estimates at 

 4^^ of the whole refraction for each degree of Fahrenheit above 

 or below the standard temperature of 50°. 



Account o/'Euler's Investigations, fom Kramp, Chap. v. 



The Memoir of Euler, contained in the Transactions of the 

 Academy of Berlin for 1759, though of no importance whatever to 

 optics or to astronomy, may however become still more useful, if 

 properly considered, in a moral point of view, than if had been 

 completely successful. It may not only teach us a proper diffi- 

 dence in our own computations, but it may serve to show, among 

 many other instances, how liable the greatest and wisest of man- 

 kind are to imperfections and errors, even in those departments 

 which they have cultivated at other times with the greatest success. 

 An extract from the account given by Kramp of Euler's results, 

 will render it sufficiently obvious, how much valuable time and use- 

 less labour might have been spared if Euler had only happened to 

 look at a few pages of Taylor's little work, which was printed 

 nearly fifty years before. 



The formula adapted by Euler for expressing the elasticity E at 



the height X is E= -^ ,f being the subtangent or modulus, 



which differs very little from the logarithmic progression of den- 

 sities when the temperature is supposed constant, that is E = e~'"^. 

 From tliis expression he deduces the fluxion of the angle described 

 by the ray; but in attempting to assign its fluent, the art of this 

 profound mathematician has completely failed him ; and he has 

 Vol. XVIIl. 2 B 



