MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



183 



The exact refractions calculated by the formula are next to be compared with the 

 numbers in Halley's table. 



The examination that has now been made fully establishes that Halley's table is 

 no other than the one which Newton computed on the supposition that the densities 

 in the atmosphere are proportional to the pressures. The discrepancies, amounting 

 in every instance to a small part of the whole quantity, are such as might be expected 

 to occur unavoidably in the intricate and laborious methods of calculation followed 

 by Newton. Some part of the differences may also arise from the elements of the 

 formula, which, being deduced from only two numbers of the table, may not exactly 

 coincide with the fundamental quantities which Newton assumed. M. Biot, by a 

 method different from Kramp's, has found other elements, which make the horizontal 

 refraction 8"'3 less than in the table ; but these small variations, which proceed from 

 calculating in different ways, only confirm more strongly that Halley's table is the 

 same which Newton constructed by his second hypothesis, and communicated to 

 Flamsteed. 



It appears from what has been said, that, as far as the mathematics is concerned, 

 the problem of the astronomical refractions was fully mastered by Newton. It would 

 be strange indeed to suppose that the author of the theories in the Principia would 

 find difficulty to apply them in a case to which he bent the whole force of his mind. 

 But he was embarrassed by the suppositions he found it necessary to make respecting 

 the physical constitution of the atmosphere. His first hypothesis is evidently con- 

 trary to nature, in admitting that air at all altitudes exerts the same power to inflect 

 the light to the earth's centre ; his second method made the refractions too great near 

 the horizon, thereby proving the necessity of searching out some new cause for the 

 purpose of reconciling the theory with observation. Averse from hypotheses, he 

 seems, on these accounts, to have declined inserting in his works a problem which 

 had cost him so much labour, and upon his solution of which he evidently set some 

 value. 



If the different attempts to solve this problem are to be tried with the same rigour 



