Astronomical and Nautical Collections. 359 



veries our astronomy would scarcely deserve the name of a science, 

 since it is to him alone that we are indebted for our knowledge of 

 the eternal laws of nature, and for the application of computation 

 to these laws ; in a word, by the immortal Neavton. Some years 

 before his death, he communicated to his friend Halley the Table 

 of Refraction, which the \a.i\.ex eagerly published \_s'empressaY\w the 

 Philosophical Transactions for 1721. We are not informed how 

 this table was constructed, nor if it is the result of analysis or of 

 observation ; if the former, it would be interesting to have the 

 mode of computation employed by Newton. He would have done 

 better undoubtedly if he had explained it : but he was at that time 

 in his eightieth year : let us respect his old age, and let us accept 

 the table such as it is, with the gratitude due to its author. 



" 60. The Table of Newton gives 33' 45" at the horizon, and 

 54" at 45° : hence the index of refraction is .0002618 [Hawkesbee's 

 .00026414]. .corresponding to a temperature of 74° of Fahrenheit. 

 And on the other hand, as the temperature of 74°, the horizontal 

 refraction of Newton is exactly what it ought to be, supposing the 

 temperature of the atmosphere uniform throughout. Now if this 

 agreement depended on direct observation, it would perhaps be a 

 case unparalleled in the whole history of the physical sciences, 

 especially as we shall see hereafter, that all the refractions in the 

 neighbourhood of the horizon, agree almost as exactly with the 

 conditions of the analysis, which they are very far from doing in 

 the three tables of Bouguer. If the table was calculated, we may 

 first ask," says Kramp, " for what reason Newton fixed on the 

 temperature of 74° rather than any other ;" but in fact he fixed on 

 no temperature : " and secondly, how he arrived at the formula, 

 which alone is capable of making the refraction exactly 33' 45" 

 at this temperature ; and this difficulty is not easily removed : for 

 in fact, that formula depends on a very refined investigation, which 

 was unknown to Euler in 1754, and of which the principles were 

 not well explained before the publication of the Essay of Laplace, 

 " On the Approximation of Formulae containing Factors raised to 

 High Powers," in the Memoirs of the Academy of Paris for 1782. Are 

 we to suppose that the great Newton obtained the same conclusions 



