538 Astronomical and Nautical Collections. 



series of angles expressing the inclinations of the ray to the verti- 

 cal line at that point. 



Account ofSiu Isaac Newton's Table. 



Dr. Halley, in the Philosophical Transactions for 1721, has pub- 

 lished a Table of Refractions, which he says was " the first accu- 

 rate table" made by the " worthy President of the Society :" " the 

 curve which a beam of light describes, as it approaches the 

 earth, being one of the most perplexed and intricate that can well 

 be proposed, as Dr. Brook Taylor in the last Proposition of his 

 Methodus Incrementorutn, has made it evident. The aforemen- 

 tioned Table, I here subjoin for the use of the curious, such 

 as I long since received it from its great author ; it having never 

 yet, that I know of, been made public." The refraction at the 

 horizon is made 33' 45" ; at 45°, 54" only, agreeing certainly in 

 the latter case with Hawkesbee's experiments mentioned by Taylor. 

 From the way in which Taylor's investigations are mentioned by 

 Halley, it might naturally be supposed that Newton's computations 

 were independent of Taylor's formulae ; and hence it was natural 

 enough, that Professor Kramp should spare himself the labour of 

 consulting Taylor's book, which has by no means been generally 

 ktiown, though there is no doubt that the table might be com- 

 puted from some of Taylor's diflferent series : and even if the hori- 

 zontal refraction were wanting, it might be obtained from the five 

 neighbouring results, by making the fourth difference constant. 

 After this explanation, it will still be interesting to observe the view 

 which Kramp has taken of the history of the problem ; for though it 

 will scarcely be practicable to claim for Taylor the whole of the merit 

 which Kramp attributes upon suspicion to Newton, yet certainly 

 muchmaybe learned from Taylor's method of conductingthe process. 



Observations on N'eivton's Table, by Kramp. Analyse des Refrac- 

 tions Astronomiques et Terrestres. 4. Strasb. 1798. 

 " I. 59. Let us take, for a last example, the table of refractions 

 left us by the greatest of all mathematicians, and the ablest of all 

 observers that have ever existed ; the man, without whose disco- 



