Astronomical and Nautical Collections. 365 



perseded that of Kramp, especially from the extreme elegance and 

 conciseness with which the definite fluent already mentioned is there 

 obtained by means of the method of partial fluxions ; and the 

 hypothesis respecting the distribution of temperature, which has 

 been practically adopted by this illustrious philosopher, has led to 

 the construction of tables possessed of accuracy abundantly suffi- 

 cient for every purpose of astronomy, and which ought never to 

 have been set aside by the German astronomers, in order to return 

 to the mere speculative suggestion of Kramp, however elaborately 

 computed and partially supported by their ingenious countryman, 

 Professor Bessel. At this period of the history of refraction, the 

 investigation had attained all the practical perfection that could 

 be desired : it will be proper to proceed in the second place to the 

 consideration of the later attempts that have been made to improve 

 it by the mathematicians and astronomers of the British empire. 



Part II. Account of the later improvements in the theory of Atmo- 

 spherical REFttACTION. 



From the time of the publication of the French tables of refrac- 

 tion, constructed from the computations of the illustrious Laplace, 

 the determination has acquired a degree of accuracy rather exceed- 

 ing than falling short of what might have been expected froia the 

 fluctuating state of the elements on which it depends. 



Our countryman Mr. Groombridge is the first astronomer 

 that seems to have undertaken an elaborate series of observations 

 almost entirely for the purpose of obtaining a complete table of 

 refractions. His first publication is contained in the Philosophical 

 Transactions for 1810. The mode of computation that he has era- 

 ployed, to obtain the mean refraction at a given altitude, is to ob- 

 serve the same star above and below the pole ; and to take the 

 sum or difference of the apparent altitudes, which, compared 

 with the double latitude, gives the sum or difference of the re- 

 fractions at the given altitudes : then by comparing tlicse results 

 with those of an approximate table, he [finds the mean factor 



