S62 Astronomical and Nautical Collections. 



A table of square numbers, like that of Professor Barlow, will 

 be found very useful in these computations. 



v. Remarlcson Mr. Plana's Researches relating to Refraction. 



In a Letter to Professor Gautier. 

 My dear Sir, 



I believe it is to you that I am indebted, or perhaps 

 to Baron Zach, for the notice that Mr. Plana has been 

 pleased to take of my papers on Refraction : and I consider 

 myself as obliged to this justly celebrated mathematician, 

 not only for the flattering terms in which he has mentioned my 

 name, but also for the forbearance with which he has hinted at 

 what appears to him to be an unfounded objection to Laplace's 

 hypothesis ; at the same time, that he has endeavoured to sub- 

 stitute another objection to that hypothesis, which will, per- 

 haps, be still more easily superseded. I hope also to be al- 

 lowed, in return for these services, to set Mr. Plana right upon 

 a point of physical optics, respecting which he is both essen- 

 tially and accidentally in error : essentially, because, he mis- 

 takes the ground upon which I have founded my optical rea- 

 soning ; and accidentally, because the error, if it had existed, 

 would have been of no consequence whatever to the result. 



I might, perhaps, be justifiable in complaining, that in a sec- 

 tion devoted to the history of the late researches on refraction, 

 Mr. Plana has only mentioned my attempts, in order to express 

 his surprise at this supposed error, and that he has not thought 

 it necessary to take the shghtest notice of the real innovation 

 that I have ventured to make in the investigation. The history 

 of my paper might have been expressed very shortly, by saying 

 that it was " a Method of computing the Atmospheric Refrac- 

 tion, upon any possible hypothesis, by means of a series which 

 expresses the density in terms of the integer powers of the re- 

 fraction itself; a series converging rapidly in all ordinary cases, 

 and converging sufficiently, even in the extreme cases near the 

 horizon. Mr. Plana not having noticed this distinguishing cha- 

 racteristic of my little invention, I shall endeavour to impress 

 it on his mind, by one more instance of the facility with which 

 it may be employed ; and I shall offer him, for this purpose, an 



