On Refraction. 4 57 



responding to it, which is readily done at the same opening 

 of the book. Double this logarithmic cosine, and it is the 

 logarithm required of 1 — h?i*. 



But in a letter dated 17th September 1810, which I 

 had the honour to receive from Mr. Groombridge, he in- 

 forms me that he has calculated on the data before men- 

 tioned a Table of Refraction for every io'down to 70° of 

 zenith distance; for every 5' from thence down to 86°; 

 for each 4' thence to 88°; each 6 thence to 89°; and for 

 everv %' from thence to 90° 18': together with an auxiliary 

 Table for the correction depending on the difference of the 

 barometer and thermometer from the mean state. He has 

 also contrived some very simple methods of performing 

 with great facility whatever arithmetic operations may be 

 requisite in using them. Every sincere lover of the science 

 will no doubt join with me in requesting that these tables 

 and methods may form the subject of another communica- 

 tion to the world, whereby it is presumed the mode of find- 

 ing the refraction will be made extremely easy, and an im- 

 portant service rendered to astronomy. 



As an appendix to what has been said on the refraction, 

 I shall take the liberty of adding the following method of 

 finding the sun's parallax, which is rather more accurate 

 than as it is usually given in the Tables. Add together the 

 logarithmic sine of Ike sun's zenith distance, the logarithmic 

 distance for the given day taken from page iii Nautical Al- 

 manack, and the constant number 094151 : their sum, re- 

 jecting the tens in the index, will be the logarithm of the 

 sun's parallax in seconds. 



It must however be observed, that 1 have taken the sun's 

 mean horizontal parallax at 8"*74: for it was found f by 

 observations made at the Cape of Good Hope, as well as 

 others made by M. Pingre and Mr. Short, 8"*8; by M. du 

 Sejour, 8*84; by M. Lexell and M. de la Lande, 8"*6. 

 The mean of these six determinations is 8"* 74, which is the 

 quantity we have adopted above. 



* When the thermometer is below zero, this expression will of course 

 become 1 + f >n, in which case it may, as above, be compared with 1 + f 1 —f 1 . 

 but instances are extremely rare where any necessity for this occurs in En- 

 gland. 



f La Lande's Astronomy, art. 1725,3d edit. 



LXXXI. Be- 



