REFRACTION. 



utmod pains to avoid errors of two or three fceoiids, to 

 find hii reduced obfervationj liable to fo great an error, ac. 

 cording to the choice of his table of refraftioii. 



Il is indeed rather extraordinary, that in a memoir pub- 

 liflied by CalTini de Thury, among thofe of tlie Acaaemy 

 for 1 745, he attempted to reconcile a number of obfervations 

 with each other, by conlidering the Hate of the thermometer 

 only, without at all noticing that of the barometer ; al- 

 though at that time Hauklhee's experiments had been 

 publiftied about 37 years. 



He concludeo his paper, as is very natural to fuppofe, 

 without being able to make the obfervations agree : nor 

 does it clearly appear that the French noticed the above- 

 mentioned experiments made by Hauklbee till about the 

 year 1749. It is alfo worthy of remark, that although the 

 ncceflity of ii-.troducing correftions on account of the alte- 

 rations of the barometer and thermometer were likewife 

 fliewn to be abfolutely neceflary by Dr. Hallcy (Phil. Tranf. 

 N°364), and the circumftance mentioned, and in fome de- 

 gree admitted by Le Monnier (Hift. Ccleil.), yet it does 

 not appear that he followed the advice of hts illutlrious con- 

 temporary, but merely endeavoured, as CafTini did, to re- 

 concile his obfervations with the ftate of the tliermometer 

 at the time of making thefe obfervations, without taking the 

 barometer into account. 



It would be endlefs to notice the different opinions re- 

 fpefting both the terreftrial and the aftronomic refraction 

 which are to be met with in the writings of various authors 

 on the fubjeft : and it would be equally ufelefs to notice all 

 the tables of its quantity given by them, fome of which dif- 

 fer very much from others. It will be fufficient to mention 

 thofe only who made fome confiderable advances towards 

 obtaining it with greater accuracy. 



The next of thefe in order was La Caillc( Mem. del'Ac. de 



Sc. 17551 p- 547-)> who in determining it certainly bcltowed 



very great pains, by makmg and reducing an immenfe number 



of obfervations, and afterwards comparing them with others 



made at Greenwich by Dr. Bradley, at Gottingen by 



Mayer, at Bologna by Zanotti, and by La Lande, who was 



then at Berlin. From thefe it appeared that the refradtiou 



at 45^ of altitude was i' 65" ; but this, as will hereafter be 



feen, was too great by fome feconds. In his paper on the 



fubjeft, which is divided into four parts, he proves, firft, 



that the mean refratlions are very nearly the fame for the 



fame apparent altitudes tliroughout the whole extent of the 



temperate zone ; fince thofe which were obferved at Paris 



did not exceed thofe obferved at the Cape of Good Hope 



but by ^V at molL In the fecond he determines the abfo- 



lute quantity of the mean refi-aftion for the apparent height 



of the pole at Paris, and gives the refult of his obfervations 



with regard to the latitude of Paris and of the Cape of 



Good Hope. In the third he gives his table of mean re- 



fraftion, and another of corrcftions depending upon the 



ilate of tiie barometer and thermometer ; concluding with 



fome refleftions on its conilrudiion and ufe. In the fourth 



he compares his new table with the moll celebrated of thofe 



that had before that time been in ufe among aftronomers ; 



and he then ihews how it agrees with the obfervations of 



Bradley, Zanotti, and Mayer. 



But bv La Caille's memoir it appears, that previous to 

 this time M. Mayer had formed and communicated to him a 

 table of aftronomic refradions which he computed by means 

 of an algel)raic formula, the co-efficients of which he de- 

 duced from his own obiervations, and took into account the 

 variations relative to thofe of the barometer and thermome- 

 ter. He found the alteration of refraftion for a depreflion 

 of 15 lines in the barometer, the fame as for a rife of 10° 

 in the thermometer, and the variation for each degree of 



the latter, according to his table, ^'^ of the whole mean 

 refraftion, wliich lie adapted for 28 inches of the barometer, 

 and o" of tlic thermometer. This proportion takes place 

 down to 80" of zenith diftatice. Mayer confidered alfo • 

 that the mean refraction is the fame for all parts of the earth ; 

 3nd that the only variation which takes place depends 

 on the changes of tfec weight and temperature of the 

 atmofphere. 



I^a Caille, in comparing Mayer's table with obfervations', 

 found that his corredtion for the thermometer was a little 

 over-rated ; and accordingly, for his new table, altered it 

 to tV ^o"" '^''ch degree. And here it may be obferved that 

 La Caille did not correct his altitudes above 36' at Paris, 

 and 30° at the Cape ; firit, becaufe he only noted the barome- 

 ter and thermometer in the night, when he obferved ftar^ 

 below 30° of altitude. Secondly, becaufe, that at 36" of 

 altitude, where tlse mean refraction is about linrinute, the 

 variation which belongs to 10° of tlie thermometer oiily 

 amounts to ^^ feconds ; a quantity about equal to tiie 

 limits of the errors of obfervations made willi an inltrument 

 of fix feet. 



The formula given by Euler (Mem. de l'.\c. de Berlin, 

 1754, p. 1 3 {.), appeared alfo about this time. It took into 

 account tlie variation of the refraction depending upon the 

 thermometer and barometer, but was certainly too com- 

 plicated to be generally adopted. He (hews, however, 

 that in very different hypothefes the refraftion will be fufii- 

 ciently exact, if taken in the inverfe ratio of the degrees 

 of heat, when the liar or planet is not too near the ho- 

 rizon, but the precife quantity of this ratio was unknown 

 to him. 



In this ftate the refraction ftood w!)en Dr. Bradley took 

 the fubjcct into confideration, and began to find its quantity 

 from his own obfervations. The rule which he adopted, 

 although a very elegant one, he neither lived to complete 

 nor to prefent to the world ; but it was pubhfhed after hi-^ 

 death by Dr. Malkelyne, (Pref. to iftvol. of Obf. 1765. 

 Phil. Tranf. i764and 1787, p. 157. Req. Tables, &c.), 

 and has commonly been ufed in England up to the prefent 

 time. He found the mean rcfradtion at 45° of altitude 

 57", and, that at all other altitudes, it was equal to 57" 

 multiplied by the tangent of the zenith diftance, diminifhed 

 by three times the refradtion. Then fuppofing the mean 

 ftate of the atmofphere to be at 2g.6 inches of the baro- 

 meter, and 50° of Fahrenheit's thermometer, he made the 

 true or corrected refradtion equal to 57" x t, (Z. D. — 3 r) 



barom. 400 ... , 



X ;^ X ; — , where it is to be underllood 



29.6 350 -1- ther. 



that the mafs of air is fuppofed to increafe in bulk ^j_ for 

 each degree of Fahrenheit's fcale. 



A variety of experiments has been made at various 

 times to afcertain the increafe in bulk of a quantity of air 

 reprefented by unity for a certain number of degrees of rife 

 of the thermometer. The following is a lift of lome of them ; 



for 1° 



M. Bonne ... 



Bradley - . . . 



Dalton . . . . 



De Luc . - . . 



Fahrenheit - . - . 



Gay Liifiac . . . 



Groombridoe . . . 



o 



Hauklbee . . . . 



La Caille . . - 



Mayer . . . . 



Shuckburg . . . 

 Mean of all except Hauklhee's 



i.oo 25777 



1. 00 2 J 000 



i.co 207C1 

 1.00 20888 



1.00 25777 



1.00 2086S 



1.00 2 1000 



1 .00 0693 ^ 



1.00 22222 



I.OO 20444 



I.OO 22222 

 1.00 22490 



The 



