REFRACTION. 



{rafted by different layers of the atmofphcre, increafing in 

 denfity as they approach the earth, and, confequeiitly, bend- 

 ing the ray more and more from the right Hue which it 

 delcribed in the vacuum previous to its reaching the atmo- 

 fphere. There are many autliors vvlio have endeavoured to 

 find from theory the curve defcribed by this ray in its 

 courfc, by the affumptiou of various hypothefes ; but pcr- 

 feftion, and our attempts to arrive at it, as is well obfervcd 

 by the elder Caflini in difcourfing on this fubjcft, are like 

 the progrefs of certani curves and their afymptotes. The 

 principal of thefe writers on the fubjeft are Bernouilli 

 (Hydrodyn. 1738, p. 221.) ; Bofcovich (Oper. tom. ii.) ; 

 Bougucr (Prix de 1729. Mcmoires, 1739, p- 407 ; 1749, 

 p. 75.) ; Caflini (Epilh ad Montanari, 1665. Retraffioni 

 e Parallofi'e, &c. 1671. Mem. for 1714, and his Aftr. vol. i. 

 p. II. Paris, 1740, in 2 vols. 4to.) ; Defcartes (Diop- 

 trique, 4to. Paris, 1637) ; De la Grange (Nouveaux Mc- 

 moires de Berlin, vol. iii.) ; Euler (Mem. de Berlin, 1754, 

 tom. X.) ; Gregory (Aitronomy, vol. i. p. 358. edit, of 

 1715, iu 8vo.) ; Hodgfon (Mathematics, vol. i. p. 367. 

 Fluxions, p. 133.) ; Huygens (Traite de la Lumiere, p. 44. 

 Dioptrica, 4to. 1703) ; Kramp (Analyfedes Refracl. Allr. 

 ct Terres, 410. Strafburg, 1799) ; Lambert (Les Pro- 

 prietcs Remarquables de la Route de la Lumiere. A la 

 Haye, 1759. Another edition in German, 1773) ; La 

 Place (Mecanique Cclelte, vol. iv. p. 231.) ; Mayer (Tables, 

 1770) ; Newton (Principia, b.i. fec't. 14.) ; Oriani (Ephem. 

 de Milan. 1788) ; Thomas Simpfon (Mathematical Differta- 

 tions, 1743) ; Brook Taylor (Methodus Incrementorum, 

 4to. Lond. 1715. PropoC. 27. p. 108.); Heinfius (Difl'er- 

 tatio dc Computo refraftionum Aftron. 410. Leipfig, 1749) ; 

 Tobias Mayer (De Retrattionibus Aftronomicis, 410. Al- 

 torf. 1781); La Hire (Mem. de I'Acad. pour 1702, 

 p. 52.) ; d'Alembert (Opulcules Mathematiques, tom. viii. 

 p. 297.) 



It was conjeftured by many of tlie early writers, that tlie 

 rcfraftion was fubjeft to variations depending upon the 

 weather : but it then amounted to little more than a con- 

 jefture, on account of the indifferent manner in which 

 allronomic inilruments were divided. Picard found by 

 meridian altitudes of the fun in 1669, that it was greatc" in 

 v.icter than in fummer. He found alfo that it was lefs by 

 day than by night. In the obfervations given at the end 

 of his journey to Uraniburg, to fettle the latitude of that 

 place, and its difference of longitude from Paris, for the 

 purpofe of comparing the obfervations of Tycho Brahe 

 with thofe made at the Royal Obferv'atory of Paris, he 

 found the horizontal refraftion for the firll limb of the fun 

 that made its appearance above the horizon there 33' 2", 

 and for the fecond 32' 37". So that in the fmall interval of 

 time that the fun was in rifmg, the refraftion was diminilhed 

 25 feconds by the warmth arifing from the fun's prefence. 



A quadrant being alio direfted by him from the top of 

 Mount Valerian towards the fummit of the church of Notre 

 Dame at Paris, he found the deprcffion 20' ; but the fun 

 had fcarcely rifen, when it was increafed to 22'; exhala- 

 tions being raifed by the fun's pnefence, and the medium 

 between Paris and Mount Valerian become more equal ; 

 whereas, before the fun rofe, the air of Paris was more denfe 

 than that of Mount Valerian. 



The denfity of the atmofphere being the immediate caufe 

 of the refraftion, it was very natural to fuppofe that it mull 

 decreafe as this denfity became lefs ; whether by caufes 

 which diminifhed its weight, or by the expanfion produced 

 by heat : and, indeed, aftronomers were not long after this, 

 before they difcovered that very fenfible differences were oc- 

 cafioned by thefe circumftances. 



But all the honour of introducing corredlions on account 



of the variation of denfity in the atmofphere, as indicated 

 by the barometer and thermometer, is due to Meffrs. Low- 

 thorpe and Haukfbee ; the former of whom, in 1698, 

 proved by a very limple experiment, in the prefence of the 

 Royal Society, that the refraftive power of air is direftly 

 proportional to its denfity : and tlie latter, by repeating and 

 extending the fame courfc of experiments in the year 1708, 

 with the- machinery pointed out by the former, found that 

 tlie variations ot reiradtion, depending on the barometer, are 

 proportional to the alteration of height of the mercury in the 

 tube : and by a feries of thefe experiments, he furnifhed us 

 with a table of the correftions which it is necefi'ary to make 

 on account of the changes of heat indicated by the ther- 

 mometer. Thefe experiments, although not quite conclufive 

 on the fubjeft, were yet made with as much accuracy and care 

 as the nature of the machinery, and the ftate of experimental 

 philofophy of that time, would admit. An example is alfo 

 given, towards the end of his paper, on the mode of apply- 

 ing them to correft the refraftion. By thefe, Haukfbee 

 found that a volume of air exprefied by unity, when the 

 thermometer was at 1 80*^ above zero, became, at 50° be- 

 low, one-eighth more denfe : or, which is the fame thing, 

 that the air loit one-eighth of its denfity, for an elevation 

 of 180'' of Fahrenheit's thermometer ; which is exaftly the 

 difference of heat between melting ice and boiling water. 

 But although tliis one-eighth, as will be fhewn hereafter, 

 was too fmall ; yet it laid the foundation for other experi- 

 ments, fince made by fevcral philofophers, by which the 

 quantity of expanfion has been determined more accurately. 



We have already flievvn that the refraftion near the pole 

 is greater than in our climate ; the degree of cold being 

 more intenfe. It was alfo found to be lefs in the torrid zone, 

 .where the heat is greater than in Europe. Bouguer made a 

 variety of obfervations at Peru, the refult of which he has 

 given us. In 1740, he came down into an ifland fituated 

 in the river of Emeralds, called ifle of Inca, where he de- 

 termined the refraftion from 1° to 7° of altitude; and the 

 table which he afterwards computed fliews the refraftion to 

 be about one-feventh lefs than in Europe. The horizontal 

 refraftion he found to be 27' : but at 6° of altitude it is 7' 4" ; 

 and at 45°, it is 44". Bouguer then gives a table for Quito, 

 which is more elevated above the level of the fea. M. le 

 Gentil found it greater at Pondicherry in India, although 

 in the torrid zone. 



The refraftion diminifhes when we are elevated above the 

 level of the fea. Bouguer obferved the quantity of it at 

 Chimboraco, 23SS toifes above the level of the fea, and 

 found it ill the horizon only 19^'. At the crofs of Pit- 

 chinca, 2044 toifes above the fea, he found it 20' 48" ; at 

 Quito, 1479 toifes above the fea, 22' 50": but at the level 

 ot the fea 27'. Thefe obfervations, when joined with the 

 tlieory, produced the following rule ; -viz. if we take the 

 excefs of 5158 toifes above the elevation of the place, with 

 regard to the level of the fea, the refraftion will be as the 

 fquare root of this excefs. Thus the fquare root of 5158 

 toifes is 27', for the horizontal refraftion, at the level of 

 the fea, in the torrid zone : and the fquare root of the excefs 

 of 5158 above the elevation of the place will be its horizon- 

 tal refraftion. The quantity 5158 is the height above which 

 the refraftive matter no longer produces any fenfible effeft, 

 at leail in the torrid zone. 



But although by this time confiderable attention had been 

 paid to the fubjeft, yet great differences were to be found in 

 the tables then moil in ufe. Thus at the altitude of 30°, 

 according to Flamfteed, the refraftion was i'23"; New- 

 ton, i'3o"; Caffini, i'42''; and de la Hire, i' 55'' ; leaving 

 an uncertainty of more than half a minute : and it mufl have 

 been very mortifying to an obferver, after having taken the 



utmoll 



