REFRACTION. 



objedle. In order to fubtnit the phenomena of rcfraftion to 

 ftridl mathematical invclligation, it mull be obfervcd that, 

 in confequence of the inconfKlerable height of the at- 

 mofphere, and its fpherical form, a himinous ray impinging 

 upon it, even in the mod unfavourable cafe, that is directly 

 in the horizon, traverfos only a fmall quantity of this me- 

 dium ; and in this fpace, if the atmofphere is calm, the den- 

 fity of the air at equal heights above the level of the fea is 

 every where the fame. Therefore, in fuppofmg the earth 

 fpherical, a fuppofition whicli may be admitted, in the prelent 

 cafe, without any fenfible error, we may coniider the at- 

 mofphere as compofed of fucceflive fpherical concentric 

 (hells, or ttrata, of which the denfity diminiflies from the 

 furface of the earth upwards. 



L.et us conceive, now, a luminous ray, coming from a 

 diftance, to penetrate into one of the fuppofed fpherical 

 (hells ; then, if through the common centre of thcfe fliells, 

 which is the fame as the centre of the earth, we fuppofe a 

 plane to pafs ih the direftion of the luminous ray, the fphe- 

 rical beds of the atmofphere will be found divided into two 

 equal portions, which afting equally upon the ray, tan pro- 

 duce no deviation of it from that plane; whence it follows, 

 that the effeft of refraftion is entirely produced in a vertical 

 direftion, and in fuch a manner as to augment the apparent 

 altitudes of the heavenly bodies, and confequently to diini- 

 ni(h their zenith diilances. 



But the intenfity of thefe effefts will not be the fame at 

 all heights, for we know that in all cafes the quantity of re- 

 fraftion depends upon the obliquity of incidence, and there- 

 fore the refraftion in the zenith is equal to zero, and iu- 

 creafes from that poffit to the horizon, where it is the 

 greatefU 



If, now, we knew the law by which the denfity ol the 

 air is diminifhed in afcending from the earth, that is, if we 

 knew the difference in the denlity of any two confeculive 

 Itrata, it would be comparatively a direft and eafy problem 

 to find the whole amount of refraftion for any given angle 

 of obfervatioii ; but unfortunately the uniformity of de- 

 creafe in the denfity of the atmofphere, which, according 

 to theory, is in geometrical progreffion, is fo much inter- 

 rupted by the multitude of caufes which may tend to pro- 

 duce this effedt, that it is found that the quantity of refrac- 

 tion computed on this principle, will by no means agree 

 with that deduced from aftual obfervation. It has been, 

 ' however, demonftrated, that the quantity of refraftion, in 

 all cafes exceeding to or 12 degrees of elevation, isnotlen- 

 fibly affefted by any irregularity in the law of denfity, in 

 the ftrata of which we have fuppofed the atmofphere to be 

 • compofed, but that it depends fimply upon its pretlure and 

 temperature at the time and place of obfervation, which are 

 indicated ,at the time by the barometer and thermometer. 

 It, was formerly thought, alfo, that refraftion was influenced 

 by the degree of humidity and drynefs of the air ; but from 

 a great variety of interefling and accurate experiments, 

 carried on by- M. M. Biot and Arrago, it appears indif- 

 putably eftablifhed, that no fenfible efFett is thence pro- 

 duced. See a memoir on this fubjeft by the former author, 

 in vol, X. of the National Inftitute. 



But before we proceed farther on this interefling fubjeft, 

 it will be proper to give a flcetch of the feveral improvements 

 which the theory has experienced in the hands of different 

 celebrated aflionomers ; in doing which we (liall avail our- 

 felves of a memoir, publilhed by Dr. T. S. Evans in the 

 Philofophical Magazine, which contains a minute and cir- 

 cumftantial detail of many important particulars connefted 

 with this fubjeft. There appears to be but little doubt 



that the aflronomic refraftion was known to the ancients, 

 fince it is exprefsly mentioned by Ptolemy, although not 

 made ufe of in his calculations. He fays, near the end of 

 the 8tli book of the Almageft, that in the rifing and fetting 

 of the heavenly bodies, there arc changes which depend 

 upon the atmofphere, and he mentions it more at length in 

 a work on optics, which, unfortunately, has not been 

 handed down to us. Alhazen, an Arabian writer, who is 

 generally fuppofed to have lived about the year iioo, and 

 to have taken the greater part of his optics from the works 

 of Ptolemy, fpeaks alio decidedly of it, and fhews the man- 

 ner of convincing ourfelves of it by experiment. " Take," 

 fays he, " an armiilary, which turns round its poles, and 

 meafure the diflance of a flar from the pole of the world 

 when it pailes near the zenith in the meridian, and when it 

 is rifing or fetting near the horizon, and you will find the 

 diflance ir«m the pole lefsin the latter cafe." He then de- 

 monflrates that this muft arife from refraftion, but he does 

 not ftate its quantity. 



In the colleftion of obfervations made by Bernard 

 Walter, and publifhed by Willebrode Snell in 161 8, it 

 is ilated, that the obfervations were fo exaft, that they 

 pointed out to Walter the quantities by which the alti- 

 tudes of the ftars and planets ivere increafed on account of 

 the refraftion. 



Tycho Brahe, however, appears to be the firfl who 

 afferted, with any degree of accuracy, that the refraftion 

 elevates the heavenly bodies rather more than half a degree 

 when on the horizon. (See Progymn. p. ij.) But either 

 his inftruments or his obfervations were not fufficiently cor- 

 reft to determine it with certainty for all degrees from the 

 zenith to the horizon ; and, accordingly, where thefe failed, 

 the refl were fupplied by conjefture. He believed that 

 the fun's refraftion was 34' in the horizon, and that it be- 

 came infenfible at 45° of altitude. For the flars, however, 

 he afTumed an entirely different quantity, -viz. 30' in the 

 horizon ; but this, according to him, terminated at only 

 20° of altitude. 



The following is the manner in which it is related 

 (Encly. Method.) that Tycho made this difcovery. He 

 had determined, with one or two inftruments extremely 

 well made, tlie latitude of the place by obfervations of 

 Polaris above and below the pole. He determined it alfo 

 by the fun's altitude in both folflices, and found it four 

 minutes lefs in the latter. At firfl he doubted the good- 

 nefs of his inilruments, and therefore conflrufted, with the 

 utmoft care, as many as ten others, of different fizes and 

 forms, but they all gave nearly the fame refults. He 

 could, therefore, no longer attribute this difference in the 

 two determinations of the latitude to any defeft in the 

 obfervations, but endeavoured, by an attentive confidera- 

 tion of the fubjeft, to find out the caufe of this'fingular 

 phenomenon. At length he fuppofed it could only arife 

 from the refraftion which elevated the fun at the winter 

 folflice, having then only ii° of elevation above the horizon. 

 This refult agreed very well with the principles of optics ; 

 but ilill Tycho Brahe could fearccly perfuade himfelf that 

 the refraftion was fufficiently large to produce fo great a 

 difference. On this account, lie made other inftruments of 

 ten feet diameter, vvhofe axes correfponded exattly with the 

 pole of the world, and with thefe he nieafured the declina- 

 tion of the ftars out of the meridian. He then found, that 

 even in fummer the refraftion, although infenfible at the 

 meridian altitude of the fun, was very confiderable near the 

 horizon, and amounted to half a degree in the horizon. See 

 Progymn. p. •;(/ — 104. Street's Aftr. Carol, p. i uj. 



4F 2 Tycho 



