REFRACTION. 



Now Z aiid « R being known, we may compute the feconj 

 iide of this equation ; whence tlie arc Z — 2 n ;• is known, 

 and coiifequeiitly 2 n r ; whicli, divldi-d by 2 7;, will give r, 

 as required. But it iray bo found itill more limply by the 

 formula, 



tan. «r = tan. n R tan. A n ; 

 tan. « being- found by means of the auxiliary equation, 



tan. a =: fin." n R . tan. Z. 



On the principle above explained, the following table of 

 vefraClions has been computed, agreeing with the tempera- 

 ture of + 14^ on the centigrade thermometer, and under a 

 preflure of 0.76 metres of the barometer ; which is the fame 

 as 57°.2 Fahrenheit, and 29.922 Englifh inches. And for 

 auv other temperature and preilure, the correfponding cor- 

 reftions muft be made as indicated in Tables II. and III. ; 

 which tables are computed by means of the general formula 

 given in the preceding part of this article. 



We had intended to give here a (hort abflraft of a very 

 interefting paper on this fubjedl, publifhed by Mr. Groom- 

 bridge, in the Philofophical Tranfaclions for i8io; but 

 having already exceeded our ufual limits, we can only refer 

 the reader to the volume itfelf, where he will find feveral 

 neat and ufeful fonuula:. 



Having thus given a fketch of the method of determining 

 the quantity of altronomical refraftion for all angles of ele- 

 vation, and under various degrees of temperature and baro- 

 metric preflure, let us add a few words on the fubjeft of 

 terreflrial or horizontal refraflion ; for the determination of 

 which, the following method has been fuccefsfully pradlifed 

 in the Englifh Trigonometrical Survey. 



Let A, A', ( Plate XIX. AJlroiwmy,fg. 1 1 .) be two elevated 

 places on the furface of the earth ; B D, the intercepted arc 

 of the earth's furface ; C, the centre of the earth ; A H', 

 A' H, the horizontal lines at A, A', produced to meet the 

 oppofite vertical lines C H', C H. Let a, a', reprefent the 

 apparent places of the objedls A, A' ; then is a' A A' the 

 refraftion obferved at A, and a A' A the refraftion ob- 

 ferved at A' ; and half the fum of thefe angles will be 

 the horizontal refraftion, if we affume it equal at each 

 ftation. 



Now an inftrument being placed at each of thefe ftations 

 A, A', the reciprocal obfervations are made at tiie fame in- 

 ftant of time, which is determined by means of fignals or 

 watches previoufly regulated for that purpofc ; that is, the 

 obferver at A takes the apparent depreffion of A', at the 



fame moment that the other obferver taker> tie apparent de- 

 prellion of A. Tiien, in the quadrilateral A C A I, the two 

 angles A, A', are right angles, and confequently the angles 

 T and C are together equal to two right angles ; but the three 

 angles of the triangle I A A', are together equal to two right 

 angles ; and confequently the angles A and A' arc together 

 equal to the angle C, which is meafured by the arc B D. If, 

 therefore, the fum of the two deprefTions li A' a, H' A a, be 

 taken from the fum of the angles H A' A, and H' A A', or, 

 which is equivalent, from the angle C, (which ib known, be- 

 caufe its meafure B D is known,) the remainder is the fum of 

 the two refraftions. Hence this rule, " take the fum of 

 the two deprefr.ons from the meafure of the intercepted ter- 

 reflrial arc, half the remainder is tlie refraction. " If, by reafon 

 of the minutenefs of the contained arc B D, one of the ob- 

 jefts, inllead of being deprefled below the tangent A H', ap- 

 pears elevated, as fuppofe A to a", then the fum of the 

 angles fl" A A', and a A' A, will be greater than the fum 

 I A A' + I A' A, or than C,' by the angle of elevation 

 a" A A' ; but if from the former fum there be taken the de- 

 preffion HA' A, there will remain the fum of the two re- 

 fraftions, fo that in this cafe the rule becomes as follows : 

 " Take the depreffion from the fum of the contained arc and 

 elevation, and half the remainder is the refraftion." 



The quantity of this terreflrial refraftion is eilimated by 

 Dr. Maflcelyne at one-tenth of the diftancc of the objcft ob- 

 ferved, expreffed in degrees of a great circle. Whence, if 

 the diftauce be 10,000 fathoms, its loth part, 1000 fa- 

 thoms, is the 60th part of a degree, or one minute, which, 

 therefore, is the refraftion in altitude of the objeft at 

 that diftance. But Le Gendre is induced, by feveral experi- 

 ments, to allow only one-fourteenth part of the diftance for 

 the refraftion in the altitude, fo that on the diftance of 

 10,000 fathoms, the 14th part of which is 714 fathoms, he 

 allows only 44" of terreflrial refraftion, fo many being con- 

 tained in 714 fathoms. (See his Memoir on the Trigonome- 

 trical Operations.) Again, Delambre makes the quantity 

 of terreflrial refraftion to be one-eleventh part of the arc of 

 diftance. And the Englifh mealurers, from many very exaft 

 obfervations, determine the quanfity of the medium refrac- 

 tion to be a twelfth part of the faid diftance. The mean of 

 all thefe is about .085 of the intercepted arc, which is pro- 

 bably not very far from the truth : this quantity, however, 

 it muft be obferved, is found to vary very confiderably with 

 the different flates of the weather and atmofphere, from 

 one-feventh to one-eighteenth of the contained arc. 



Table- 



