ALT 



We may hence deduce a method of finding the height of 

 one objeft, as AC, fitiiatc upon anotlier HC. Find, firft, 

 the wholo altitude AC, and then the altitude of HC, as 

 above, and tlieir difference will be the altitude of AH, as 

 e. g. of a fpire above the tower of a lleeple. If the height 

 of the tower HC be known, any diftance DF in the hori- 

 zontal line DC may be meafured from H. This is the 

 rcverfc of the preceding problem. 



To meafure the altitude of a balloon, cloud, or other 

 moveable obiect, C ; (Ji^^. 1 1.) let two obfer\'ers at A and 

 B, in the fame hori/.ontal plane, take, at the fame time, the 

 angles CAD and CBD, and meafure the dillance AB be- 

 tween the ftations ; and then the altitude may be calculatud 

 as bffore. The height of a cloud may be found by its 

 fliadow in the following manner. Obferve the cloud C, 

 (fg. 1 2.) in its direft accefs to or recefa froin you ; and mark- 

 ing the inllaiit in which the middle of the (hadow is at fome 

 remarkable point upon the ground as at A, at that mo- 

 ment take the altit\ide ABC of the middle of the cloud. 

 Then, take the fun's altitude at your ftation B, and that 

 will be equal to the angle BAC, and meafure the diilance 

 between your llation and the place of the ihadow. In the 

 triangle ABC, as all the angles and one fide are known, it 

 may be eafily projeftcd, and the height of C above B A may 

 be determined : or it may be refolved trigonometrically thus : 



S. B 



fine of C 



AC = 



rad. : AC 



i4 



s.c 



X AB; and 



S.A 



; the perpendicular; 

 S. B : the height. 



AB : : fme of B 

 S.B \ 



or rad. x S. C : AB : : S. A X 



If the cloud be direftly over your head at the time of ob- 



fervation, CBA will be a right angle ; and rad. : AB : : 



tangent of the fun's altitude CAB : the height CB. 



N. B. The cloud (liould be fmall, becaufe the obfervation 



muft be at a point. If the cloud be large, its edge as well 



as the edge of the fhadow muft he obfei-ved ; and the ftations 



muft be upon a large plain or open ground. 



To find an inacccflible altitude by the fhadow, or the 



geometrical quadrat. — Choofe two ftations in D and H 

 (j/ff. 9.) and find the diftance DH, orCG; obferve what 



part of either the right or verfed fliadow is cut by the 



thread. 



If the right ftiadow be cut in both ftations, fay, as the 



difference of the right ftiadow in the two ftations, is to the 

 fide of the fquare ; fo is the diftance of the ftations GC to the 

 altitude E A. — If the thread cut the verfed ftiadow at both 

 ftations, fay, as the difference of the verfed fliadow marked 

 at the two ftations, is to the leffer verfed fhadow ; fo is the 



diftance of the ftations GC, to the interval AE Which 



being had, the altitude E B is alfo found by means of the 

 verfed ftiadow in G ; as in the problem for acceffible alti- 

 tudes. Laftly, if the thread in the firft ftation G, cut the 

 right fliadow, and in the latter, the verfed fhadow ; fay, 

 as the difference of the produftof the right ftiadow into the 

 verfed, fubtrafted from the fquare of the fide of tlie quadrat, 

 is to the produA of the fide of the quadrat into the verfed 

 fhadow ; fo is the diftance of the ftations GC, to the alti- 

 tude required AE. 



The utmoft diftance at which an objeft may be feen in 

 the horizon, being given, to find its altitude. 



Snppofe the top H of a tower FH {Jig. 13.) juft vifibte 

 at E, the diftance EF being 25 miles; and fuppofe the 

 circumference of the earth to be 25000 miles, or the radius 

 3979 miles, or 21009120 feet. Then 25000 : 25 : : 360° 

 J 21' 36" =the angle EGH} and radius : fecant of the 



ALT 



angle G : : EG : GH = 21009536 feet ; and 21009536 

 — 21009120 =: 416 feet or FH the height of the tower. 



Otherwife. — In thu right-angled triangle G EH, GH'or 

 GF' + 2 OF X FH + FH' = GE' -t- EH'. But GE 

 being = GF, 2 GF X FH -!- F,H^ = EH', or, FH being 

 comparatively very fmall, 2 G F x F H = E H" = E F', 



EF' 

 and FH =: "TTT^' but 2 GF, or the earth's diameter, is 



2vTi. 



EF' . . EF'xi76o 



79,58 miles, therefore ^= FH in miles, and 5 



'-^■^ . 795*^ 7958 



= FH in yards. 



Or, the altitude FH may more eafily be found thus. 

 The horizon dips nearly eight inches or f of a foot, at the 

 diftance of one mile, and according to the fquare of the 

 diftance for other intervals ; therefore, as i' or 1 : 25' or 

 625 : : f : f of 625 or 416 feet. 



The method of taking confiderable terreftrial ahitmles, 

 of which thofe of mountains are the gixateft, bv means of the 

 barometer, is very eafy and expeditious. This is done by 

 obferving on tliL- top of the mountain how many inches, &c. 

 the mercury is fallen below what it was at the foot of the 

 mountain. When this is done, you will have its altitude by 

 the help of a table calculated for that purpofe. A very 

 accurate table of this kind may be found in the Hift. de 

 I'Acad. Roy. des Scien. 1703, and 1705, calculated by M. 

 Caflini ; and alfo in the Phil. Tranf. Eames's and Martyn's 

 Abr. vol. vi. p. 34. See Barometer. 



Altitude of the eye, in Perfpedi-ve, is a right line let 

 fall from the eye, perpendicular to the geometrical plane. 

 See Perspective. 



Altitude, in AJlronomy, is an arc of a vertical circle, in- 

 tercepted between the fun, moon, ftar, or other celeftial 

 obieft', and the horizon. 



This altitude may be either tnii or apparent. If it be 

 taken from the rational, or real horizon, the altitude is faid 

 to be true, or real; if from the apparent or fenfible horizon, 

 the altitude is apparent. Or rather, the apparent altitude is 

 fuch as refults from obfervations made at any place on the 

 furface of the earth, and the true is that which has been 

 correfted, on account of the refrattion and parallax. 



The true altitudes of the fun and fixed ftars differ but very 

 little from their apparent altitudes ; becaufe of their great 

 diftance from the centre of the earth, and the fmallnefs of 

 the earth's femidiameter, when compared with it. The 

 quantity of refraftion is different at different altitudes, and 

 the parallax is different according to the diftance of celeftial 

 objects ; in the fixed ftars it is too imall to be obferved ; 

 that of the fun is about 8f feconds, and that of the moon 

 about 52 minutes. The altitudes of the heavenly bodies 

 are obferved by a quadrant or fextant, or by the ftiadow of 

 a gnomon, and by various other ways may be found without 

 a quadrant, or any the like inftrument, by ereCling a pin or 

 wire perpendicularly as in the point C {^AJlronomy, Plate I. 

 Jig. 5.) from which point you have defcribed the quadrantal 

 arc A F. Make C E equal to the height of the pin or 

 wire, and through E draw ED parallel to CA, and make 

 it equal to CG, the length of the ftiadow ; then will a ruler, 

 laid from C to D, interfetl the quadrant in B ; and B A is the 

 arc of the fun's altitude, when meafured on the line of chords. 

 The fun's altitude may be computed by the following 

 rule, propofed by Mr. Lyons for nautical purpofes. By 

 the rules in the Nautical Almanac, for 177 i, fisd the lo- 

 garithm ratio ; fubtraft it from the rifing found anfwering 

 to the given diftance of time from noon, in the tables of the 

 fame Ahnanac ; the remainder is the logarithm of a number, 

 4 which 



