1114 



NAVIGATION-NAUTICAL ASTRONOMY. 



[THE TEENIER. 



approximate contact, the telescope, previously aet to 



net vision, will at once show the objnct more clearly 



j.-l. and give the contact more accurately ; of course, 



whatever shades may be necessary to protect the eye, 



ami to distinguish the object from the image, are to be 



put in front. 



If the altitude of a star is to bo taken, the operation is 

 just the same, care being taken to keep tho star's image 

 in view during the whole of its descent to the horizon, 

 to avoid the mistake of bringing down the wrong star. 

 The moon's altitude is taken in the same way as the sun's, 



i shades as may bo found necessary, 

 i a lunar distance is to be observed, the .plane of 

 the sextant must be held so that both objects may lie in 

 that plane, and the sight is to be directed, through the 

 IL !;/ .n ::lua, to the fainter of the two, so that when the 

 ijivt is to the left, the instrument must be held 

 face downwards. 



The practical management of the instrument, in 

 making observations at sea, can be efficiently acquired 

 only on ship-board ; the movements of the body must be 

 accommodated to the motion of the vessel, and peculiar 

 attitudes and positions will be necessary in peculiar cir- 

 cumstances : the observer sometimes stands erect, some- 

 times reclines against a support, and sometimes lies on 

 his back on tho deck, wl.oii taking a lunar distance. It 

 is plain that nothing but experience can dictate to him 

 the best way of handling his instrument on the various 

 occasions that may require its use. Supposing the 

 observation to have been made, it remains to nod off 

 the angular measure ; this is done by aid of the Vtrnier, 

 a contrivance so called from the name of its inventor. 



TUB VERNIER. This is a small scale attached to the 

 ind.'X-limb, F, Fig. 33, of the instrument ; it is slightly 

 inclined to the face of the divided limb A A, and moves, 

 with the index-limb, in close contact with the divided 

 arc AX It is attached to many other scales as, for 

 instance, to those of the barometer and thermometer as 

 well as to the scales of the quadrant and sextant, and is, 

 in fact, an appendage to many astronomical instruments 

 used for angular measurement; its object and utility 

 may be explained as follows : 



Let C D (Fig. 36) represent any graduated scale, and 

 A B a line which we wish to measure by it ; the scale and 

 line must of course be of the same character both 

 straight or both circular. If, upon applying the scale to 

 the line, as in the following figure, we find the extremity 



Fig. M. 



4 I ,,,,,, f i 



1 ' ' ' ' ! 11^ 



i i i i i 



i i 



B to fall accurately upon one of the divisions of the 

 scale, we, of course, obtain the measure without any 

 fractional parts of a division : we may, for illustration, 

 call the divisions degrees, and we shall conclude the 

 measure to be so many degrees exactly. 



I'.ut if, as would be most likely, the extremity, B, of 

 the lino project beyond the boundary of a division 

 without reaching the next, the length would be so many 

 degrees and some fractional parts of a degree, which the 

 scale affords us no efficient means of measuring. In the 

 figure, the measure of A B U eight degrees, with a frac- 

 tional part, a B, of the ninth degree, the exact amount 

 of which can only be guessed at. The object of the 

 Vernier U to make known the value of this fractional 

 part. 



Imagine a second scale, B E (Fig. 37), with its com- 

 mencement placed in contact with the extremity, B, of 

 the proposed line, to be applied to the scale C D : sup- 

 pose the whole length of this second scale to be 8 degrees, 



thus placed, there will necessarily bo found one whirh 

 exactly corresponds to a divisional mirk <>:i the first 

 scale, C D : in the figure below it is the fourth mark ; 

 and we accordingly conclude tint aB measures four- 

 tenths of a degree, so that the whulo measure of A B is 

 8}. That such is the case will be readily seen from con- 

 sidering that one of the division* of li K is only ,'.,t,hs of 

 one of tho divisions of C D, so that one of the latter 

 divisions exceeds one of tho fornmr by iVth of a d> 

 two of the latter exceed two of the former by Votlis, and 

 so on. 



Now from 4 to B, on B E, there are four divisions ; and 

 from 6 to/, on C D, there are also four divisions ; th i 

 latter four, in their whole length, exceed tho former 

 four by ^tlis of a degree ; but this excess is tho length 



B, consequently a B = i*bths. It follows, then 

 that if a B be only an exact number of tenths of a degree ; 

 we shall be able to measure those tenths by this contriv- 

 ance ; and the error of measurement, if a B be not an exact 

 number of tenths, and therefore the mark 4 not strictly 

 the continuation of the mark l>, must bo less than iVth. 

 In like manner, if the scale B E had the length of 10 

 degrees of C D, and were divided into 20 equal parts, o B 

 could have been measured accurately to within l th of a 

 degree, and so on. The scale B E is the Verii, 



The annexed figure (Fig. 38) will give an idea how 

 the Vernier, attached to tho index-limb of the quad- 

 rant or sextant, adapts itself 

 to tho circular graduated 

 limb of tho instrument. Tho 

 point marked a on the Ver- 

 nier is the index of the gra- 

 duated arc of the limb, and 

 is that which marks out the 

 integral part of the measure 

 of tho angle, the fractional 

 part being indicated by the 

 Vernier divisions, as already 

 explained. It is the mark a 

 which ought to correspond 

 with the mark on the gra- 

 duated limb, when tho index and horizon glasses of tho 

 instrument are parallel : it is common, however, to 

 speak of the whole movable limb A as the index. 



Suppose each of the divisions on the graduated limb to 

 denote n minutes, and let m be the number of those divi- 

 sions which make up the whole extent of the Vernier 

 scale, then the Vernier will contain m n of tho 

 minutes of the graduated limb. If this extent be 



1 i) divided into m + 1 equal parts, then the difference 



I I I I I I T 



but that it is divided, M in the figure, into 9 equal parts ; 

 n>l let ns anume, moreover, that a B may be expressed 

 in tenth* of degrees. 

 Among the divisional marks of the second scale B E, 



D between one division on the graduated limb and one 

 division on the Vernier, will be 



mn n 



n ~ m + I " m-fl 



If n - 20 1 , and m - 19', .'. -- T-f - !' M - 10', 



and m - 69', then ^_-j- =10', ic. 



TUB INDEX ERROR. If when tho index and horizon 

 glasses are parallel, the beginning a of the divisions on 

 the Vernier does not coincide with the mark on tho 

 graduated limb, tho distance between them is the to 

 error subtractivo when tho Vernier mark is to the left 

 of the 0, and additive when it is to the right. To dis- 

 cover tho amount of index error, move the index till a 

 point of the horizon, or some more distant object, coin- 

 cides with its iin:i','u : tlm distance of tho index mark a, 

 from on tho graduated limb, is the amount of 

 index error. 



The sextant just described is only a modification of 

 U the quadrant ; both instruments are in principle tho 

 same. The first published description of the quadrant 

 appeared in the Philosophical Transactions, No. 420, for the 

 year 1738, the paper communicating it having been laid 

 before the Society in May, 1731. It was the production of 

 John Hndley, and the instrument he described was con- 



