. 



ANT. 



SEXTANT. 



Hence the gnat excellence of the method of equal altitudes for 

 determining the time, <o far a* instrumental error U concerned ; it in 

 an additional advantage that an error in the auppoeed latitude U also 

 without sensible influence. Again, if time U deduced by absolute 

 altitudes of a sUr rising in the east, the result will be affected one 

 way by the errors above described ; if a second star be observed 

 at nearly the same altitude setting in the west, the altitude will be 

 affected to the same amount ; and if the stars hare declinations which 

 do not widely differ, the result deduced from the second star will be 

 affected to the same extent, but in a contrary way from the first ; a 

 mean of the two results will be nearly free from any error, except the 

 casual error of observation. A latitude by the sun or a star to the 

 south, which is erroneous from the above-mentioned causes, will be 

 balanced and corrected by a star of nearly the same altitude to the 

 north ; or a star to the north may be balanced by two to the south, 

 one of higher and the other of lower altitude. It is scarcely credible 

 how nearly the time or latitude may be thus determined. We have a 

 series of such latitudes with an 8-inch sextant, observed by Mr. Lasaell 

 at Liverpool, which scarcely differ more than 2" or 3" from each 

 other, though deduced from different groups of Greenwich stars. 

 When tlif longitude is to be obtained from lunar distanced, a consider- 

 able number of observations should be taken from the objects east 

 and those west of the moon. If a pair can be selected on different 

 aides of the moon, and nearly at the same distance from her, the result 

 will be liable to the effect of casual error only, and to the error of the 

 lunar tables. This Utter error cannot be got rid of at the time of 

 observation ; but after the Greenwich, Cambridge, Edinburgh, Cape 

 of Good Hope, and Oxford observations for the year have been pub- 

 lished, it will generally be possible to find the error of the moon at the 

 time of observation with considerable accuracy. This must be done 

 whenever a sure longitude U to be deduced from lunar distances, and 

 lunar observations must be taken in great numbers, so as to destroy 

 casual error, to settle nice points in geography. 



When a few more fundamental points in longitude are fixed, it will 

 not be necessary to use lunar distances, except in long voyages, or in 

 the centre of large and uncivilised countries. The recent improve- 

 ments in chronometers, and the reduction in their price, have greatly 

 superseded this kind of observation already, and will continue to do so 

 more and more. 



When the arc of the instrument is limited to 90, which U usually 

 the case in the common wooden instrument, it is called a quadrant 

 (and sometimes an octant, as being in form an eighth of a circle), and 

 a second horizon-glass and sight are sometimes appended for the back 

 observation. A sight-vane (a plate of brass pierced with a small hole) 

 is placed below the ordinary horizon-glass, and a second horizon-glass is 

 fixed near this vane, so that lines from the centre of the index-glass, 

 and from the latter vane, make equal angles with its plane. The plane 

 of this second horizon-glass should be at right angles with the index- 

 glass, when the index is at zero. This adjustment may be verified by 

 making the sea-horizon seen directly through the second vane and 

 unsilvered part of the second horizon-glass, coincide with the sea- 

 horizon at the back of the observer, which is seen by two reflections from 

 the index-glass and silvered part of the second horizon-glass. The angle 

 between the fore and back sea-horizons is evidently equal to 180 + 

 twice the dip of the horizon. The dip is known from the observer's 

 height above the sea-level Suppose it to be 4', and that the reading 

 on the back arc is 5' ; it should be twice the dip, or 8' : therefore the 

 zero position of the index for the back observation is at 3' on the 

 forward arc. This may be corrected by altering the second horizon- 

 glass, if there are the means of adjustment ; that is, by making the 

 front and back sea-horizon coincide when the reading is 8' on the bock 

 arc. By moving the index forward, the reflected sun, which ia behind 

 the observer, can be brought to touch the sea-horizon in front ; and 

 the reading, when the index error has been corrected, is 180 the 

 tin's distance from the front horizon. Now this latter angle is evi- 

 dently 180 + 2 x dip sun's altitude ; hence it is clear the angle read 

 off is the sun's altitude above the horizon 2 x dip. Hence sun's 

 altitude dip (the altitude required) = angle read off + dip. If the 

 index error be not adjusted, the angle must be corrected for the index 

 error; in the preceding instance the 3' must be added to the sun's 

 altitude. The back observation, however, though useful in certain 

 circumstances, is not much used at present, and many quadrants are 

 fitted up without the second vane and horizon-glass. 



If a sextant be used in the manner we have attempted to describe 

 the results will be found to be very satisfactory. The attentive reader 

 will see that the principle to be seized upon is tliat of always making 

 two observations at nearly the same time, in which the errors, except 

 the casual errors of making the contacts and of reading off, are the 

 same, but the effects of which on the final result are different It is 

 not always convenient to afford the time which these balanced observa- 

 tions require; and, in fact, they are often impracticable. It will 

 therefore, be well worth the careful observer's while to determine tin 

 constant errors of his sextant, at different angles, where he has a good 

 opportunity, and to use this knowledge where circumstances do not 

 allow him to make a balanced set. 



Very small sextants are sometimes fitted in a box, and are callec 

 tnuff-bax sextants. These admit of considerable accuracy ; but, except 

 in particular cases, they are not carefully adjusted, Ac. The principle 



i, of course, the same as in the larger sextants, and they have a small 

 telescope and dark glasses. It is desirable that the box should be wide 

 enough to admit a finger to wipe the glasses, especially when the snuff- 

 lox sextant is used, as it frequently is, for maritime surveying. The 

 alt spray very soon clouds the glasses, and there ia no light to spare. 

 For all sea-going purposes, except taking lunar distances, and for mili- 

 tary and maritime surveying, the snuff-box sextant will be fmmd very 

 convenient and sufficiently accurate. If made with the utmost 

 and skilfully used, we think it capable of determining the latitude 

 within 1', and the time to 8* or 4' ; but an instrument-maker could 

 not be expected to take so much trouble, unless for a favourite 

 customer or for an expedition of some importance. 



After the invention of Borda's repeating reflecting circle, Trough t< MI. 

 who was averse to the principle, produced a non-repeating circle, whirh 

 to called the British circle ; but it more commonly goes by his name. 

 This may be understood by conceiving the circle, of which the sextant 

 is a part, to be completed, and that while the telescope and glasses are 

 at the front of the instrument, the divisions and three equidistant 

 verniers attached to the index-glass are at the back. The observations 

 ought always to be made in pairs, and for this purpose there ar 

 handles, one to the front and another at the back. Thus, suppose it 

 were required to take the altitude of the sun : this is first observed 

 exactly as with the sextant, and the three verniers read off, the index- 

 jlass being above the line which joins the telescope ami horizon-glass. 

 Let the instrument be conceived to turn round this line through 180', 

 then the index-glass is below, and with the face downwards. By 

 moving the index backwards to zero, it will become parallel to the 

 horizon-glass, and continuing this motion until it is at the original 

 angle, but on the back arc, the sun will be brought down exactly as in 

 the former observation; when the contact is to be made with the 

 tangent-screw, and the indices again read off. By combining the 

 observations it is clear the index error is destroyed, and this ia one 

 point of superiority to the sextant. Again, the three readings wholly 

 destroy any effect of excentricity, and very greatly diminish those 

 errors which may arise from accidental injury to the figure 

 circle, while the six readings greatly reduce the errors of division. 

 The errors caused by defects in the dork glasses and horizon-glass are 

 eliminated, and such as arise from a defect in the index-glass are 

 diminished, and this too by the principle of the instrument, using it 

 independently upon one object. These advantages are undoubtedly 

 very great ; but the additional weight of the circle and troubl. in 

 handling it, the trouble of reading three verniers for every observation, 

 the shortness of the radius, and consequent necessity of limiting the 

 subdivision to 20" , seem to overbalance them in the opinion of most 

 seamen. We think that an intelligent observer will get results of 

 nearly equal value from the sextant or from Troughton's circle, but 

 that the sextant requires much care in selecting and balancing observa- 

 tions, which the circle does not. Whenever time or latitude is to be 

 deduced from observations of one object at one time, as where the 

 sun alone is used on geographical expeditions, or where lunar distances 

 are taken from the sun alone, or from one star, the sextant cannot 

 enter into comparison with the circle. A very excellent Spanish 

 observer, Don J. J. Ferrer, determined the obliquity of the ecliptic 

 with one of Troughton's circles more accurately than the (Imimicli 

 quadrant could do, at a time when that quadrant was still the prin- 

 cipal declination instrument in the Royal Observatory. And if frequent 

 reading off is not too great an objection, Troughton's circle may be 

 recommended as the safer and more independent instrument, and as 

 demanding less thought and care from the observer. 



We have already, in the article REPEATING CIRCLE, described the 

 original discovery of the principle by Tobias Mayer, and his first appli- 

 cation of it. After Mayer had greatly improved the lunar tables, he 

 proposed the following construction for measuring the angle between 

 the moon and any other object with the greatest exactness. (' Tabula; 

 niotuuin Sou's et Luno>, auctore Tobias Mayer,' London, 1770.) The 

 instrument is an entire circle, on the centre of which the index-bar 

 turns, the index-glass being over the centre. The telescope and 

 horizon-glass are fixed on a second bar, which also turns, but cxcen- 

 trically, on the same centre. The two bars can be clamped indepen- 

 dently of each other, and each in any position, and there is an index or 

 fiducial line to each, by which the divisions of the circle may be read 

 off. Now, suppose a distance between the moon and sun to be required 

 (the dark shades, &c., may be understood from what has been said on 

 the sextant) : First, having fixed the index-bar at zero, bring the 

 hnri/oii-glass to be parallel to it by observing the sun (as in 

 mining index correction) ; then move forward the indr\ bar, ml 

 observe the distance between the moon and sun's nearest limbs, as 

 with the sextant. If the angle were now read off, we should have the 

 simple distance affected with the whole error of graduation, and 

 no advantage over the sextant. By moving the horizon-bar, bring the 

 two glasses to be parallel exactly as before, and make the measure 

 between the limbs of the moon and sun also as before, by moving the 

 index-bar alone. The angle, if read off now, would be twice the angle 

 required, but the errors of division and reading off would be only those 

 which affect the first and last poxition of the index-bur. In this way 

 the angle may be repealed as often as you please, until the bars have 

 travelled once, twice, or even ofteuer round the circle; and it ia c, 

 that the errors of division and reading off are those at the first and 



