The index.

The indexglass.

The index N is a flat bar of brass, and turns on the centre of the sextant; at the lower end of the index there is an oblong opening; to one side of this opening the vernier scale is attached to subdivide the divisions of the arc; at the end of the index there is a piece of brass which bends under the arc, carrying a spring to make the vernier scale lie close to the divisions. It is furnished with a fingerscrew C, by which the index is fixed in any position to the limb of the instrument. There is also an adjusting-screw B attached to the index, capable of moving it with greater accuracy than the hand; this screw does not act until the index is fixed by the finger-screw C. Care must be taken not to force the adjusting-screw when it arrives at either extremity of its adjustment. When any considerable movement is required to be given to the index, the screw C at the back of the sextant must be set free; but where the index is brought nearly to the divisions required, this back screw should be tightened, and then the index gradually moved by the adjusting-screw.

Upon the index, and near its axis of motion, is fixed a plane speculum or mirror of glass I, quicksilvered. It is set in a brass frame, which is firmly fixed by a strong cock to the centre plate of the index, with its face perpendicular to the plane of the instrument. This mirror being fixed to the index, moves along with it, and has its direction changed by the motion thereof. As has already been observed, this glass

is to receive the rays from the sun or other object, and reflect Observathem upon the horizon-glass. It is furnished with screws tion Instruat its back, the object of which is to replace it in a perpen- ments. dicular position, if by any accident it has been deranged.

To the radius PL is attached a small speculum F, whose The horisurface is parallel to the index-glass when zero on the zon-glass. index coincides with zero on the limb. The under part only of this speculum is silvered, the upper half being left transparent, and the back part of the frame cut away, that nothing may impede the sight through the unsilvered part of the glass. The edge of the foil of this glass is nearly parallel to the plane of the instrument, and ought to be very sharp, and without a flaw. It is set in a brass frame, which turns on axes and pivots which move in an exterior frame; the holes in which the pivots move may be tightened by four screws in the exterior frame. G is a screw by which the horizon-glass may be set perpendicular to the plane of the instrument. Should this screw become loose, or move too easy, it may be easily tightened by turning the capstan-headed screw H which is on one side of the socket through which the stem of the finger-screw passes; this screw G is in some instruments under the glass, in others behind it, and in others at the side.

There are four coloured glasses at D, tinged red and The colour green, each of which is set on a separate frame that ed glasses turns on a centre. They are used to defend the eye from D and E. the brightness of the solar image and the glare of the moon, and may be used separately or together as occasion may require. There are three more such glases placed behind the horizon-glass at E, to weaken the rays of the sun or moon when viewed directly through the horizon-glass. The paler glass is sometimes used in observing altitudes at sea to take off the strong glare of the horizon.

The sextant is furnished with a plane tube K; and in The teleorder to render objects distinct, it has two telescopes-one a scopes. Galileo's telescope, representing the objects erect in their natural position; the longer one, an astronomical telescope, shews them inverted. It has a large field of view; and has parallel wires placed in the principal focus, where a true image of the object viewed by it is seen; thus rendering the position of the image more exact and more easy to be read off, and is that which should be used in taking observations at sea when great accuracy is required. A little use will soon accustom the observer to the inverted position, and to manage the instrument with ease. By a telescope the contact of the images is more perfectly distinguished; and by the place of the images in the field of view, it is easy to perceive whether the sextant is held in the proper position for observation. By sliding the tube that contains the eye-glasses in the inside of the other tube, the object is suited to different eyes, and made to appear perfectly distinct and well-defined.

The telescopes are to be screwed into a circular ring at K; this ring rests on two points against an exterior ring, and is held to it by two screws; by turning one of these screws, and tightening the other, the axis of the telescope may be set parallel to the plane of the sextant. The exterior ring is fixed on a triangular brass stem which slides in a socket, and, by means of a screw at the back of the sextant, may be raised or lowered so as to move the centre of the telescope to that part of the horizon-glass which shall be deemed most fit for observation. Tinged glasses are provided to screw on the eye-end of either of the telescopes or the plane tube.

The limb of the sextant is divided from right to left into Reading of 120 primary divisions, which are to be considered as divisions degrees; the degree is subdivided in some cases into two on the equal parts, each of which is 30'; in others into three limb. equal parts, each of which is 20'; and in others again into six equal parts, each of which is 10'. If the zero of the index stand exactly at one of the divisions of the limb, the

Observa- reading off in that case is immediately known. If, how tion Instru- ever, the zero of the index do not stand exactly at one of the divisions, but distant from it by a small space, the value of this space is known by means of the divisions of the vernier-ple to the left of 0.

ments.

Reading off The Vernier contains a space equal to nineteen divisions divisions on of the limb, and is divided into twenty equal parts; hence the vernier. the difference between a division on the vernier and a division on the limb is one-twentieth of a division of the limb, or 1, if the interval between divisions on the limb is equal to 20'. Or supposing the limb divided into intervals of 10, and that fifty-nine divisions of the limb correspond to sixty divisions of the vernier; it is then evident that the difference between a division of the instrument and of the vernier is th part of 10', i.e., 10". This is the most usual kind of division.

Adjust

ments of

To find the actual reading off in any particular case, we must observe which division of the vernier coincides with a division of the limb; the number denoting this, multiplied by the value of the difference between a division of the limb and of the vernier, will give the additional reading. Suppose, for instance, the nearest division of the limb to the zero of the vernier to be 25° 30', and the eighth division of the vernier to be coincident with a division of the limb, the additional angle will be 80" or 1' 20", and the reading off will be 25° 31′ 20′′.

The adjustments of the sextant are to set the mirrors perpendicular to the plane of the instrument, and parallel to the sextant. one another when the index is at zero; and to set the axis of the telescope parallel to the plane of the instrument. Adjustment 1.-To set the index-glass perpendicular to the plane of the sextant.

Set the index towards the middle of the limb, and hold the sextant so that its plane is nearly parallel to the horizon; then look into the index-glass, and if the portion of the limb seen by reflection appears in the same plane with the limb seen directly, the speculum is perpendicular to the plane of the instrument. If they do not appear in the same plane, i.e., if the image be seen above or below the arc itself, its position must be gradually and carefully changed by means of the screws at its back until the error is rectified. Adjustment 2.-To set the horizon-glass perpendicular to the plane of the instrument.

Place the instrument horizontal, and direct the sight to a distant well-defined object, as the sun, so as to view it directly; then move the index until the image of the object seen by reflection is on the field of view, and move the index backwards and forwards so as to make the image pass over the object. If it pass exactly over the object, the fixed mirror is perpendicular to the plane of the instrument; if not, move the screw G until their exact coincidence takes place.

Adjustment 3.-To set the horizon-glass parallel to the index-glass when the zero of the index or vernier-plate coincides with the zero of the graduations of the limb.

Set O on the index exactly to O on the limb, and fix it in that position by the screw on the under side of it; hold the sextant with its plane vertical, and direct the sight to a well-defined part of the horizon; then if the horizon seen on the silvered part coincides with that seen through the transparent part, the horizon-glass is adjusted; but if the horizons do not coincide, the position of the glass must be altered by moving a screw placed near the fixed reflector, which gives it a motion about an axis perpendicular to the plane of the instrument.

This adjustment is seldom made, as turning the adjustingscrew too often renders this part of the instrument very apt to get out of order. It is usual, therefore, to determine the error in the reading called the Index Error.

To do this, direct the sight to the horizon, and move the index until the reflected horizon coincides with that seen

by direct vision; then the difference between O on the limb Observaand 0 on the vernier-plate will be the index error, which is tion Into be added when O of the vernier is to the right of O on struments the limb; otherwise subtracted.

A more accurate method than the above is to measure the sun's apparent diameter twice with the index placed alternately on the right and on the left of the zero point of the graduated limb. Half the difference of these two measures will be the index error, which must be added to, or subtracted from, all observations, according as the diameter measured with the index to the left of O is less or greater than the diameter measured with the index to the right of the beginning of the divisions. Care must be taken to measure the sun's horizontal diameter, as the vertical diameter is often affected with refraction. This must be done by keeping the plane of the instrument at right-angles to the vertical diameter of the sun.

For example, on January 2, 1857, the sun's diameter, measured with the index first to the right and secondly to the left of the zero point of division, was 33′ and 32′ 20′′ respectively, and the index error obtained by taking the semidifference is - 20".

Adjustment 4.-To set the axis of the telescope pa rallel to the plane of the instrument.

Turn the eye-end of the telescope until the two wires are parallel to the plane of the instrument; and let two distant objects, or two stars of the first magnitude, be selected, whose distance is not less than 90° or 100°; make the contact of these as perfect as possible at the wire nearest the plane of the instrument; fix the index in this position; move the sextant until the objects are seen at the other wire, and if the same points are in contact, the axis of the telescope is parallel to the plane of the sextant. If, however, the objects are apparently separated, or overlap one another, correct half the error by the screws in the circular part of the supporter, one of which is above, and the other between the telescope and sextant; turn the adjusting-screw at the end of the index till the limbs are in contact; then bring the objects to the wire next the instrument, and if the limbs are in contact, the axis of the telescope is adjusted; if not, proceed as at the other wire, and continue till no error remains. In practice, this adjustment is usually made by means of the sun and moon. The mode of bringing the limbs of the sun and moon into contact will be explained when the use of the sextant is treated of. It is sometimes necessary to know the angular distance between the wires of the telescope; to find which, place the wires perpendicular to the plane of the sextant, hold the instrument vertical, direct the sight to the horizon, and move the sextant in its own plane till the horizon and upper wire coincide; keep the sextant in this position, and move the index till the reflected horizon is covered by the lower wire, and the difference of readings off in these two positions will be the angular distance between the wires. Other and better methods will readily occur to the observer on land.

The Quadrant.

It has been already observed, that this instrument differs from a sextant in the extent of the divided limb and in its rougher manufacture. It is only calculated for observing altitudes. Fig. 46 represents a quadrant of the common construction.

The frame, index, index-glass, and F the fore horizonglass, are much the same as in the sextant. There is, besides, another horizon-glass G, called the back horizonglass attached to the same radius as F. Instead of a tube or telescope, the quadrant is furnished with vanes or sights H and I. There are but three coloured glasses, two of which are red and the other green. They are fixed at K, as shown in the figure, when the fore horizon-glass is used

Observa- If the back horizon-glass be used, they are transferred to N. tion Instru- The back horizon-glass is silvered at both ends, but has a

ments.

Adjustments of

quadrant.

Use of

sexiant

H

M

Fig. 46.

transparent slit in the middle through which the horizon may be seen. Each of the horizon-glasses is set in a brass frame, to which there is an axis passing through the wood-work, and is fitted to a lever on the under side of the quadrant, by which the glass may be turned a few degrees on its axis, in order to set it parallel or perpendicular, according as it is the fore or back horizon-glass, to the index-glass. The lever has a contrivance to turn it slowly, and a button to fix it. To set the glasses perpendicular to the plane of the instrument, there are two sunk screws, one before and the other behind each glass; these screws pass through the plate on which the frame is fixed into another plate; so that by loosening one and tightening the other of these screws, the direction of the frame, with its mirror, may be altered, and set perpendicular to the plane of the instrument.

The sight-vanes H and I are perforated pieces of brass, designed to direct the sight parallel to the plane of the quadrant. The vane I has two holes, one exactly at the height of the silvered part of the horizon-glass, the other a little higher, to direct the sight to the middle of the transparent part of the mirror.

The limb is divided into ninety primary divisions, which are considered as degrees, and each degree subdivided into three equal parts, which are therefore of 20' each. The vernier-plate is generally so divided as to enable the observer to read off accurately to minutes.

These consist in setting the mirrors perpendicular to the plane of the instrument, and the fore horizon-glass parallel, and the back horizon-glass perpendicular to the index-glass, when the zero of the index or vernier-plate coincides with zero of the graduations on the limb.

The adjustments for the index-glass and fore horizon-glass are performed nearly in the same way as for the sextant. The index error, however, must be ascertained by bringing the horizon by reflection into the same line with the horizon seen directly. The method by taking the distance of two stars of the first magnitude, or the sun and moon, is inapplicable here.

The back horizon-glass is so seldom used, that for its adjustments and the mode of taking observations with it, the reader is referred to Norie's Navigation, and other works in which this subject is treated.

The altitude of an object may be determined by either Hadley's instrument, and is the reading off on the limb, with the proper index error applied, when by reflection that object appears to be in contact with the horizon. The distance between the sun and moon, or other heavenly bodies, may

and quad

rant.

be observed by the sextant when the limbs of the bodies Observawhose distance is required appear to be in contact. If the tion Instru quadrant be used for taking the altitude of the sun, when ments. it is so bright that its image may be seen in the transparent part of the fore horizon-glass, the eye is to be applied to the upper hole in the sight-vane, otherwise to the lower hole; and in this case the quadrant is to be held so that the sun be bisected by the line of separation of the silvered and transparent parts of the glass. The moon is to be kept as nearly as possible in the same position, and the image of the star is to be observed on the silvered part of the glass adjacent to the line of separation of the two parts.

With the quadrant two different methods of taking observations may be employed. In the first, the observer faces the sun, and looks to that part of the horizon which is immediately under the sun, and the observation is therefore called the fore observation. In the other method, the observer's back is towards the sun, and he looks to the part of the horizon opposite to that which is under the sun; and this is consequently called the back observation. It is not to be employed except when the horizon under the sun is obscured, or rendered indistinct by fog or other impediment.

In all cases of taking altitudes, it must be considered that it is necessary to be quite sure that the distance of the sun or other body from the horizon is the least possible, otherwise it would not be the altitude that is observed. Consequently, after the instrument has been placed as nearly as possible in a vertical position, and a contact made, a motion about the line of sight of the sun must be communicated to the instrument, so as to keep the image always in the same part of the silvered mirror, the plane of the instrument being inclined. In this way we keep the angular distance of the sun from the line through the eye by which it is viewed the same, and the sun's image describes a small circle, whose angular radius is this distance. The horizon being fixed and viewed directly, will always occupy the same position. If, then, on giving this vibratory motion to the instrument, the arc described by the sun touches the horizon, the angular distance observed is the altitude. If it should cut the horizon, so that a portion of the sun's image goes below it, the index must be moved back until this are simply touches the horizon. In the back observation with the quadrant, and in observing with the sextant furnished with the inverting telescope, the images are inverted, and the arc described by the sun's image lies below the horizon, to which line it is convex.

The motion must be given round the axis passing through the observer's eye and the sun. To do this, a motion about the axis of vision must be given to the instrument, and at the same time the observer must turn himself about upon his heel; for the motion about the line of sight of the sun may be resolved into these two motions; and the observer has no means of giving the requisite motion directly by one movement. When the sun is near the horizon, the line from the eye to the sun will not be far removed from the axis of vision, and the principal motion of the instrument will be performed on this axis; while that part of the motion made about the vertical axis will be small. On the contrary, if the sun be near the zenith, the line from the eye to the sun is nearly vertical and perpendicular to the axis of vision; hence the motion about the vertical axis is the greatest, and that about the axis of vision very trifling. In intermediate positions of the sun the motions of the instrument about these two axes will be more equally divided. When the distance between the moon and sun, a planet or a star, is to be observed, the sextant must be so held that its plane may pass through the eye of the observer and both objects; and the reflected image of the brighter of the two is to be brought into contact with the other seen directly. To effect this, therefore, it is evident that when the brighter object is to the right of the other, the face of the sextant

ments.

ments.

loosen the screw which fastens the index, and it will Observa immediately, if the instrument is not remarkably well tion instru constructed, be seen to start from its former situation, more or less according to the perfection of the joint and strength of the index. This starting, which is due to the index recoiling after being released from the confined state it was in during the observation, will sometimes amount to several minutes; and its direction will be opposite to that in which the index was moved by the screw at the time of finishing the observation. But how far it affects the truth of the observation depends on the manner in which the index was moved in setting it to 0, for adjusting the instrument, or in finishing the observations necessary for finding the index error.

Observa- must be held upwards, and if to the left, downwards. When tion Instru- the face of the sextant is held upwards, the instrument should be supported with the right hand, and the index moved with the left hand. But when the face of the sextant is from the observer, it should be held with the left hand, and the motion of the index regulated with the right hand. Sometimes a sitting posture will be found convenient for the observer, particularly when the reflected object is to the right of the direct one. In this case the instrument is supported by the right hand; the elbow may rest on the right knee; the right leg at the same time resting on the left knee. If the sextant be provided with a ball and socket, and a staff, one of whose ends is attached thereto, and the other rests in a belt fastened round the observer's body, the greater part of the weight of the instrument will be supported by his body. In all cases where the sextant is used, when the contact is nearly made, the index should be fixed by the under screw, and the remaining small motion given by the adjusting screw. Error may arise from two kinds of causes: one inherent error in the in the construction of the instrument as defect of parallelism or perfect planeness in the fore and back surfaces of the quadrant. mirrors, as also of the coloured glasses, and of the true circular form of the arc, and true centring, for which no remedy can be provided; and the other arising from the bending and elasticity of the index or moveable radius.

Causes of

use of sextant or

The parallelism of the two surfaces of the mirrors may be tested by viewing through them obliquely a distant distinct object. If the image is perfect and well defined, the surfaces are parallel; otherwise not.

To ascertain whether the surfaces of the mirrors are

plane, observe the angle between two distant objects which are nearly of the same altitude, the image of the left-hand object being brought into contact with the right-hand object viewed directly; then move the instrument in its own plane so as to bring the image of the right-hand object into contact with the left-hand object viewed directly. If they continue in contact, the surfaces are plane; otherwise not. To test the form of the dark glasses, measure the sun's diameter to the right and to the left of the zero point with different combinations of the glasses. If the sum of the diameters so measured be nearly equal to four times the semidiameter given in the Nautical Almanac, the form of the glasses is satisfactory. For the true centering of the arc, and its truly circular form and correct graduation, the navigator must trust entirely to the skill of the maker.

By reason of the bending and elasticity of the index, and the resistance it meets with in turning round the centre, its extremity, on being pushed round the arc, will sensibly advance before the index-glass begins to move, and may be seen to recoil when the force acting on it is removed. Mr Hadley, in order to remedy this defect, which he seems to have apprehended, gave special directions that the index be made broad at the end next the centre, and the centre or axis itself have as easy a motion as is consistent with steadiness; that is, an entire freedom from looseness or

shake, as the workmen term it. By strictly complying

with these directions, the error in question may indeed be greatly diminished, so as to be nearly insensible, when the index is made strong, and the proper medium between the two extremes of a shake at the centre on the one hand, and too much stiffness there on the other, is nicely hit; but it cannot be entirely corrected, for to more or less of bending the index will always be subject, and some degree of resist ance will remain at the centre, unless the friction there could be totally removed, which is impossible.

Of the reality of the error to which he is liable from this cause, the observer, if he is provided with an instrument furnished with an adjusting screw for the index, may thus satisfy himself:-After finishing the observation, lay the instrument on a table, and note the angle; then cautiously

The easiest and best rule to avoid these errors seems to be this :-In all observations made by Hadley's quadrant or sextant, let the observer take notice constantly to finish his observations by moving the index in the same direction which was used in setting it to 0 for adjusting, or in the observations necessary for finding the index error. If this rule is observed, the error arising from the spring of the index will be obviated. For as the index was bent the same way, and in the same degree, in adjusting as in observing, the truth of the observations will not be affected by this bending.

To Observe the Sun's Altitude at Sea.

Turn down one of the dark glasses before the horizon-glass (if the instrument be the quadrant, the fore horizon-glass is to be used) according to the sun's brightness; direct the sight to that part of the horizon which is under the sun, and move the index until the coloured image of the sun appears in the horizon-glass. Then give the instrument a slow vibratory motion about the axis of vision, as already described; move the index until the upper or lower limb of the sun is nearly in contact with the horizon at the lowest or highest part of the arc (according as the image is seen erect or inverted) described by this motion; and complete the contact by the tangent-screw, if the sextant be usedif not, by moving the index. The reading off of the limb will be the altitude of the sun.

To Observe the Moon's Altitude at Sea.

Turn down the green glass, and observe the moon in the silvered part of the horizon-glass, the eye being directed towards the horizon; move the index gradually, and proceed as already described in the case of the sun, until the enlightened limb is in contact with the horizon at the lowest or highest point of the arc described by the vibratory motion. The reading off will be the altitude of the moon's observed limb. If the lower limb be observed, the moon's semidiameter must be added; and if the limb be observed, it must be subtracted from the observed upper altitude, in order to obtain the altitude of the moon's centre. If the observation is made in the day-time, the coloured glass is not to be used. i

To Observe the Altitude of a Star or Planet.

Put the index to zero; then direct the sight to the star so as to see it through the unsilvered part of the horizonglass; turn the instrument a little to the left, and the image of the star will be seen in the silvered part of the glass. Now move the index, and the image will be seen to descend; continue to move the index gradually, until the star is in contact with the horizon at the lowest point of the arc described by the vibratory motion; in the case of the sextant, clamping the index when the contact is nearly made, and completing it with the adjusting or tangent screw.

Observa To find the Altitude of the Sun on Shore with an Artificial Horizon.

tion Instruments.

A flat dish, containing a small quantity of mercury, is generally used for this purpose. The surface of the mercury is horizontal, and is a good reflector of the sun's rays. Let the observer so stand that he may receive on his eye rays from the sun which have been reflected from the surface of the mercury. He will then, according to the principles of optics, see the reflected image of the sun as much below the surface of the mercury as the sun is above it. If, then, he looks at the image through the unsilvered part of the horizon-glass, instead of at the horizon, and brings the image of the sun reflected at the index-glass and horizon-glass into contact with this, it is evident that the angle observed will be double of the sun's altitude. The details of this process are the same as have been already explained. Having read off the angle when the contact has been made, it must be corrected for the index error; and the result, divided by 2, will be the apparent altitude

of that limb of the sun which has been observed.

To Observe the Distance between the Moon and any
Celestial Object with the Sextant.

1. Between the Sun and Moon.-Put the telescope in its place, and the wires parallel to the plane of the instrument; and if the sun is very bright, raise the plate before the silvered part of the speculum; direct the telescope to the transparent part of the horizon-glass, or to the line of separation of the silvered and transparent parts, according to the brightness of the sun; and turn down one of the coloured glasses. Then hold the sextant so that its plane produced may pass through the sun and moon, having its face upwards or downwards, according as the sun is to the right or left of the moon; direct the sight through the telescope to the moon, and move the index till the limb of the sun is nearly in contact with the illumined limb of the moon; now clamp the index, and, by a gentle motion of the instrument, make the image of the sun move alternately to one side and the other of the moon; and when in that position, where the limbs are nearest each other, make the contact of the limbs perfect by the tangent-screw; this being effected, read off the degrees and parts of a degree shown by the index on the limb, using the magnifying-glass; and thus the angular distance between the nearest limbs of the sun and moon is obtained.

2. Distance between the Moon and a Planet or Star.Direct the middle of the field of the telescope to the line of separation of the silvered and transparent parts of the horizon-glass; if the moon is very bright, turn down the lightest-coloured glass, and hold the sextant so that its plane may be parallel to that passing through the eye of the observer and both objects; its face being upwards if the moon is to the right of the star, but downwards if it be to the left. Now direct the sight through the telescope to the star, and move the index till the moon appears by the reflection to be nearly in contact with the star; clamp the index, and turn the adjusting or tangent screw till the coincidence of the star and the enlightened limb of the moon is perfect; and the reading off of the limb at the index will be the observed distance between the moon's enlightened limb and the star.

The contact of the limbs must always be observed in the middle, between the parallel wires.

It is sometimes difficult for those not much accustomed to observations of this kind, to find the reflected image in the horizon-glass; it will perhaps, in this case, be found more convenient to look directly to the object, and, by moving the index, to make its image coincide with that seen directly.

VOL. XVL

SECT. II.-OF THE CORRECTIONS TO BE APPLIED TO OBSERVED ALTITUDES AND DISTANCES.

1. Parallax.

in space, it is necessary to suppose that all observations are In order that the place of a heavenly body may be fixed taken from one point. This point is the centre of the earth. Consequently the places of the sun, moon, and planets, whose distances from the earth are measurable, as observed, must be reduced to what they would be if seen The correction for this object is called parallax. The fixed stars are at so great a distance from the earth that they have no sensible parallax, and this correction is not to be applied to them.

from the centre.

Let C (fig. 47) be the centre of the earth, P the place of the observer on its surface, and Z his zenith; and let S be a heavenly body whose position is observed. Then ZPS is the observed zenith distance, or complement of the observed altitude, and ZCS the true zenith distance, -i.e., the zenith distance as observed at the earth's centre.

Ꮓ

P

Then clearly the angle ZPS is greater than the angle ZCS by the angle PSC, which is also in the plane of the vertical circle through S. It is evident from the figure that a heavenly body is depressed by parallax; and the observed altitude is less than the true altitude by a certain amount depending on the altitude, which is called the correction of parallax. The correction of parallax, therefore, must always be applied with the positive sign. Its amount may be easily found; for, let _ZPS=z', and ZCS=z, and PSC the parallax=p; then, in triangle PSC,

Fig. 47.

Observation Instruments.

Refraction is a correction to be applied in consequence of the rays from every heavenly body being bent or refracted as they pass through the successive layers of the earth's atmosphere, in consequence of which they describe curvilinear paths, having their convexity turned towards the zenith of the observer. The tangent to this curve at the eye of the observer is the direction in which he sees the object, and is evidently, from what has been said, bent towards the zenith. Hence the effect of refraction is to raise the heavenly bodies in the heavens above their true

E