135. In the reflecting octant, sextant, or circle, the index glass A and the horizon glass B should be perpendicular to the plane of the instrument; and, with respect to the former glass, this position is verified by observing that, on looking obliquely into it, the parts of the arch which are seen by direct view and by reflection, are coincident. The perpendicularity of the horizon glass is proved by looking at the direct and reflected images of the sun when the index is at or near zero (the plane of the instrument being vertical), and observing that the eastern and the western limbs of both images are respectively coincident.

136. When the two images entirely coincide with one another, the index of the vernier should be at the zero point of the graduated arch: if this be not the case, the deviation of the index from that point is called the index error, and it may be determined by taking half the difference between the angles read on the arc, when the lower edge of the sun seen directly is placed in contact with the upper edge of the sun seen by reflection, and again when the upper edge of the former is placed in contact with the lower edge of the latter.

137. The remaining correction consists in placing the optical axis, or the line of collimation, in the telescope, parallel to the plane of the instrument. This condition is verified by bringing in contact, upon the wire nearest to the plane of the instrument, two celestial objects, as the sun and moon, when distant 90 or 100 degrees from each other; and then, by a general motion of the instrument bringing the objects upon the wire which is parallel to the former. If the contact remains good, the edges of the images having crossed in the centre of the field, the position of the telescope is correct: if the images separate on being brought to the second wire, the object glass is too near the plane of the instrument: a contrary error exists if the images overlap each other at the second wire. The correction is to be made by means of screws in the ring which carries the telescope.

a

138. The desire of measuring angles greater than those of 120 degrees, by means of reflecting instruments, has led to the construction of sextants in several different ways for the purpose of obtaining this end. Captain Fitzroy uses sextant in which the quicksilvered part of the horizon glass is divided into two portions by a plane parallel to that of the instrument, the upper part being fixed so as to make a constant angle, suppose a right angle, with the lower: by this contrivance, if the instrument be held vertically, the image of an object above or below the horizon, or, if held horizontally,

A

on the right or left hand of another, is seen in the field of view when the index is at zero; so that on moving the index till the two objects appear to be in contact, the whole angle is obtained by adding the constant angle to that which is expressed on the graduated arch. Thus, let Bn be that part of the divided horizon glass which is parallel to the index glass A when the index is at the zero of the graduations, and let мm be the part which makes a constant angle (90 degrees) with the former: then if E be the place of the observer's eye, o be T one of the objects, and s the other, the former object will, after one reflection, appear in the mirror M, in the direction ET; and by moving the index to such a

m

E

n

position, as AC, that the object s may appear after two reflections, as usual, to coincide with the image of o in the line ET, the arc of a great circle of the sphere between o and s will be measured by the sum of the angles OMT and SET. Therefore, if Ex be supposed to be parallel to Oм, and the distance of o be so remote that ME subtends at o no sensible angle, the angular distance of o from s will be equal

to SEX.

S

H

139. Captain Beechey has the horizon glass fixed in the usual way, but his index glass is divided into two parts Mn and мm by a plane parallel to that of the instrument; one part as Mm is fixed, and the other turns on its axis with the motion of the index bar. By placing the eye at a sight vane, or telescope, at E opposite the horizon glass, angles to the extent of about 120 degrees may be taken as usual, the degrees being read on a graduated arch from P towards Q. On the limb of the instrument, there is a second arc concentric with the former and gra

m

n

E

duated like it, but the numbers on this arc proceed in a contrary direction, or from Q towards P. There is a sight vane, or telescope, at K at the distance of about 95 degrees from P, the zero of the former arc; and to this the eye being applied, an object o on the right of the observer, if the instrument is

held horizontally, appears in the fixed index glass Mm at o', 90 degrees from that object: then, on moving the index to the position MC, so that KMC is half a right angle, an object at H in the direction Oм produced would appear, by the reflection of a pencil HM from the mirror Mn, which has now the position Mn' to coincide with o', and the angular distance between the objects o and H would be equal to two right angles the point c on the second line of graduations is numbered 180, the point K being numbered 135 degrees. If the index were in any other position as MC' the point c' being numbered 200 degrees, for example, an object at s would appear to coincide with o', and the angular distance between s and o, that is, the sum of the angles SMO' and OMO' would be 200 degrees.

140. Reflecting circles which, like those of Borda and Dollond, possess the property of repetition, consist of two concentric rings, one within the other, and in the same plane, and both are divided into 720 parts (corresponding to 360 degrees) with their usual subdivisions. The telescope and horizon glass are attached to two of the three radii belonging to the interior ring, and the horizon glass is at or near the circumference of the ring. The index glass is at the common centre of both rings, and turns on its axis, being attached to a revolving arm carrying a vernier.

In order to take a repetition of the angle between two objects, the index attached to the inner or revolving ring is fixed at 720 degrees, or zero, in which state the index and horizon glasses are parallel to each other; then the radius carrying the revolving index glass is moved till the objects are in contact, and the angle is read. Leaving the latter radius fixed to the outer ring, the inner ring is unclamped and turned, in the same direction as the index had been moved, through an angle equal to that which has been read; this will put the index and horizon glasses again parallel to one another. The bar carrying the revolving index glass is afterwards moved till the objects are again in contact, and then the angle will have been twice taken. The operations are continued in this manner till the index attached to the inner circle has got near, or even beyond 720 degrees (or has made the whole circuit): then the whole number of degrees being read, and divided by the number of repetitions of the angle, the quotient will be the correct angular distance of the objects.

When the angle between the objects is constantly changing, as the altitude of the sun, the whole arc passed over by the index of the inner ring is not a multiple of one angle, but the

sum of several different angles: in this case, the time must be registered when each contact was made, that is, when each angle was taken; and then, the change of the angle being supposed to be uniform during the continuance of the observations, the whole arc passed over by the index being divided by the number of observations, gives an angle which corresponds to the mean of all the registered times of the observations.

CHAP. V.

REFRACTION: LATITUDE OF A STATION: PARALLAX.

141. BEFORE the observed positions of celestial bodies can be employed as data for the solution of astronomical or geographical problems, they require corrections on account of the refraction of light in the atmosphere, and also on account of the situation of the observer with respect to the earth's

centre.

*

The atmosphere, being an elastic fluid, diminishes gradually in density from the surface of the earth upwards till at a certain height, which is estimated to be between forty and fifty miles, it becomes so much attenuated as to be incapable of producing any sensible effect on light; and, as the force of attraction increases with the density of the medium, it is evident that a ray of light emitted from a celestial body must, in its passage through the atmosphere to the eye of the spectator, be continually deflected from a rectilinear direction and be made to describe a curve line; hence the visible place of the object will be in the direction of a tangent to the curve at the place of the eye. Since the atmosphere is, or may be considered, symmetrical on both sides of a vertical plane passing through the spectator and a celestial body, the attraction on opposite sides of that plane will be equal: hence, disregarding the lateral and extraordinary refractions which in some states of the atmosphere have been found to exist, the path of the ray is in a vertical plane, and the convex part of the curve is upwards; consequently, the visible place of the object is above the place which it would appear to occupy if there were no refraction. The symmetry of the atmosphere on all sides of a vertical line passing through the spectator, is also the cause that a ray of light descending to the earth in that direction suffers no deviation: that is, there is no refraction of light when the celestial body is in the zenith of the observer. But the density of the air above and below the path of a ray of light differing more, in proportion as the path deviates from the vertical direction, it follows that the refraction increases from the zenith downwards, and is the greatest when the celestial body is in the horizon.

* On the undulatory hypothesis a different cause should be assigned, but the effects would be the same.