clamp the plates together, loosen the lower clamp so that the transit moves easily upon its lower socket, set the instrument approximately north and south, the object end of the telescope pointing to the north, turn the proper solar lens to the sun, and with one hand on the plates and the other on the revolving arm, move them from side to side until the sun's image is brought between the equatorial lines on the silver plate.

The lower clamp of the instrument should now be fastened, and any further lateral movement be made by the tangent screw of the tripod. The necessary allowance being madə for refraction, the telescope will be in the true meridian, and being unclamped, may be used like the sights of the ordinary solar compass, but with far greater accuracy and satisfaction in establishing meridian lines. Of course when the upper or vernier plate is unclamped from the limb, any angle read by the verniers is an angle from the meridian, and thus parallels of latitude or any other angles from the true meridian may be established as with the solar compass.

The bearing of the needle, when the telescope is on the meridian, will also give the variation of the needle at the point of observation.

If the instrument has a movable compass circle, the variation of the needle can be set off to single minutes, the needle kept at zero, or "with the sun," and thus lines be run by the needle alone when the sun is obscured.

APPENDIX B.

THE SEXTANT.*

(BY PROF. J. K. REES, COLUMBIA COLLEGE.)

This instrument is especially useful to the scientific explorer on account of its portability and simplicity of manipulation. It requires no fixed support, and furnishes data with the least expenditure of the time of the obThe accuracy of fixed instruments is not to be expected from it, since it is held in the hand and is of small dimensions.

server.

The Principle of the Instrument.-The optical principle upon which the sextant is made is :-If a ray of light suffers two successive reflections in the same plane by two plane mirrors, the angle between the first and last directions of the ray is twice the angle of the mirrors.

Let I and H be two plane mirrors perpendicular to the plane of the paper,which is taken as the plane of reflection.

A ray of light from A is reflected, first from the mirror I in the direction CO, then by the mirror H along от. The angle between the first and last direction of the ray after these two reflections is ATO.

Draw CN and OM normal to the mirrors I and H respectively. Then NKO

equals the angle of the mirrors.

B'

N

C

K

From the law of the reflection of light it is known that the angle

and also,

ACN or i = angle NCO;

COM or i = MOT.

*For a full description of this instrument, sec Chauvenet's Spherical and Practical Astronomy, published by Lippincott in 1863.

Suppose now that the glass His unsilvered on the upper half; then a ray of light coming from B will pass through this unsilvered portion to T, and the angle ATO will measure the angular distance of A from B as seen at T.

To apply this principle the mirror I, revolving about a pivot at C, has attached to it an arm or bar ID, which, as the mirror is turned, moves over a graduated arc ER. The mirror H is fixed in position. There will be one position of the index arm where the two mirrors will be parallel. Then since the angle between the first and last directions of the ray of light which is reflected by both mirrors is zero, or the two directions are parallel, the indicated point of the graduated arc is marked zero. The graduations are then continued to the left, calling each degree two degrees, in order to read off at once the required angle.

The best form of the common sextant is seen in the accompanying cut, furnished by Messrs. Stackpole & Brother, N. Y. :

from a distant object may not be interrupted. To give greater distinctness to the images a small telescope T is placed in the line of sight OT. The telescope is supported in a ring D, which can be moved in a direction at right angles to the plane of the sextant. Thus the axis of the telescope can be directed either towards the silvered or the unsilvered part of the mirror. This motion changes the plane of reflection, which, however, remains always parallel to the plane of the sextant; the use of the motion being merely to regulate the relative brightness of the direct and reflected images. The vernier is read with the aid of a glass G which is attached to the index bar. The central mirror I, or index glass, is fastened in a brass frame which is firmly attached to the index bar by three screws. This glass is generally set by the maker so as to be perpendicular to the plane of the sextant. There are no adjusting screws usually connected with it. The fixed mirror H, or horizon glass (so called because through it the horizon is observed in taking

altitudes), is specially provided with screws by which its position with respect to the sextant plane may be rectified.

At P and Q are colored glasses of different shades, which may be used separately or in combination, to defend the eye from the intense light of the

sun.

Common Adjustments of Ordinary Sextant.

1. The Index Glass must be perpendicular to the plane of the sextant.

2. The Horizon Glass must also be perpendicular to the plane of the sextant. 3. The central sight line of the telescope must be parallel to the plane of the

sextant.

4. The true zero of the are must be found.

1. Adjustment of the Index Glass. - Bring the vernier to about the middle of the graduated arc; then, placing the eye a little above the plane of the sextant and near the index glass, examine the direct and reflected images of the graduated arc. If the one appears to run into the other the index glass is perpendicular to the plane of the sextant, and the adjustment is complete.

If the reflected image appears too high or too low the glass leans forward or backward. The glass may then be adjusted to perpendicularity by placing a piece of paper under one edge of the plate by which the glass is held to the index arm, first loosening the screws; or the glass may be taken out of the frame, and the supports against which the glass leans may be filed so as to bring the glass, when set back, perpendicularly to the plane of the sextant.

2. Adjustment of the Horizon Glass.-This glass must also be perpendicular to the plane of the sextant. The index glass having been adjusted to perpendicularity, if it is found that in any one position the horizon glass is parallel to the index glass, then the horizon glass is perpendicular to the plane of the sextant.

In order to test this parallelism, put in the telescope and direct it to a star or any distant, well-defined terrestrial object. Move the index bar until the direct and reflected images are in the field of view, then clamp the vernier, and by moving the tangent screw cause one image to pass the other; if they pass exactly one over the other the adjustment is complete; if they pass one at the side of the other, the horizon glass must be adjusted. There are adjusting screws attached to the glass whereby it can be inclined to or from the sextant plane, and also turned around an axis perpendicular to the sextant plane. By means of the first set of screws the adjustment for perpendicularity can be made, and by means of the second set the position of the zero of the limb can be altered to a small extent.

3. Adjustment of the Telescope. The sight line of the telescope is the line from the centre of the field of view through the centre of the object glass. This line must be parallel to the plane of the sextant. In order to test for this, choose two distant objects like the sun and moon, 90° to 120° apart; direct the telescope to one of these objects, holding the plane of the sextant so as to pass through both; then moving the index bar, bring the second object into the field of view; clamp the vernier, turn the tangent

screw until the two objects are tangent to each other on the thread of the telescope nearest to the instrument. Then by moving the instrument, cause the objects to come on the thread farthest from the instrument. If the tangency is still perfect, the adjustment is complete. If the objects separate upon the thread farthest from the instrument, then the object end of the telescope droops towards the plane of the instrument; if the images overlap, then the telescope inclines upward from the plane of the instrument. The adjustment is made by means of the screws that work into the collar which carries the telescope.

4. Index Correction.-When the two glasses are parallel the zero of the graduated limb should coincide with the zero of the vernier. This adjustment must be very carefully looked after before taking any observations, because it is an adjustment that is liable to change. Rather than make this adjustment accurately every time an observation is made it is preferable to determine the place of the true zero of the graduated arc and allow for the correction. This correction is simply the distance between the graduated zero of the instrument and the reading of the vernier when the two mirrors are parallel. This correction is minus when it is on the graduated arc towards the increasing numbers of the graduation, and plus when on the opposite side.

The index correction may be determined by observations upon a star, or a distant, well-defined, terrestrial object, or upon the sun.

First, by a star: Direct the telescope to a star of the third or fourth magnitude; move the index bar until the reflected image of this star comes into the field of view; then clamp the vernier; turn the tangent screw until the direct and reflected images of the star are exactly in coincidence; take the reading of the vernier; apply the proper sign, and the arc reading is the index correction.

Second, by a distant, well-defined terrestrial object, or the reflection of sunlight from-for example-the bulb of a thermometer or a drop of water. This can be observed in the same way as a star, although not giving as accurate results.

Third, by the sun : Turn on the colored glasses until the light from the sun is diminished sufficiently to suit the eye; bring the direct and reflected images of the sun into the field of view; clamp the vernier; turn the tangent screw until one image of the sun is tangent to the other; take the reading; turn the tangent screw until the contact is broken; bring the images back to tangency; take the reading again; in this way make five readings; then turn the tangent screw until the images change places and tangency is made on the other side; take the same number of readings here.

In order to read always from the same end of the vernier, call the zero of the vernier 360°, and read the vernier accordingly. Take the mean of the readings in the first and second cases, add them together, and divide by two. Subtract the result from 360°, and the difference will be the index correction. In order to avoid the effect of refraction it is best to measure the horizontal diameter of the sun. To check the observations compute the diameter of the sun from data given in the Nautical Almanac, for the day of the observation, and compare it with the diameter of the sun as obtained from the obser

vations.