He turns the upper plate of the theodolite and moves the telescope until he can see P through it.

He then clamps both circles EFD and XYZ.

And by means of the tangent screws brings the point P exactly into the centre of the field of view.

He then reads both verniers.

He then unclamps both circles.

And repeats the operation for the point Q.

The difference between the reading of the horizontal vernier gives the horizontal angle MON.

By unclamping the vertical circle and reading the vernier when the level d shews that the telescope is horizontal he can obtain each of the angles of elevation POM, QON (from his reading of the vernier of the vertical circle when it pointed first to P and then to Q.)

THE SEXTANT.

315. There are three experimental facts connected with Optics which the student must understand who wishes to understand the principle of the sextant.

I. When a telescope is pointed at a plane mirror (or looking-glass) the eye sees exactly what it would if the telescope were placed on the other side of the mirror as in the following diagram.

Let the plane of the mirror be perpendicular to that of the paper. Let ADB be the line in which the mirror is supposed to cut the plane of the paper.

Let EF be a section of the telescope and CD the line of sight.

Make the angle C'DB equal to CDB.

And draw E'F' a dotted section of a telescope round C'D so that C'D=CD.

Then an eye placed at C and looking directly at the plane mirror in the direction CO' would see in the direction DO, exactly what an eye placed at C', the eyepiece of a telescope whose line of sight is C'D, would see if the mirror were removed.

It follows that the angle BDC between the mirror and the axis of the telescope is half ODO', the angle between the direction of the axis of the telescope and the direction from D of the object 0.

II. When the half of the object glass (or large glass) of a telescope is covered over, then an eye looking through

the telescope will see exactly what it saw before except that the image will be half as bright.

The effect is very similar to the effect of looking at a picture in the first case by the light of two candles and in the second by the light of only one candle.

L. E. T.

18

III. When looking through the eyepiece of a telescope the eye looks at an image (which is a small picture formed by the rays of light coming from the object looked at, inside the tube of the telescope) of the distant object at which the telescope is pointed.

The eyepiece or small glass of a telescope forms in fact a microscope with which the eye sees this image magnified.

Thus in the figure, O is the object-glass, E is the eyepiece or microscope; I is the position of the image.

I is called the focus of the object-glass.

316. To describe the arrangement of a Hadley's Sextant.

Let the axis AB of a telescope be directed to the edge C of a plane mirror perpendicular to the plane of the paper whose section is CD.

And let EGF be the section of another plane mirror arranged so that light coming from a distant object Q

falls on EF and on being reflected by the mirror falls on CD and on being again reflected is in the direction of the axis of the telescope AB.

Then an eye looking through the telescope would see the images of two distant objects P and Q.

These two images would be superposed.

One image that of a distant object P in the direction ACD the light from which is direct.

The other image is that of a distant object Q in the direction GQ the light from which is reflected.

The mirror EF is arranged so that it can turn about G keeping always perpendicular to the plane of the paper and the angle through which it turns can be observed.

When the mirror EF is turned so as to be parallel to CD the reflected image and the direct image would be that of the same very distant object.

The angle through which the mirror EF is turned, from the above position, until the image of Q is visible in the telescope is half the angle between CP and GQ; that is, half the angle subtended by P and Q at the observer's eye.

[P and Q are always very distant objects such as the horizon at sea or the sun or a star.]

For, produce GC to A'B'; then the angle PCB' is fixed.

Draw GK perpendicular to EF; the angle turned through by EF in any moment, is equal to the angle turned through by EK; and the angle QEC is always double of KEB'; therefore the amount of turning of EQ relative to EC (which is fixed) is double that of EK relative to EB'; that is is double of the amount of turning of EF.