Fig. 1 represents the field of view of a positive eye-piece of high magnifying power. In this are arranged, in the manner shown in the figure, images of wires for ordinary use and of webs for more delicate observations.

Fig. 2 is the position circle. This is made of very stout block-tin, and is wired at the back to prevent its warping. Its circumference is divided into degrees (the minutes are to be estimated). The circle is fastened on a central cap, like that which is used for a sun-shade, so that the circle can be screwed on to the eye-piece with facility. Every care must be taken to set the plane of the circle at right angles to the axis of the telescope.

Before the circle is put on the eye-piece, the index I, fig. 3,is placed on the telescope, tube T”, and temporarily secured by means of the clamp and screw Cs. Then the circle is put on, and the apparatus will be in the condition represented in fig. 3. If the telescope used is equatorially mounted and properly adjusted, it may be now turned on a double star in any part of the heavens; if it is an alt. azimuth, a star must be chosen on or near the meridian, the nearer the better. The star, or rather one of the component stars, is now made to run along between the wires TT, fig. 1, by turning the eye-piece tube of the telescope round until it does so. Then the index I, fig. 3, must be made to point accurately to the zero of the position circle, and be firmly secured there by means of the clamp.

Next the eye-piece tube is turned round until the line joining the centres of the two stars is exactly parallel to the two wires. Then the circle indication is read off, and, if necessary, 180° must be added to the angle so obtained. Then, evidently, the angle of position with the meridian has been obtained. Several observations of the same star on different nights should be taken. It is advantageous, too, to use different parts of the circle as the zero point. If this be done, the mean of all the observations will be a very close approximation to the truth.

Having found the angle of position, we next proceed to obtain the distance. This operation should be attempted only in the very finest weather. The writer always measures distances either in morning or evening twilight, or in full moonlight when the moon is near the meridian. Thus the illumination difficulty is avoided.

The clepsydra, the use and construction of which will easily be understood from the section of it given in fig. 4, is placed in a convenient position near the telescope. The tanks T and T” are filled with water, the eyepiece tube is turned round as in the previous operation. until one of the components of the double star runs along the wire TT or the web w.w. Then the star is recalled and raised in the field a litttle, so that it may transit the oblique wire TW, or the oblique web w.T. The instant that the first star is bisected by the wire or web, the lever is pressed sharply down to the peg P

To Illustrate Paper by J. H. Pope

Explanation of Plate I.
Rough Plans of Position Circle, etc.
Fig. I.—Field of Oblique Transit Eye-piece.

• M M Meridian transit wire.

• T T Declination parallel wire.

• W W Declination parallel web.

• T W 20° oblique transit wire.

• T W 10° oblique transit web.

Fig. II.—Position Circle.

• E Eye-hole.

• C Cap for fastening circle to tube of telescope.

Fig. III.—Vertical Section.

• C Position circle.

• E Eye lens.

• W W Wires.

• F Field lens.

• T Eye-piece tube.

• T′ Telescope tube.

• C Clamp and screw for index.

• I Index.

Rough Section of Clepsydra.
Fig. IV.

• T Upper tank.

• T′ Lower tank.

• V′ Upper valve.

• V Lower valve.

• 1 1 Brass rods connecting valves.

• B′ Brass pipe.

• G Glass pipe.

• T′ Waste tap.

• S Waste saucer.

• E Excess bucket.

• S″ Graduated scale.

• B Bars, supports.

• L Lever.

• F Fulcrum.

• S″ Spring.

• P Peg to limit movement of lever.

• F″ Fastening of spring.

• A Iron arm.

• W Waste pipe.

• s s s Stand.

• S″ Spring to keep valve shut.

and firmly held there, this raises the valves VV', and water flows up the glass tube G, which has previously been filled up to the zero point of the scale. The instant that the second star is bisected by the wire or web the lever is released, the valves are immediately closed, and the flow of water ceases. The height of the column of water is then accurately measured by means of the graduated scale. Then the water is allowed to escape through the waste-tap T”, and the operation is repeated. A mean of all the observations gives the quantity of water that flows into the glass-tube during the interval between the transits of the two stars. Let this quantity be 2.25 inches. Then an observation is made, by means of a watch, of the time required to fill the tube, that is to say for 30 inches of water to run into it; let this time be 21.5 seconds. A rule of three sum shows us the time elapsing between the transits of the two stars:—

1.612 seconds of time is, therefore, the interval between the transits of the two stars.

Having found this interval, a simple trigonometrical calculation gives us the distance between the two stars:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Let p = the North Polar distance of the star.
α = angle of position of the wire; and
θ = angle of position of the line joining the stars.
T = interval between the two transits in seconds of time.
Δ = distance in seconds of arc between the two stars.
T X 15. sin p. cos α.
Then Δ = / sin (α − θ).

These calculations are not very troublesome. A very little practice enables one to do them very rapidly. It may be as well, in conclusion, to give an example just to show how very little labour is really involved in this process.

On April 5th, 1876, twelve oblique transits were taken of the star 4763 (of Brisbane's catalogue), R.A. 14h. Om., Decl. 53. 6′ S. The average duration of time between the transits of the component stars of the double over a wire inclined 78° 5′ to the meridian, was 9.61 secs. The angle of position had been found to be 22° 0′. Then—

The natural number corresponding to this is 21.53. Hence the distance between the stars is 21 ½ seconds of arc. This measure was taken before apparatus described in this paper had been made as perfect as it is at