height so noted. This angle will give the time before or after 6, either A.M. or P.M., by taking 15° for an hour and 15' for

a minute.

In all this it will be perceived that to obtain the time thus we require to know the latitude. To proceed therefore to find the latitude of any place, adjust the instrument on its level edge truly North and South, and level. Open the instrument, with the Mirror raised, so that the shadow reflected from the Mirror may fall upon the zero point on the disc. As soon as it is 12 o'clock, which is the time at which the shadow is most particularly required, it will vanish by reason of the Sun drawing round so as to leave the side of the instrument in the shade. But this will be of no consequence, as by a slight inclination of the Mirror the disc will be reillumined by it. This is the critical moment at which the operation must be completed. The angle thus taken is the altitude of the Sun, but the reading of the instrument gives the complement only of this angle, which in this instance happens to be convenient, inasmuch as the addition to or subtraction from it of the Sun's declination for the day gives the latitude of the place; the angle given by the observation being the complement of the zenith distance.

This operation may be briefly described thus: find the Sun's altitude at 12 o'clock, and to or from this altitude add or subtract the Sun's declination for the day. The result will be the complement of the latitude of the place.

The Sun's altitude may also be found by holding or resting the instrument with the level edge uppermost; the hinge turned from the Sun. The sight-vane must be erected as if for observation of bearings. When the instrument is so adjusted that the shadow of the scratch on the Mirror falls through the slit in the sight-vane, while the level shews horizontality,

the reading at the outer edge will give the half angle of the Sun's altitude. This process is like that to be described in the next page, only with the instrument inverted.

The declination for every day for the next four years will be given according to tables furnished to the author by the courteous permission of Mr Hind.

The declination, however, may be calculated for any day by the instrument itself, independently of the tables, thus*:

1. Count the number of days to the nearest equinox.

2. Take a degree minus a minute for a day.

3. Set the instrument to the angle thus given.

ΤΟ

4. Find the sine for this angle to radius 4. Obs. 1 is very approximately the sine of the angle of the ecliptic.

5. Find the angle which has the same sine for radius 10. This angle is the declination.

Owing to the inconvenience attending measurements of very small angles it will be better to compute the declination for days very near the equinoxes, as changing regularly at a rate of 23 minutes a day, or a minute an hour. The whole of the inaccuracy arising from taking 59 minutes for a day will be thrown upon the solstices, when the variation of the declination is so small that the error arising will never be appreciable.

The exact equinoctial moment from which the time ought to be reckoned varies every year, that is, it changes a little more than six hours every year, so coming round to the same moment nearly every fourth year. For a convenient approximation to the true moment we may make it,

⋆ This part, involving a simple operation of trigonometry, may be read after the fourteenth section.

It has been assumed in these operations that the true meridian is known. The operation for discovering it by the Polymeter may be performed thus:-At some time considerably before noon, when the Sun is visible, set the instrument in a line with its own shadow, the hinge from the Sun, the Compass-box turned over, the sight-vane and Mirror erected, and the instrument standing on its level edge, perfectly level. Open the Mirror-leg till the light of the Sun thrown from the Mirror falls on the back of the sight-vane, the shadow of the scratch falling through the slit. If the instrument is rightly set, the bright image of the Mirror will fall close into the hinge on the sight-vane, without being at all shortened by falling in too close. Draw a line on the level ground along the lower leg of the instrument to note its position. In the afternoon, watch for the Sun's approach to the same altitude, and set the instrument opened as in the morning, so as again to receive the same bright reflection on the same spot of the sight-vane: the instrument again will then be in a line with its own shadow. Again rule a line on the ground along its leg crossing the first line drawn already in the morning. The lines bisecting the angles between these two lines point very nearly due North, South, East, and West, not exactly so, on account of the small change of the Sun's declination between the forenoon and afternoon operations. This change of declination about the equinoxes is nearly 1' per hour. Towards the solstices there is no perceptible change of declination, a phenomenon which has given their name to these periods.

If it be impossible to take the morning and afternoon observations on the same spot, note the magnetic bearing on the first line, and commence the afternoon observation by drawing a line with the same bearing from the magnetic meridian, and proceed as above.

XI. THE SQUARE.

The Square of the Polymeter, or Sining Rod, is an instrument, composed as it were of two Metal Rulers joined into one, forming a right angle: the length of these Rulers being respectively 6 and 24 inches. The implement fits into a groove cut in the ends of the two legs of the Sector, and along the outer edge of the Mirror-leg.

This is a substitute for a pair of Compasses, and, in conjunction with the Sector, serves for Proportional Compasses, Ready Reckoner, Ruler, General Line-divider, Trigonometer, and likewise, when so needed, for a Plumb. It is also in itself, with the Line of Lines, Scales, and the graduated joints of the Sector, the practical substitute for all those lines which represent the secants, tangents, and sines of a circle, whose radius is 6 inches, engraved and divided on the common sectors; as by means of its right angle it shews the sine and cosine, the tangent and cotangent, of whatever angle you can set on the graduated disc of the instrument.

On this Square will be observed four sets of numbers, viz. 1 to 11 on its bevelled side, 8 to 12, and 13 to 17 on the other side, and also a numeration of 1, 3, 5, 7, 9, 11: the first and last mentioned shew the length of the Square in half-inches from its angle. The other two sets of numbers are for use when the

Sector is employed as a Sliding Rule to measure inner dimensions; as the inside of a mortar, or a water pail. See Article II.

Should the thing to be measured internally, be less than 6 inches, a small mortise will be seen under that Sight-Vane which covers in the screw key. If the instrument be opened out, and the end of the long arm of the Square be entered into that mortise through the long groove, you will be able to measure internals from 14 inch to 7 inches.

THE BEVEL.

To gauge large angles. Open the instrument wider than 90o, and then set the Square into its place, in the compass leg of the Sector, just as if the instrument were closed: the long side of the Square will now be found to rest against the brass sheaf of the circular joint. Apply now the instrument against the two faces of the angle to be bevelled. If necessary, the angle can be read off on the graduated disc and be noted.

To gauge small angles. Open the Sector to 90°, and grasping the M Needle-leg with the right hand, hold the Square firmly, in flat contact with the outer side of one leg of the Sector, projecting as far as is convenient beyond the hinge. The angle required is that included between the other leg when opened out and the Square so held. The complement of the reading will be the angle required.

Should the required angle be re-entering instead of salient, it will be taken without the aid of the Square, by merely so opening the Sector, as to lay its two outer edges in contact with. the two faces of the angle whose measure is required; the graduation will be read off on the disc as before.