If the telescope is turned on its axis and clamped at any desired altitude, and the whole instrument revolved around the upright axis, the sight line will describe a small circle parallel to the horizon. A few seconds only are required for the mercury and float to come to perfect rest. It is evident that the transit of stars, as they rise or fall over this horizontal circle, may be observed, and will furnish the means of finding the clock error, and the latitude, by a proper selection of the stars in different azimuths.

The mathematical theory of the instrument is succinctly indicated as follows:

From the spherical triangle between the pole, the zenith, and the star

Let,,, and ., be assumed approximate values, which employed in eq. (1) give 0, and to.

Also let ', ', be the apparent place of the star,

the actual zenith distance at which the instrument is pointed,

r the refraction.

Then we have the final equation for the clock correction 4T, T being the observed clock time of the star's passing the middle thread,

ST=Z (z + r) + Ll + 0. − T + a + Dd

(5)

where (z+r), treated as a single unknown quantity, is the deviation of the collimation line of the telescope from the assumed horizontal small circle. The term LZ disappears if the correct latitude has been used in the computation of 1 and 0. The rest of the second member contains only known quantities.

For reducing the observed time T' of the star's passage over a side thread, whose interval (in time) from the middle or mean thread is f,

we have

TTZ-Z2

cos A cos q
sin t

15
20

sin 1′′ ƒo

(6)

where the last term is insensible for observations made near the prime vertical, and is in general small except near the meridian. For the special case where 90, that is, for the small horizontal circle passing through the pole, the above formulas are very much simplified, as follows:

Cos t

Sin A=

tan tan (45° — 1 )

cos & sin t

cos ф
1

D= 15 cos 8 tan t

q=t

(6)

In the practical use of the instrument at any given station, it will be convenient to compute once for all, for some one appropriate horizontal circle, or value of, the values of 0 and also the co-efficients D and Z for all Nautical Almanac stars, with

assumed approximate values of and . These values will last and. for a series of years. I would suggest for these latitudes the small circle passing through the pole, being one which possesses many practical advantages, as the plane in which the instrument should be used. Whatever circle is chosen, the instrument can be quickly and approximately set to the altitude in question by methods which I need not stop to describe. As many stars as are desired may then be observed alternately east and west, preferably near the prime vertical. A single pair of stars will of course suffice to determine the deviation of the instrument from the assumed plane and the clock correction, or (z+r) and 4 T. A set of several stars can be treated by the method of least squares. If the latitude is only approximately known, the pairs of stars can be selected so as to eliminate the unknown error in latitude. Also stars can be chosen which have large latitude co-efficients, and the correction to assumed latitude found with great accuracy. I will only mention that by the application of a weight which, by a screw, may be moved longitudinally along the float, a micrometer of great delicacy would. be furnished, operating on the principle of gradual and minute alterations of the centre of gravity, and thus of the altitude of the sight line. This would permit of the employment of the methods used with the zenith telescope for latitude.

The advantages which are claimed for this instrument, over the transit instrument, are principally:

1st. Simplicity in use, there being only one adjustment to make, and only one instrumental error to determine. There are no levellings or reversals to make, operations which take fully onehalf the time and labor of using a transit. The observation of slow moving polar stars may be dispensed with, which is another economy of time.

2d. The greatly lessened danger of disturbing the adjustment of the instrument by blows or jars, or want of steadiness in the mounting. A jar, which would infallibly throw a transit out of level or azimuth, produces in this instrument only a slight oscillation, which ceases in a few seconds, the instrument returning to absolutely the same plane as before disturbance.

3d. Greatly diminished cost; there being no parts requiring great nicety of construction, such as the pivots of the transit.

4th. Combination of a time and latitude instrument in one.

FIG. 2.

As to accuracy, I find that, even with this experimental instrument, in many respects provisional in its construction, with an object glass of very poor definition (of 12 inches aperture and 25 inches focus), employed in the open air with no protection whatever from the wind, and placed merely upon an ordinary table, or box of sand, I obtain results of at least equal precision with those given by transit instruments of about the same size, under the best circumstances. The probable error of the clock correction found by this instrument, from a set of stars such as would ordinarily be taken with a transit, for clock and instrumental corrections, is not over ±0.05 sec. From my practical experience with transits in actual work, I do not hesitate to assert the belief that for instruments of moderate size, this new construction is more serviceable than the meridian transit.

The second instrument to be described is also an equal altitude instrument, but is constructed on a totally distinct principle, and is of a very different order of accuracy. It is intended to supply the place of a sextant for land use, and of small, portable transits in the determination of time by surveyors, exploring parties, watchmakers, and all who desire a simple means of finding the time within a second.

vertical position, without any torsional revolution. To the bar is affixed a small telescope, the object glass near the bottom, the eye-lens at the top of the bar, with a horizontal wire in the common focus. Below the object glass a frame is fixed to the bar, carrying a plane mirror swinging on a horizontal axis, and provided with a clamp for fixing the mirror at any desired inclination. Below this is a metal bob. The whole construction thus forms a pendulum, which is suspended inside a large tube, at the base of which are approximate levelling screws. (FIG. 2.)

It is evident that if the instrument be turned towards the sun, and the mirror revolved until rays pass after reflection directly up the telescope tube, an eye looking into the telescope will see. an image of the sun in the field which, as the sun rises or falls in altitude, will appear to cross the horizontal wire, which, in fact, represents a section of a small circle in the heavens, parallel to the horizon.

For

This brief explanation will indicate clearly the use of this instrument in getting the time by equal altitudes of the sun. this purpose it possesses the most surprising facility and accuracy. The instrument can be adjusted in a few seconds so as to bring the sun to the proper place in the field. The mirror being clamped, the transit of both limbs of the sun over the horizontal wire may be observed to within a half a second by an ordinary watch. The instrument is then set aside until a corresponding time, afternoon, or next morning, when the transit is again observed. The watch error from noon, or midnight, of course follows by applying to the mean of the observed times, the "equation of equal altitudes, and the "equation of time," as explained in the text book.

For cheapness and simplicity, this instrument has, of course, very greatly the advantage over the sextant with the artificial horizon, and over the small portable transits used for this purpose by watchmakers and others; while in point of accuracy it is equal or superior to them. By an extended series of tests made on twelve instruments of this construction, I find the probable error of a single determination of time to be 0.8 sec., which could be somewhat reduced by employing three wires instead of one. The degree of accuracy already attained is, however, sufficient for the purposes of those for whose use the instrument is intended.