A pretty severe attack of the prevailing epidemic, with a good deal of sickness in the family, must be my excuse for not sending on your Time-piece somewhat sooner. It was, however, last saturday shipped on board the Guinea Hen, &, according to your directions, consigned to messrs Gibson & Jefferson of Richmond.1

On examining the pendulum mentioned in my last, & which I proposed to substitute for the one now in use, I find that it would be attended with too much difficulty & danger in transportation, & be very unmanageable in the adjustment. It consists of a large glass cylinder attached to the lower extremity of an iron rod, which is filled to the height of over 7 inches with mercury, (about 10 pounds) & serves as the bob of the pendulum. This pendulum possesses the principle of compensation, on account of the change of temperature in the air. For, on the increase of temperature, which would lower the center of oscillation, by lengthening the rod of the pendulum, the expansion of the mercury, from the same cause, would raise the center of oscillation. But the pendulum now attached to the clock is more simple in its construction, or at least much less expensive, & from a trial of some years, in all states of temperature, appears to preserve a very uniform rate. It is, I believe, (as I mentioned formerly) the invention of David Rittenhouse, & is sufficiently described in the Memoirs of his life by Wm Barton, p. 584–5.

I have not very much confidence in the cylindrical pendulum as a standard of lineal measure, ☞when suspended by a spring2☜ for, according to a series of experiments made by mr Adrain of N.Y. a difference in the length or strength of the spring, produces an incalculable difference in the time of oscillation. But Mr Hassler suggests a manner of suspension which would be free from this sourse of error; namely, to suspend the cylindrical rod on what is termed a knife-edge, passing thro a perforation made at the distance of ⅓ of its length from the upper extremity. A small cylindrical pendulum, thus suspended, would make its oscillations very nearly isochronous with a bob pendulum of the same length, & would furnish a true universal standard of lineal measure. For, having given—the latitude of the place, the elevation above the surface of the sea, the mean temperature of the air, the metal of the pendulum, the proportion between its length & thickness, the proportion between the length of the parts above & below the center of suspension, the number of oscillations in a sidereal day3 and what proportional part of the Length is to be considered as the unit of measure (an English foot for instance) then it could be found by calculation, from data well enough ascertained, what proportional part of any other pendulum of the same form, where all the above data should be different, would be the same unit of measure.

You will find in a small tin box, along with the clock, the artificial reflecting horizon which I formerly mentioned, with a very accurate spirit level, made by mr Hassler. He has determined, in a very simple manner, which I may hereafter describe, & with the utmost accuracy, the two oblique angles of the inclined plane, which you will find engraved on the same.

The manner of using this apparatus, for measuring any altitude of a celestial or terrestrial object, is as follows.—

	1.	Place the horizontal reflecting plane on any convenient stand, as the cill of a window, a table, or the like. On this plane, & parallel to the longer side, lay the spirit level, &, by turning one or other of the screws, bring the bubble to the middle of the glass tube.
	2	Lay the spirit level accross the plane, &, by turning the side screw, bring the bubble again to the middle of the tube The plane will then be level, or horizontal, in all directions.
	3.	If the altitude to be measured be not less than 15° nor greater than half the graduated limb of the reflecting sector, then the altitude may be measured, in the common way, by means of the reflecting horizontal plane.
	4.	If the altitude be less than 15° then, on the horizontal plane, place the inclined plane, with its lesser angle directly towards the object, & measure the altitude above this plane, & then the real altitude above the horizon will be this measured altitude, diminished by the quantity of the lesser angle of the plane, (29° 40′)
	5.	If the altitude exceeds the limits of the sector—place the lesser angle of the inclined plane directly opposite to the object, & then the true altitude of the object will be its measured altitude above this plane, increased by the lesser angle of the plane.

If a sextant be used, then all possible altitudes, from 0 to 90° may be measured as above; but if an octant be used, then to measure altitudes from 45° to 75° you must place the lesser angle of the inclined plane opposite to the object; & to measure altitudes exceeding 75° you must place the greater angle of the inclined plane on the horizontal plane, & opposite to the object; for then the true altitude will be the measured altitude above the inclined plane increased by the greater angle (60° 53′ 17″)

Remarks

1. In taking the altitudes of objects, by means of a reflecting surface, it is found very difficult, & in some cases impracticable, to measure small altitudes; but, by following the above directions, no angle less than 15° above the reflecting plane, will ever be required to be measured, whether the sextant or the octant be used.

2. With respect to terrestrial objects, it is frequently necessary not only to measure altitudes but depressions; Now, with the above described apparatus, any depression not exceeding 45° may be readily measured by turning the reflecting surface of the inclined plane towards the object.

3. The reflecting surfaces are made of a piece of good [broken] looking-glass, with the polish ground off from one surface, & attached to the brass plane by black sealing-wax. The reflection is then made from the upper surface of the glass, & gives a very perfect image; nearly of the same degree of brightness with that made by a double reflection from the specula of the sector.

4. The use of this apparatus may be very readily extended to the measurement of all possible angular distances, even up to 180° & will thus render the reflecting sector the most complete & accurate surveying instrument that can be made use of

But not to put your patience to any further trial, I shall, for the present, conclude