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% RAJA RAM SING, of Khota, to the Government of India.-By J. J. o

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ART. V.—Description of an Astronomical Instrument presented by

MIDDLEton, Esq. of the Hindoo College, Calcutta.

The instrument of which I am about to attempt a description, was presented some time ago by the Raja of Khota to the Government of India, as a very good specimen of its kind. The body of the instrument consists of a square plate of pure and massive silver, in addition to which, on one side, is a plummet or index-rod, which revolves freely in the vertical upon an axis fixed at one of the angles of the plate, and at the termination of a tube of about one-sixth of an inch in diameter, which runs the whole length of one side of the instrument. On the other side an index, consisting of four hands, at right angles to each other, and of nearly the radius of the plate, is screwed on to the centre of the plate, around which it revolves at pleasure. The drawings which accompany this description will render the above observations quite clear.

The Sanscrit inscription on the obverse of the plate, and occupying a triangular space at one of its angles, informs us at once of the class of instruments to which it belongs. The inscription may be rendered as follows—“In the year 1891 Sumbut, (1756) “Shokabdha, in the “month of Assar, on the 7th day of the moon, the son of Boidhanath,

“constructed this astronomical instrument, in accordance with the

“principles of an astronomical work, styled Jontro Chintamony, “under the direction of Raja Ram Sing of Khota, (blessings be upon “his head) who is an encourager of learned men.” We learn from this, that the instrument is of very modern construction, a circumstance which however in no way detracts from its substantial interest, since it is not indebted, so far as I can discover, to modern principles of science, but might have been fabricated or used by the Indian astronomer of some thousand years ago. This, and the great rarity of astronomical instruments in India, at least in this part of it, contribute to it considerable importance. Of several learned Brahmins with whom I have consulted regarding the instrument, no one could give any account of it; indeed, with the exception of some unimportant facts, it was to them only a subject of astonishment; some, it is true, had read of such instruments in Bhascara, and other commentators on the Siddhants, but their notions of them, thus derived, were in the highest degree obscure. No additional fact is necessary to prove how rapidly Indian astronomy is fading away in its native soil,—a decay which the Brahmins themselves readily admit; and which they attribute to the little encouragement held out to those who profess it. Although the relaxation of the grasp in which the Brahmins have long held the Indian mind, can be no subject of regret, and the discredit of their vaticinations no ground for lament; yet those who delight to trace the history of the human mind, and who contemplate with satisfaction the monuments of its industry and power, must ardently desire that Indian astronomy should be embalmed, as entire and perfect as possible, in scientific history. To effect this, the lover of science should allow no fact to escape him, being assured, that so soon as the sciences of the West have been diffused over India, so soon will Indian astronomy be but a name. I shall begin my particular description of the instrument by showing its use in finding the time of the civil, or bhūmi sãvan, day, which with the Indian extends from sunrise till sunset. For this purpose the inner quadrantal arc, described upon the obverse of the instrument, is graduated from right to left to fifteen prime divisions, these again being subdivided into six equal parts; the former being the number of dundas in half the Indian equinoctial day, and the latter being arcs of ten pulahs each, equal to four of our minutes. This will be rendered more plain by the following table of Indian divisions of time.

6 Respirations = 1 Vicala.
60 Vicala = 1 Dunda.
60 Dundas = 1 Nachshatral day"

In order to find the time of the day, the observer places the index rod upon its axis, which is fixed near one extremity of the tube, and raises the instrument in the vertical plane till he can see the sun through the tube ; he now marks what part of the circle of time just described is cut by the rod, and reads off the number of hours and minutes, proximately, which the sun has of altitude, and this being added to the time of sunrise, or subtracted from that of sunset, (data which their almanacks supply) gives him the hour of the day. I need scarcely mention, that though the result is not strictly true even within the tropics, yet it is sufficiently so for the Indian astronomer, who diminishes its errors by compensations, a mode of correction to which he is accustomed, and in the application of which he is exceedingly skilful. The outer circle is an arc of the meridian intercepted between the equator and the pole, and is graduated to 90°, the divisions being num

* Nachshatral day, the time of an entire revolution of the earth.

bered from left to right. By this, the index-rod being adjusted as in the last case, the zenith distance may be readily found ; but when taken in connexion with other parts of the instrument, the latitude of places is also easily found. Before describing the manner in which this is done, however, it may be as well to enter into a brief exposition of the principles involved.

Of all the observations which the Indian astronomer makes, none are so generally important to him as those made with his gnomon and graduated horizontal plane, for any error committed here vitiates almost every calculation to which he is accustomed. When the practical imperfection of this instrument is considered, and the difficulty which the Indian artist has to encounter in its construction and adjustment from the rude tools he uses, it is a matter of much astonishment that he attains such accuracy as he will be presently seen to do.

Having fixed a conical gnomon perpendicularly upon a plane, which he graduates into ungolas, or digits, each equal to a twelfth part of the height of the gnomon, he again subdivides these into beungols or 60ths of an ungol. Thus provided, he proceeds at noon on the day of the equinox, to measure the length of the sun's shadow—an operation upon the accuracy of which depends his reputation as an astronomer. Having carefully ascertained the length of the shadow, he next proceeds to the determination of his latitude, which he effects in the following manner:—

Let A B be the gnomon, B C the graduated plane upon which the shadow is to be measured, S A D a ray from the sun S, then B D is the shadow.

Draw D G at right angles to B D, and upon it let fall the perpendicular S E, and from G draw G F perpendicular to D G.

Then VA B2 + BD2 = AD by the 47th of Euclid (a proposition well known to Indian mathematicians, and probably borrowed from

B D S E - - - - - them) and i = To = the sine of the zenith distance.

Indian mathematicians do not appear to have been acquainted with the nature and use of tangents; had they been so, they would certainly have used them in the present case, as their object would thereby

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- - , B D G F have been less indirectly attained; since xi = Tri = tan. zen. dist.

These observations being premised, let us again return to the examination of the plate. It will be observed that its surface within the circles is crossed by equidistant straight lines, intersecting each other at right angles, and that at the twelfth division counting from the angle where the axis of the index-rod is placed along on the one side, the perpendicular has the points of intersection of the other lines numbered 1, 2, 3, 4, &c. If then the outer line thus intercepted by the line last mentioned be taken to represent the axis of the gnomon, the lines 1, 2, 3, 4, will represent the section of its shadow, and if the edge of the rod, adjusted as before, be brought over the number signifying the length of the shadow, that edge will also intercept a segment of the quadrant of latitude equal to the zenith distance. This will readily appear on inspection of the diagram just given. Thus the length of the shadow at any place being known, our instrument at once reveals the latitude. The only use of this side of the instrument, so far as I can make out, which remains to be explained, is in the determination of heights and distances. To show its A. usefulness in this respect, little Loy more will be necessary than to o / adduce an example of its appli _ f cation; let A B be an inacces- __ / sible object standing on the __ 2^ / horizontal plane B D, whose 5. U TB height is required. Observe through the tube the summit A, and mark what division of the line 1, 2, 3, the index allowed to revolve freely on its axis intersects, and let that be, for example, at the number 12; then go backwards in a direct line from the object to any new station D and observe the summit of the object as before ; let us suppose that now the edge of the rod is found to intersect at the number 16, then we have 16-12: 16 : DC : D B=4CD and 16 : 4CD : 12: BA=3CD, the height required. It is unnecessary to multiply examples, as from the one now given the readiness with which trigonometrical measurements of a simple kind may be effected without the introduction of angular functions, is sufficiently evident. As to the accuracy with which they can be performed, it may be perhaps sufficient to state that, after a little practice, I found

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