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The Palace of the Maharajah is neither particularly interesting nor beautiful, and we did not visit it further than to inspect the ancient observatory built by Jey Singh, with its huge sundial, whose gnomon stands 80 feet above the ground!
Eratosthenes improved upon this. He observed that at the summer solstice at Syene, at noon, the sun cast no shadow, while at the same moment the upright gnomon at Alexandria cast a shadow corresponding to an angle between the gnomon and the sun's rays of 1/50th of four right angles.
Then, of the nine parts between the plane and the centre on the gnomon, take eight, and mark them off on the line in the plane to the point C. This will be the equinoctial shadow of the gnomon. From that point, marked by C, let a line be drawn through the centre at the point A, and this will represent a ray of the sun at the equinox.
If, instead of two sticks, we cut out a piece of metal or wood to fill up the enclosed angle, we get the earliest form of the sun-dial, known as the gnomon, and according to the shape of the gnomon the latitude of a place is determined.
It is due to the divine intelligence and is a very great wonder to all who reflect upon it, that the shadow of a gnomon at the equinox is of one length in Athens, of another in Alexandria, of another in Rome, and not the same at Piacenza, or at other places in the world. Hence drawings for dials are very different from one another, corresponding to differences of situation.
Every night as I gazed up at the window I said softly to myself the word paralysis. It had always sounded strangely in my ears, like the word gnomon in the Euclid and the word simony in the Catechism. But now it sounded to me like the name of some maleficent and sinful being. It filled me with fear, and yet I longed to be nearer to it and to look upon its deadly work.
He says, that the change in the obliquity of the ecliptic in this interval was only 2' 36". "A gnomon, therefore, at Syene, of the length of twelve inches, if it cast no shadow on the day of the solstice in the time of Eratosthenes, should have cast a shadow in the time of Plutarch of the length only of 9/1000th, or not quite 1/100th part of an inch.
There were two sun-dials on different sides of the house, both the dial-plates of which were of stone; and on one the figures, so far as I could see, were quite worn off, but the gnomon still cast a shadow over it in such a way that I could judge that it was about noon. The other dial had some half-worn hour-marks, but no gnomon.
Hipparchus had the gnomon of Eratosthenes doubtless in a perfected form to aid him, and he soon proved himself a master in its use. For him, as we have said, accuracy was everything; this was the one element that led to all his great successes. Perhaps his greatest feat was to demonstrate the eccentricity of the sun's seeming orbit.
Much more striking, at least in its appeal to the popular imagination, was that other great feat which Eratosthenes performed with the aid of his perfected gnomon the measurement of the earth itself.
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