which we have found in those deducted from the co-efficients of the square of a binomial.

In case n-1 should be a prime number, we may find formulæ divisible by (n-1), thus: If instead of subtracting the two extreme terms of the co-efficients, we subtract the two first and two last, we have,

and since, if n-1 is a prime, each term on the right side of the equation is divisible by (n-1); the expression on the left side is always divisible by (n-1) in the same circumstances; or the expression

is always divisible by (n-1), if n-1 is a prime number, otherwise it is not divisible. It is obvious that similar theorems might be deduced, in which the prime divisors should be (n—2)3, or (n—3)o, &c.

ART. VIII.-Description of the Diamond Mine of Panna. By FRANCIS HAMILTON, M. D. F. R. S. & F. A. S. Lond. & Edin. Communicated by the Author.

DURING the rainy season of the year 1813, on my way

from Agra to Chunar, I made an excursion from the Yamuna (Jumna, Rennell,) to visit the Diamond Mine at Panna, and first proceeded up the Ken in my boats for two days; but I made very little progress, owing to the strength of the current, and the badness of the ground on the bank for tracking. The Ken is not a great deal smaller than the Yamuna, and resembles it much in having very high banks intersected by numerous ravines. Its channel abounds in pebbles of agate and jasper; but, in the rainy season being entirely filled with water, scarcely any were procurable; nor did I obtain any good specimens. These pebbles are not so much variegated by zones of different VOL. I. NO. I. JUNE 1819.

D

colours, or dendritical figures, nor do they contain so much crystallized matter, as those of the Son; but the jaspers are more perfect, and are red, honey colour, and black, some of the latter especially admitting of a fine polish.

After two days labour, with a strong fair wind, I was told that I was only four coses nearer Banda, than when I left the Yamuna, the whole distance being reckoned ten coses; but, leaving my boats and travelling by land, it took me from six in the morning to eleven to reach the town in a palanquin, during which time I must have gone twenty miles. The coses of Bandelkhand, the district of which Banda is the capital, are therefore very long. From Banda to the Diamond Mine is reckoned twenty-nine coses: but I took eighteen hours to perform the journey in a palanquin, with relays of bearers, and making no halt that was avoidable. The distance, therefore, must be seventy miles, as the roads, when I went, were tolerably good. As it rained much on my return, the roads were bad, and I took much longer time. I must here observe, that the latest maps of India, which I have seen published, even by far the best, that of Mr Arrowsmith, represent this part of the country very imperfectly.

Singhapur is a small town at the northern side of the hill, on which is built Ajaygar, or the Invincible Fortress, and is twentyfour computed coses from Banda. The country between the Yamuna and Singhapur is in general level, with, however, many projecting insulated rocky hills. That immediately adjacent to Banda consists chiefly of a small-grained granite; some of which contains red felspar, white quartz and black mica; and some is composed of white felspar and quartz, with black mica. Besides the granite, this hill contains also large masses of quartz and felspar, very irregularly intermixed rather than aggregated into one solid rock. From the ruggedness of their appearance I judge that the other small detached hills are of similar materials; but I had no opportunity of examining them.

At no great distance to my left, in going to Singhapur from Banda, I had a ridge of hills, which is a continuation of that which, commencing at Rohitasgar and Sahasran on the banks of the Son, passes behind Mirzapur and Allahabad, and which, from the last-mentioned place, takes here a large sweep to the

south, and then bends north to Goyaligar, and from thence behind Agra and Dilli, being the northern boundary of the Vindhyan mountains. The portion of this ridge passing through Bandelkhand, has a very similar appearance to the part of the same range that passes through the Shahabad district, only it is less sterile and rugged; for the trees in most places ascend to the very summits of the hills, and it is only in some places that the table land on the top is bounded by an abrupt precipice of rock, such as surrounds the whole eastern end of the ridge. The nature of the strata seems, however, perfectly similar throughout its whole extent, consisting of horizontal rocks, which, near the surface, are a kind of free sandstone, very fit for building; but in the interior of the mountain, the rock is too hard, approaching near in nature and appearance- to hornstone or granular quartz. The colour is various, red, brown, and white; and, in general, it is more or less dotted with black.

On the summit of this range, is a table-land of great extent, and from about 500 to 1200 feet of perpendicular height above the level of the Gangetic plain. To the side of this table-land most remote from this plain, I have not reached; but from the side next the Ganges, there project many small ridges of the same materials, which run towards the Ganges and Yamuna, as at Sahasran, Chunar, Mirzapur, Allahabad, and at Famos, where a ridge not only penetrates across the channel of the Yamuna, as others in several places do, but rises into a small rocky hill on the left bank, thus forming the only hill in the ancient kingdom of Antarbeda, now called the Dooab by the Muhammedans.

The very strong and remarkable fortress of Kallangjar is on one of these ridges, projecting to the west from the main range of hills, but separated by a narrow gap. I passed it both coming and going in the dark, so that I had no opportunity of examining the strata; but the buildings of the town, no doubt taken, from the hill, are of the free sandstone usual in this range.

Ajaygar, another fortress, seven computed coses from Kalangjar, stands also on a ridge projecting to the Ken river; but the portion of the hill occupied by the fortress, is separated from the east and west ends of the ridge by two deep ravines that penetrate the hill almost to the level of the plain. Al

though the upper part of the hill occupied by the fort, consists of the usual freestone, the lower part, on the south side at least, towards the market-place called Katra, consists of a very fine perfect granite, with large concretions of red felspar. According to a manner of reasoning usual with several mineralogists, we should call this granite incumbent on the sandstone, the latter occupying the higher and central part of the ridge. I will venture to say, that in the world there is not a more perfect granite, nor one which has less the appearance of stratification; and it must be observed, that in many parts between the Sandstone range and the Ganges and Yamuna, there are scattered small detached peaks of the rocks usually called Primitive, as at the hill near Banda, already described. Beyond these peaks there is no rock whatever, until we come to the Himalya mountains.

From Singhapur, adjacent to Ajaygar, I proceeded in an easterly direction, through a narrow valley, for about four miles, to Vizramgunj, at the bottom of the main sandstone range of hills. Here, as the name implies, had been a neat resting-place, with a reservoir of water, and various accommodations for travellers. From the style of the buildings, they would appear to have been erected by the Muhammedans, and are said to have been destroyed out of mere wantonness by the last Marhatta officer stationed at the place. From this resting place, I ascended the hill by a very bad road, but practicable for loaded cattle or palanquins, and conducted with total disregard to art, as it leads straight up the steepest ascents. The total height is very considerable, perhaps five or six hundred feet perpendicular. In the middle of the way has been another place of refreshment, built in the same style with that below, and probably also a Muhammedan work. The hills here abound in Sagwan (Tectona grandis), and in a species of Diospyrus producing Abnus (Ebenus). The former, so far as I can learn, never reaches to a size fit for use; the latter is nowhere larger or better. The tree is by the natives called Tenged; it is only the black heart that is called Abnus,-a Persian term, from which our Ebony is derived; and I am well informed that, in the Sangskritta, there is no term for this wood, polished timber, it would seem, having

entered little into the economy of the ancient Hindus. Bamboos are also abundant on these hills.

The table land above the ascent is more level, and freer from rocks, than that in the Shahabad district; but, although I advanced on it about three miles, and to within full view of the town of Panna, I saw not the slightest trace of cultivation. I did not proceed to Panna, because I found the people at work in search of diamonds, and thus satisfied my curiosity without being obliged to remain a night destitute of comfort in the formality of a visit to the Raja.

The whole plain on the table land for several miles round Panna in all directions, wherever it happens to be of a gravelly nature, is said to produce diamonds. In most parts, the soil is very red, in others it has only a slight tinge of that colour, and is of a dark brown. This soil is from two to eight cubits deep; and, where the diamonds are found, contains many small pebbles, a good deal resembling some ores of iron that I have seen in Bhagalpur. The diamonds are found intermixed with this, but never adhering to any stone or pebble. The workmen lift up the gravelly earth in baskets, throw it into a shallow pit filled with water, and wash out the earth. They then spread the washed gravel thin on a smooth piece of ground, and separate the useless pebbles with their hands, moving eight or ten pieces at a time, so that no diamond can possibly escape their notice. Many days are thus often spent without success; but a very few diamonds in the year repay the workman for his labour. The greater part of the diamonds are not worth more than 500 rupees*. A good many, however, are found worth from 500 to 1000. Very few are found worth above the latter value. The Raja is said to have at present one valued at 50,000 rupees; but he has not been able to find a merchant, and has placed the gem in the head of an image. The workmen assured me, that the generation of diamonds is always going forward, and that they have just as much chance of success in searching earth which has been fourteen or fifteen years unexamined, as in digging what has never been disturbed; and, in fact, I saw them digging up earth which had evidently been

The rupee contains 1793 grains of silver.