Lieutenant-Colonel MACKENZIE's commission, we must admit that his merits have not been merely confined to the duty of a geographical surveyor; and finding that his representations on the subject of the inadequacy of his allowances are seconded by very strong recommendations from you, we direct that you present him with the sum of 9000 pagodas, as full remuneration for his past labours, and as a mark of our approbation of his work.

6. We next proceed to notice the statistical researches. in which also Lieut.-Colonel MACKENZIE employed himself. These are nearly allied to inquiries of a geographical kind, and answer the same end in an improved degree; they have, too, the merit of being in India much more uncommon; and though they were adverted to in the original instructions given to Lieut.-Colonel MACKENZIE, the ample and successful manner in which he has pursued them, in the midst of other arduous labours, proves the zeal by which he has been actuated, and adds to the value of his services and his discoveries.

7. This observation applies with at least equal propriety to his superadded inquiries into the history, the religion, and the antiquities of the country; objects pointed out indeed in our general instructions, to India, but to which, if he had not been prompted by his own and public spirit, his other fatiguing avocations might have been pleaded as an excuse for not attending.

8. Real history and chronology have hitherto been desiderata in the literature of India, and from the genius of the people and their past government, as well as the little success of the inquiries hitherto made by Europeans, there has been a disposition to believe that the Hindus possess few authentic records. Lieut.-Colonel MACKENZIE has certainly taken the most effectual way, though one of excessive labour, to explore any evidences which may yet exist of remote eras and events, by recurring to remaining monuments, inscriptions, and

grants, preserved either on metals, or on paper; and his success in this way is far beyond what could have been expected. The numerous collections* of materials he has made under the different heads above noted, must be highly interesting and curious; and the specimens he has adduced in the manuscript volumes he has sent us abundantly answer this character, whether the grants, which are generally of lands, to Bráhmans, are all authentict (which we mention, not to assert a doubt, but to suggest a reasonable point of inquiry), or whether the whole of the materials shall be found to form a connected series of historical facts respecting a country. which seems to have been always subject to commotions and changes, and unfavourable to the preservation of political records. Still, it must be allowed, that this effort promises the fairest of any which has yet been made to bring from obscurity any scattered fragments of true history which exist, and undoubtedly encourages the expectation of ultimately obtaining both considerable insight into the state of the country and its governments in more modern periods, and some satisfactory indications of its original institutions and earlier revolutions. We are therefore very desirous that Lieut.-Colonel MACKENZIE should himself digest and improve the materials he has collected; and we hope the office which you have conferred on him in Mysore will afford him leisure for this work. After he has accomplished it,

* This collection has been augmented in a quadruple proportion since 1803, both in the peninsula in Hindùstán, and ultimately extended to a new field, the oriental islands, seas, and coasts of Asia.

There can be no doubt of their authenticity; not an instance of forgery has been discovered or even suspected, save one, (and that rather assists history). As they are all before 1620, there is no inducement to fraud; and no one has yet adduced any claims upon them.

the original materials are to be transmitted to us, to be deposited in our Oriental museum. In the meantime, we wish to indemnify him for the disbursements he has made in procuring this collection of materials, trusting that it will not amount to any large sum; and we desire that he will state to us an account of it, which, from his character, we are persuaded will be correctly done; but not to suspend all payment till the arrival of such an account, we permit you, on receipt of the present letter, to make him a reasonable advance on this score. (Signed) D. HILL,

Jan. 27, 1817.

--

Head Assistant to Chief Secretary.

VI. Observations on the value of the cipher and on the mode of computing the time of the Moon's rising and setting.-BY GODAY VENCAt Juggarow.

To the Editor of the Madras Journal of

SIR,

Literature and Science.

I am not fond of writing; but being on the eve of my return to Vizagapatam, my native country, I am unwilling to leave Madras without once more occupying a few pages of your Journal. I am far from attaching any importance to my former contributions; I must not therefore be suspected of mistaking your motive in distinguishing them as you have done; I am contrariwise. well aware, that they are indebted for the honor which has been conferred upon them, to your disposition to encourage such attempts in your Hindoo fellow subjects, rather than to any merit which they can pretend to. In the present state of letters in this part of India, any literary production from a Hindoo will be considered a curiosity, and must as such at least be acceptable to the conductors of periodicals like yours; to which, from the

novelty of its character, it cannot but give an additional degree of interest; and emboldened by this consideration, I flatter myself that I can hardly fail of success in my present attempt, so great is my confidence in the polite indulgence which I may expect at your hands. If then the fate of this attempt be equally auspicious with that of my former essays, this will be my third article in your journal, in reference to each of which 1 am almost painfully sensible, that the nature of my subject on each of these occasions, will gain me but little credit as an utilitarian.

I can assign no satisfactory reason for my choice in this respect; but this is certain, that it should be otherwise if I could help it: this however is not the case at present, and hence my present subject of NOTHING, the most unpromising perhaps in the world.

According to arithmeticians a cipher is an arithmetical symbol, used for denoting the value of nothing, and is denominated insignificant to distinguish it from other figures. Hence a cipher added to, or subtracted from, any number does not increase or diminish its value, so that any multiple of the cipher is still nothing; but there are cases, in which it acquires other properties: for example:

=

Sine 90o 1. Cosine 90° 0 Tan 90° = By the relation of trigonometrical lines,

sin a tan x cos x

therefore sin 90° = tan 90° x cos 90°

or 1 = infinity x 0

infinity.

We will now examine the value of the quotient ofthe cipher. Any number divided by an unit does not change its value, but when it is divided by a number greater or less than one the value is decreased or augmented; therefore any number divided by a cipher increases its value infinitely. Let x represent any number then

we get

infinity, divide both sides of the equation by 0 and

but 0x0 = 0... infinity

multiplying the equation by x, 0 = x.

thus from the foregoing instances we see that a cipher, or nothing has after all some particular value of itself, and is therefore far from being quite so insignificant as it is generally considered.

No. II.-On computing the time of the Moon's rising and setting.

It was not my intention to have presented you with more than one article this time, but after I had disposed of my subject of the cipher I felt as if I had rather have devoted my time to a more congenial subject, and so without further ado I set about preparing the following observations:

It invariably happens that all eclipses of the Moon are visible in some part of the earth when the Sun and Moon are both above the horizon; hence the uninitiated observer would at first sight be led to consider the hypothesis of eclipses as erroneous, yet if he should extend his enquiries into the laws of refraction and other circumstances connected with this phenomenon, he will be convinced that his suspicions are groundless.

There will be an eclipse of the Moon on the 24th October, 1836, which we may expect to be visible here immediately before sun-set: as this cannot but be an interesting phenomenon to many, I have endeavoured for their convenience to investigate a formula for computing the times of the Moon's rising and setting, which, I believe, will be acceptable to such as may need its assistance on the occasion.

The mean time of the transit of any heavenly body is expressed by the difference between the right ascensions