The system of survey and measurement, as promoting the interests of civilization having deeply engaged the attention of His Majesty, directions were issued for the ascertainment of distances and their determination by the standard measure of the kós. The kós was fixed at 100 tanábs,* each consisting of 50 Iláhi gaz, or of 400 poles (<Arabic> báns) each pole of 12½ gaz. Both of these measurements give 5000 gaz to the kós.

Whenever His Majesty travels, the distances are recorded in pole-measurements by careful surveyors, and their calculations are audited by the superintendent and inspector.

Shér Khán fixed the kós at 60 jaríbs, each of 60 Sikandari gaz which measurement is employed in the Delhi country. In Málwah it consists of 90 tanábs of 60 gaz each and in Gujarát is called the cow kós, that is, the greatest distance at which the ordinary lowing of a cow can be heard, which is put by experts at 50 jaríbs. In Bengal it is called dhapiyah,* which is the distance that a fast runner can traverse at one breath. Some assert that it is the distance within which a green leaf placed on the head of one who walks rapidly, will become dry.

In ancient tables of measurement by farsakh of distances and magnitudes, it is recorded that the circumference* of the globe according to the method of the old geographers, was 8000 farsakh, but 6,800 of the modern school, while all agree in defining a farsakh as three kós. The former made the kós 3000 gaz, each gaz of 32 digits. The latter fixed it at 4000 gaz, each of 24 digits. The digit with both was the breadth of six ordinary barley-corns placed front to back in succession, and the breadth of each barley-corn was equal to the thickness of six hairs of the mane of a Turki horse. To short-sighted superficial observers, it would appear that these two sys­tems differ in their estimate of the kós, but it is clear to the perspicacity of the far-seeing that their conclusion is the same, and the apparent difference is caused by the variance in the number of the digits as may be proved by the rule of proportion. This consists of four numbers, the first bearing the same ratio to the second, as the third does to the fourth, as for instance, two is to four as eight is to sixteen. Of the properties of this relation one is this that the product of the extremes is equal to the product of the means, as is evident from the example above mentioned. The proof is given in the 19th proposition of the 7th book of Euclid* where the apparent contradic­tion is removed. The ratio of 3000 to 4000 is the ratio of 24 to 32. Although the four numbers are here severally distinct, the product of 3000 and of 32 which are the extremes, is equal to the product of 4000 and of 24 which are the means, namely, 96,000. Thus the result in both is the same, and the discrepancy in the number of yards is through the difference in the number of digits. Each farsakh therefore consists of 12,000 gaz (of 24 digits) according to the measure of the moderns or of 9000 (of 32 digits) according to the gaz of the ancients. The properties and virtues of these proportional numbers are manifold. Among them are the following: If one of the extremes be unknown, multiply the means together and divide by the known extreme, and the quotient is the unknown extreme. For instance in the given example, if 2, the first extreme, be unknown, by multiplying the means together which are 4 and 8, we get 32. Dividing this by 16, the quotient (2) is the unknown extreme. In the same way, if the other extreme, which is 16, be unknown, by dividing the product of the means by 2, the known extreme, the quotient is 16. Again, if the unknown quantity be one of the means, we divide the product of the extremes by the known mean, and the quotient is the unknown mean. For example, if 4, the first mean, be unknown, by dividing the product of the extremes, which is 32, by the known mean which is 8, the quotient is 4. And if the second mean, 8, be unknown, by dividing the product of the extremes by 4, the quotient is 8.

By the same means the distance and altitude from the base of a given object can be ascertained. A staff of a given height is fixed upright. Its shadow and that of the elevate object are measured. The ratio of the shadow of the staff to the staff is proportional to the ratio of the shadow of the object-height to the height itself. Again, a staff is fixed in the ground in the same line with the height to be measured and regarded from such a point that the line of vision may pass over the top of the staff to the sum­mit of the object-height; the ratio of the distance from the stand-point of vision to the base of the staff is to the height of the staff as the ratio of the distance from the same point to the base of the object is to the height of the object. And if the altitude of an object be measured in a mirror or water and the like, a position must be taken whence the incident line of vision may strike the summit of the (reflected) object-height. The ratio of the distance of the reflected summit from the foot of the spectator is to his height as the ratio of the distance of the same point from the base of the object is to the height of the object. And if it be required to find the depth of a well, the observer must stand where his line of vision traversing the brink of the well touches the level bottom of the well on the side opposite to him. The ratio of the distance of the brink of the well from the foot of the observer is to his height as the breadth of the well is to its depth.*

Some take the baríd as the standard measure of length and make.

According to the Hindu philosophers—

Some measure by the steps of a woman with a water-jar on her head and carrying a child in her arms, reckoning a thousand such steps to a kós.

Praise be unto God that the institutes of imperial administration have been completed and a general survey of the Empire, by the aid of divine grace, placed upon record. The numbers of the tribal contingents and the chronology of the ancient kings with some other particulars have cost considerable labour, and from the conflicting accounts received, I was well nigh relinquishing the task, but the decrees of fate cannot be resisted. I have set down what has best commended itself to my judgment, hoping that it may win lustre from the light of public acceptance and its errors escape the carping of illiberal criticism.