Page:Encyclopædia Britannica, Ninth Edition, v. 3.djvu/277

Rh trict had upwards of 2000 inhabitants, viz., Hattd, popula tion, 2608, and Lanji, population, 2116. About 60 years ago the upper part of the district was an impenetrable waste. About that time one Lachhmau Xaik established the first villages on the Paraswdrd plateau, on which there are about 30 flourishing settlements. But a handsome Buddhist temple of cut stone, belonging to some remote period, is suggestive of a civilization which had disappeared before historic times.  BALANCE. For the measurement of the &quot; mass &quot; of (i.e., of the quantity of matter contained in) a given body we possess only one method, which, being indepen dent of any supposition regarding the nature of the matter to be measured, is of perfectly general applicability. The method to give it at once in its customary form consists in this, that after having fixed upon a unit mass, and procured a sufficiently complete set of bodies representing each a known number of mass-units (a &quot; set of weights &quot;), we determine the ratio of the u eight of the body under examination to the weight of the unit piece of the set, and identify this ratio with the ratio of the masses. Machines constructed for this particular modus of weighing are called balances. Evidently the weight of a body as determined by means of a balance and it is in this sense that the term is always used in everyday life, and also in certain sciences, as, for instance, in chemistry is independent of the magnitude of the force of gravity ; what the merchant (or chemist) calls, say, a &quot; pound &quot; of gold is the same at the bottom as it is at the top of Mont Blanc, although its real weight, i.e., the force with which it tends to fall, is greater in the former than it is in the latter case. To any person acquainted with the elements of me chanics, numerous ideal contrivances for ascertaining which of two bodies is the heavier, and for even determining the ratio of their weights, will readily suggest themselves ; but there would be no use in our noticing any of these many conceivable balances, except those which have been actually realised and successfully employed. These may be con veniently arranged under six heads.

1. Spring Balances.—The general principle of this class of balances is that when an elastic body is acted upon by a weight suspended from it, it undergoes a change of form, which, cceteris paribus, is the greater the greater the weight. The simplest form of the spring balance is a straight spiral of hard steel (or other kind of elastic) wire, suspended by its upper end from a fixed point, and having its lower end bent into a hook, from which, by means of another hook crossing the first, the body to be weighed is suspended, matters being arranged so that even in the empty instru ment the axis of the spiral is a plumb-line. Supposing a body to be suspended at the lower hook, it is clear that the point where the hooks intersect each other will descend from the level it originally occupied, and that it must fall through a certain height h before it can, by itself, remain at rest. This height, provided the spiral was not strained beyond its limit of elasticity (i.e., into a permanent change of form), is proportional to the weight P of the body, and consequently has to the mass M the relation A &#61; c^M, where c is a constant and g the acceleration of gravity. Hence, supposing in a first case h and M to have been h and M, and in a second case, h and M&quot;, we have h : h&quot; : : &amp;lt;7 M : #&quot;M&quot;; and it is only as long as g is the same that we can say h : k&quot;: : M : M&quot;. Spring balances are very extensively used for the weighing of the cheaper articles of commerce and other purposes, where a high degree of pre cision is not required. In this class of instruments, to com bine compactness with relatively considerable range, the spring is generally made rather strong ; and sometimes the exactitude of the reading is increased by inserting, between the index and that point tbe displacement of which serves to measure the weight, a system of levers or toothed wheels, constructed so as to magnify into convenient visibility the displacement corresponding to the least difference of weight to be determined. Attempts to convert the spring balance into a precision instrument have scarcely ever been made ; the only case in point known to the writer is that of an elegant little instrument con structed by Professor Jolly, of Munich, for the deter mination of the specific gravity of solids by immersion, which consists of a long steel-wire spiral, suspended in front of a vertical strip of silvered glass bearing a millimetre scale. To read off the position of equilibrium of the index on the scale, the observing eye is placed in such a position that the eye, its image in the glass, and the index are in a line, and the point on the scale noted down with which the index apparently coincides. FIG. 1. Diagram illustrating Chain Balance.

2. Chain Balances.—This invention of AYilhelm Weber s having never, so far as we know, found its way into actual practice, we confine ourselves to an illustration of its prin ciple. Imagine a flexible string to have its two ends attached to the two fixed points C and D (fig. 1), forming the ter- minal points of a horizontal line CD shorter than the string. Suppose two weights to be suspended, the one at a point A, the other at a point B of the string ; the form of the polygon CDBA will depend, cceteris paribus, on the ratio of the two weights. Assuming, for simplicity s sake, CA to be equal to DB, then, if the weights are equal, say, each &#61; P units, the line AB will be horizontal. But if now, say, the weight at B be replaced by a heavier weight Q, the point A will ascend through a height h, the point B will descend through a lesser height h in accordance with equation Ph &#61; Qh, and the angle between what is now the position of rest of the base line A B, and the original line AB will depend on the ratio of P : Q. The exact measurement of this angle would be difficult, but it would be easy to devise very exact means for ascertaining whether or not it was horizontal, and, if not, whether it slanted down the one way or the other ; and thus the instrument might serve to determine whether P was equal to, or greater or less than, Q; and this obviously is all that is required to convert the contrivance into an exact balance.

3. Lever Balances.—This class of balances, being more extensively used than any other, forms the most impor tant division of our subject. There is a great variety of lever balances ; but they are all founded upon the same principles, and it is consequently expedient to begin by summing up these into one general theorv.