A quantity assumed at pleasure, and considered as unity, or one, to which the ratio of other quantities being determined, their relative magnitude, both to the assumed unit, and to each other, will be known. The quantity assumed as unity, is called the measuring unit. Thus, to measure any proposed line, we assume a line of an inch, a foot, a yard, etc, as the measuring unit; suppose this to be an inch; then as many times as it is contained in the proposed line, so many inches will that line be in length. If the proposed line be less than the measuring unit, whatever part that line is of the measuring unit, the same part of an inch will the measure of that line be, and the like of feet, yards, etc. To measure a superfices, a square whose sides are an inch, a foot, a yard, etc. is the measuring unit; and as many times as this is contained in, or contains the given superfices, such will be the measure of that superfices, as was shown in the hue. To measure a solid, a cube whose lineal side is an inch, a foot, a yard, etc, is assumed as the measuring unit; and as many times as this unit is contained in, or contains the given solid, so many cubic inches feet, yard, etc, or parts of one of them, will the proposed solid be.
The measure for lines or length is termed lineal or long measure: that for surfaces superficial measure; and that for solids or capacities, cubic or solid measure.
In 1825 a Bill was passed through Parliament for altering weights and measures previously in use, the preamble of which states, "whereas it is necessary for the security of commerce, and for the good of the community, that weights and measures should be just and uniform: and whereas notwithstanding it is provided by the Great Charter, that there shall be but one measure and one weight throughout the realm, and by the treaty of union between England and Scotland, that the same weights and measures should be used throughout Great Britain, as were then established in England; yet different weights and measures, some larger, and some less, are still in use in various places throughout the United Kingdom of Great Britain and Ireland, and the true measure of the present standard is not verily known, which is the cause of great confusion and of manifest frauds; for the remedy and prevention of those evils for the future, and to the end that certain standards of weights and measures should be established throughout the United Kingdom of Great Britain and Ireland, the new standards are denominated imperial, and the rationale of the system by which they have been determined is thus explained.
Take a pendulum which will vibrate seconds in London, on a level of the sea, in a vacuum: divide all that part thereof which lies between the axis, of suspension and the centre of oscillation into 39.1393 equal parts; then will ten thousand of those parts be an imperial inch; 12 whereof make a foot, and 36 whereof make a yard.
The standard yard is determined to be, "that distance between the centres of the two points in the gold studs in the straight brass rod, now in the custody of the clerk of the House of Commons, wherein the words and figures 'standard Yard, 1760,' are engraved, which is declared to be the genuine standard of the measure of length called a yard;" and as the expansibility of the metal would cause some variation in the length of the rod in different degrees of temperature, the act determines that the brass rod in question shall be of the temperature of 62° Fahr. The measure is to be denominated the " Imperial Standard Yard," and to be the only standard whereby all other measures of lineal extension shall be computed. Thus the foot, the inch, the pole, the furlong, and the mile, shall bear the same proportion to the imperial standard yard as they have hitherto borne to the yard measure in general use. And should it happen that the aforesaid brass rod of 1760 be lost, defaced, or destroyed, a reference to the invariable natural standard afforded by the pendulum before mentioned, will enable it to be restored with the utmost exactness.
The standard gallon is determined by the act to be such measure as shall contain 10 lbs. avoirdupois weight, of distilled water, weighed in air, at the temperature of 62°. of Fahr., the barometer being at 30 inches, to be used as well for wine, beer, ale, spirits, and all sorts of liquids, as for dry goods, not measured by heaped measure; and that all other measures shall be taken in parts or multiples of the said imperial standard gallon, the quart being the fourth part of such gallon, and the pint one-eighth part; two such gallons making a peck, eight such gallons a bushel, and eight such bushels a quarter of corn, or other dry goods not measured by heaped measure."