MEASLES

mediate value between several others which are formed according to any a igned law of succe ion. Tlie arithmetical mean of several quantities is simply the average formed by dividing the sum of all the quantities by their number. In physical inquiries, where a great number of values of a quantity have been determined by observation or experiments, of which the error is as lilcely to be in exce as defect, the average or arithmetical mean is the most probable result. Tlie geometrical mean between two quantities, or the mean proportional, is a quantity which forms the middle term of a duplicate ratio, or continued proportion of three terms: viz. such that the first given term is to the quantity sought as that quantity is to the other given term. In arithmetic, it is the square root of the product of the two given terms. The harmonical mean is such a number that, the first and third terms being given, the first is to the third as the difference of the first and second is to the difference of the second and third: or, if o, b, c be the numbers, 6 being the mean, —, lac 2 11 ME'ASLES. See Rubeola. MEA'SURE. (Lat. mensura.) In Geometry, a magnitude or quantity taken as unit, and employed to expte the relations of other magnitudes or quantities of the same kind. Euclid defines the measure of a quantity to be that which, being repeated a certain number of times, becomes equal to the quantity measured. Thus, in Arithmetic, the measwre of a number is any number which divides the given number without leaving a remainder; but this definition rather corresponds to the notion of aliquot part. In a general sense, the term measure is applied to that bv which any thing is compared in respect of quantity, 'f'hus, we have measures of extension, of weight, time, force, resistance, temperature, .; in short, of every thing of which greater and le can be predicated; and it frequently happens that the unit or measure is not taken in the thing or property which is the immediate subject of consideration, but in something else which depends on it, or is proportional to it. Angular space, for example, is measured by an arc of a circle; time, by the rotation of the earth about its axis, or its revolution about the sun; force, by the quantity of motion it impre es on a body; degrees of heat, by the expansion of metals or other substances; muscular strength, by the resistance of a spring, . See Angle, CHRO^OLOGY, GKAVirv, Thermometer, Dynamometer, . By measure, in an absolute sense, is tmderstood the.jin it or standard by which we measure extension. We have, therefore, measures of length, of superficies, and of volume or capacity; but, as the two latter may be deduced in all cases from the former, it is only nece ary to establish a unit, or standard of length. The choice of such a standard, and the different multiples and parts of it taken for the uses of society, form a metrical system, or system, of metrology. Standards of Measure^ — As no precise notion can be formed of the magnitude of a line in any other way than by comparing it with another line of a known length, the nece ity of having recourse, for the interchange of ideas, to measures not entirely arbitrary, but fixed by nature, and intelligible alike to all mankind, seems to have been perceived in the earliest ages. Hence originated the foot, the cubit, the span, the fathom, the barleycorn, the hair's breadth, and other denominations of measure, taken from parts of the human body, or from natural objects, which, though not of an absolute and invariable length, have a certain mean value sufficiently definite to answer all the purposes required in a rude state of society. But, as civilization advanced, the nece ity of adopting more precise standards would be felt, and the inadequacy of such measures as the foot, the cubit, . (referred only to the human body) to convey accurate notions, would be rendered most apparent in their application to itinerary measures, or the estimation of great distances; where differences of the fundamental measure, of no account when one or two units only are taken into consideration, would amount, by repeated multiplication, to enormous quantities. In order to avoid this inconvenience, recourse was had to other methods of estimation; but which, in fact, amounted only to descriptions more or le vague, and not to measures. Thus, in ancient authors, we frequently read of a day's journey, a day's sail, and so forth; and in many parts of the continent of Europe, even at the present time. It is the custom of the peasantry to reckon itinerary distances by hours. On looking among the objects of nature for a standard of measure perfectly definite, and, at the same time, invariable, and acce ible to all mankind, a very slender acquaintance with geometry and natural philosophy wiil suffice to show that the subject is beset with innumerable difficulties. In fact, nature presents only two or three elements which, with the aid of profound science and a refined knowledge of the arts, can be made subservient MEASURE. to the purpose; and none at all which are applicable without such aid. The earth is nearly a solid of revolution, and its form and absolute magnitude are presumed to remain the same in all ages: hence the distance between the equator and the pole is an invariable quantity; and any a igned part of that distance, as the 90th, or a degree of the meridian, is constant, and will furnish a precise and unalterable standard of measures, fit for the purposes of metrology, provided we have the means of comparing it with the rods or scales which must nece arily be used in comparing distances, or the magnitudes of bodies. The force of gravity at the earth's surface is constant at any given place, and very nearly the same at all places under the same parallel of latitude and at the same height above the level of the sea; hence the length of a pendulum which makes a given number of oscillations in a day is also constant at a given place, and, with proper skill and precautions, may be determined in terms of any a umed scale. These two elements, the length of a degree of the meridian, and the length of the seconds' pendulum, are the only ones furnished by nature which have yet been used as the basis of a system of measures. One or two others have been suggested, as the height through which a heavy body falls in a second of time, determined, like the length of the pendulum, by the force of gravity; or the perpendicular height through which a barometer must be earned till the mercurial column sinks a determinate part — for example, a 30th of its own length; but, for reasons which it is unnece ary here to state, these distances are not so susceptible of being accurately determined as the terrestrial degree, or the length of the seconds' pendulum. It has been supposed (Paucton, Metro logie; Bailly, His to ire de V Astronomic ancienne) that some ancient nations referred their measures of length to a unit chosen from an aliquot part of the earth's circumference, and that the different stadia were only different aliquot parts of the same great unit; but the supposition is altogether improbable, for the ancients had no means of determining the magnitude of the earth with any tolerable precision, and do not themselves make any reference to such a standard. Mouton, an astronomer of Lyons, about 1670, proposed as a universal standard of measure a geometrical foot, of which a degree of the earth's circumference should contain 600,000; and remarked that a pendulum of this length would make 3959i vibrations in a half hour. In 1671 Picard proposed a similar idea; and Huygens first suggested the pendulum as the unit or standard of measures. Cond a mine, one of the French academicians engaged in the measurement of the terrestrial arc in Peru, proposed that the equatorial pendulum ought to be adopted, as being the most natural measure, and independent of the pretensions of different countries. No attempt, however, was made to establish a regular system of measures on any of these standards until the time of the French revolution, when a system of weights and measures, referred to the terrestrial degree, and accommo. dated to our arithmetical scale, was adopted in that country. English Standard Measures. — The unit of lineal measure in this country is the vard, all other denominations being either multiples or aliquot parts of the yard. But as this is an entirely arbitrary measure, and, until the year 1824, was never strictly defined by the legislature, great perplexity has often arisen in attempting to ascertain the exact portion of space it was meant to represent. For the purpose of preserving some degree of uniformity among the ordinary measures of the kingdom, certain standards were preserved in the exchequer, with which all rods were required to be compared before they were stamped as legal measures. The oldest of these standards in existence dates from the reign of Henry VII.; but it has long been disused; and that which, till the year 1824, was considered as the legal standard, was a bra rod, of the breadth and thickne of about half an inch, placed there in the time of Elizabeth. There was another similar rod of the same date, called an ell. The ell, however, does not appear ever to have been established as a legal measure; but was conventionally considered as equal to a yard and a quarter. To these rods belonged a bra bar, on one edge of which was a hollow bed or matrix fitted to receive the square rod of a yard, and on another a like bed fitted to receive that of an ell; and into these beds were fitted the yard and ell measures brought to be examined and stamped with the standard marks. All rods so stamped became standard measures. It is abun-i dantly obvious that measures determined in this coarse' manner could have no strict claim to be considered as accurate copies of the original standard; but it would seem that the standard itself was incapable of affording any definite or correct measure. It is thus described by Mr. Baily, in his Report on the new Standard Scale of the liojal Astronomical Society: — " I have had an opportunity of seeing this curious instrument, of which it is impo ible, at the present day, to speak too much in derision or contempt. A common kitchen poker, filed at the ends in the rudest manner, by the most bungling Page 738