# MEASURE

, denotes any quantity, assumed as unity, or one, to which the ratio of other homogeneous or like quantities may be expressed.

Measure of an Angle, is an arc of a circle described from the angular point as a centre, and intercepted between the legs or sides of the angle: and it is usual to estimate and express the Measure of the angle by the number of degrees and parts contained in that arc, of which 360 make up the whole circumference. So, the measure of the angle BAC, is the arc BC to the radius AB, or the arc bc to the radius Ab.

Hence, a right angle is measured by a quadrant, or 90 degrees; and any angle, as BAC, is in proportion to a right angle, as the arc BC is to a quadrant, or as the degrees in BC are to 90 degrees.

Common Measure. See Common Measure.

Measure of a Figure, or Plane Surface, is a square inch, or square foot, or square yard, &c, that is, a square whose side is an inch, or a foot, or a yard, or some other determinate length; and this square is called the measuring unit.

Measure of a Line, is any right line taken at pleasure, and considered as unity; as an inch, or a foot, or a yard, &c.

Line of Measures. See Line of Measures.

Measure of a Mass, or Quantity of Matter, is its weight.

Measure of a Number, is any number that divides it, without leaving a remainder. So, 2 is a Measure of 4, of 8, or of any even number; and 3 is a Measure of 6, or of 9, or of 12, &c.

Measure of a Ratio, is its logarithm, in any system of logarithms; or it is the exponent of the power to which the ratio is equal, the exponent of some given ratio being assumed as unity. So, if the logarithm or Measure of the ratio of 10 to 1, be assumed equal to 1; then the Measure of the ratio of 100 to 1, will be 2, because 100 is = 102, or because 100 to 1 is in the duplicate ratio of 10 to 1; and the Measure of the ratio of 1000 to 1, will be 3, because 1000 is = 103, or because 1000 to 1 is triplicate of the ratio of 10 to 1.

Measure of a Solid, is a cubic inch, or cubic foot, or cubic yard, &c; that is, a cube whose side is an inch, or a foot, or a yard, &c.

Measure of a Superficies, the same as the Measure of a figure.

Measure of Velocity, is the space uniformly passed over by a moving body in a given time.

Universal or Perpetual Measure, is a kind of Measure unalterable by time or place, to which the Measures of different ages and nations might be reduced, and by which they may be compared and estimated. Such a Measure would be very useful, if it could be attained; since, being used at all times, and in all places, a great deal of confusion and error would be avoided.

Huygens, in his Horol. Oscil. proposes, for this purpose, the length of a pendulum that should vibrate seconds, measured from the point of suspension to the point of oscillation: the 3d part of such a pendulum to be called horary foot, and to serve as a standard to which the Measure of all other feet might be referred. Thus, for instance, the proportion of the Paris foot to the horary foot, would be that of 864 to 881; because the length of 3 Paris feet is 864 half lines, and the length of a pendulum, vibrating seconds, contains 881 half lines. But this Measure, in order to its being universal, supposes that the action of gravity is the same on every part of the earth's surface, which is contrary to fact; for which reason it would really serve only for places under the same parallel of latitude: so that, if every different latitude were to have its foot equal to the 3d part of the pendulum vibrating seconds there, any latitude would still have a different length of foot. And besides, the difficulty of measuring exactly the distance between the centres of motion and oscillation are such, that hardly any two measurers would make it the same quantity.

M. Mouton, canon of Lyons, has also a treatife De Mensura post<*>ris transmittenda.

Since that time various other expedients have been proposed for establishing an universal Measure, but| hitherto without the perfect effect. In 1779, a method was proposed to the Society of Arts, &c, by a Mr. Hatton, in consequence of a premium, which had been 4 years advertised by that institution, of a gold medal, or 100 guineas, ‘for obtaining invariable standards for weights and Measures, communicable at all times and to all nations.’ Mr. Hatton's plan consisted in the application of a moveable point of suspension to one and the same pendulum, in order to produce the full and absolute effect of two pendulums, the difference of whose lengths was the intended Measure. Mr. Whitehurst much improved upon this idea, by very curious and accurate machinery, in his tract published 1787, intitled ‘An Attempt towards obtaining invariable Measures of Length, Capacity, and Weight, from the Mensuration of time, &c. Mr. Whitehurst's plan is, to obtain a Measure of the greatest length that conveniency will permit, from two pendulums whose vibrations are in the ratio of 2 to 1, and whose lengths coincide with the English standard in whole numbers. The numbers he has chosen shew great ingenuity. On a supposition that the length of a seconds pendulum, in the latitude of London, is 39.2 inches, the length of one vibrating 42 times in a minute, must be 80 inches; and of another vibrating 84 times in a minute, must be 20 inches; their difference, 60 inches or 5 feet, is his standard Measure. By his experiments, however, the difference in the lengths of the two pendulums was found to be 59.892 inches instead of 60, owing to the error in the assumed length of the seconds pendulum, 39.2 inches being greater than the truth. Mr. Whitehurst has fully accomplished his design, and shewn how an invariable standard may, at all times, be found for the same latitude. He has also ascertained a fact, as accurately as human powers feem capable of ascertaining it, of great consequence in natural philosophy. The difference between the lengths of the rods of two pendulums whose vibrations are known, is a datum from which may be derived the true length of pendulums, the spaces through which heavy bodies fall in a given time, with many other particulars relative to the doctrine of gravitation, the figure of the earth, &c, &c. The result deduced from this experiment is, that the length of a seconds pendulum, vibrating in a circular arc of 3° 20, is 39.119 inches very nearly; but vibrating in the arc of a cycloid it would be 39.136 inches; and hence, heavy bodies will fall, in the first second of their descent, 16.094 feet, or 16 feet 1 1/8 inch, very nearly.

It is said, the French philosophers have a plan in contemplation, to take for a universal Measure, the length of a whole meridian circle of the earth, and take all other Measures from sub-divisions of that; which will be a very good way.—Other projects have also been devised, but of little or no consideration.

Measure

, in a legal, commercial, and popular sense, denotes a certain quantity or proportion of any thing, bought, sold, valued, or the like.

The regulation of weights and Measures ought to be universally the same throughout the nation, and indeed all nations; and they should therefore be reduced to some sixed rule or standard.

Measures are various, according to the various kinds or dimensions of the things measured. Hence arise

Lineal or Longitudinal Measures, for lines or lengths:

Square Measures, for areas or superficies: and

Solid or Cubic Measures, for the solid contents and capacities of bodies.

The several Meafures used in England, are as in the following Tables:

1. Englisb Long Measure.
Barley Corns 3 = 1 Inch 36 = 12 = 1 Foot 108 = 36 = 3 = 1 Yard 594 = 198 = 16 1/2 = 5 1/2 = 1 Pole 23760 = 7920 = 660 = 220 = 40 = 1 Furlong 190082 = 63360 = 5280 = 1760 = 320 = 8 = 1 Mile Also, 4 Inches = 1 Hand 6 Feet, or 2 yds = 1 Fathom 3 Miles = 1 League 60 Nautical or Geograph. Miles = 1 Degree or 69 1/3 Statute Miles = 1 Degree nearly 360 Degrees, or 25000 Miles nearly = the Circumference of the Earth.
2. Cloth Measure.
Inches 2 1/4 = 1 Nail 9 = 4 = 1 Quarter 36 = 16 = 4 = 1 Yard 27 = 12 = 3 = 1 Ell Flemish 45 = 20 = 5 = 1 Ell English 54 = 24 = 6 = 1 Ell French.
3. Square Measure.
Inches 144 = 1 Foot 1296 = 9 = 1 Yard 39204 = 272 1/4 = 30 1/4 = 1 Pole 1568160 = 10890 = 1210 = 40 = 1 Rood 6272640 = 43560 = 4840 = 160 = 4 = 1 Acre.
4. Solid, or Cubical Measure.
Inches 1728 = 1 Foot 46656 = 27 = 1 Yard.
5. Wine Measure.
Pints 2 = 1 Quart 8 = 4 = 1 Gallon = 231 Cubic Inches. 336 = 168 = 42 = 1 Tierce 504 = 252 = 63 = 1 1/2 = 1 Hogshead 672 = 336 = 84 = 2 = 1 1/3 = 1 Puncheon 1008 = 504 = 126 = 3 = 2 = 1 1/3 = 1 Pipe 2016 = 1008 = 252 = 6 = 4 = 3 = 2 = 1 Tun. Also, 231 Cubic Inches = 1 Gallon 10 Gallons = 1 Anker 18 Gallons = 1 Runlet 31 1/2 Gallons = 1 Barrel.|
6. Ale and Beer Measure.
Pints. 2 = 1 Quart. 8 = 4 = 1 Gallon = 282 Cubic Inches. 72 = 36 = 9 = 1 Firkin. 144 = 72 = 18 = 2 = 1 Kilderkin. 288 = 144 = 36 = 4 = 2 = 1 Barrel. 432 = 216 = 54 = 6 = 3 = 1 1/2 = 1 Hogshead. 576 = 288 = 72 = 8 = 4 = 2 = 1 1/3 = 1 Puncheon. 864 = 432 = 108 = 12 = 6 = 3 = 2 = 1 1/2 = 1 Butt.

Note, The Ale gallon contains 282 cubic inches.

7. Dry Measure.
Pints. 8 = 1 Gallon = 268 4/5 Cubic Inches. 16 = 2 = 1 Peck. 64 = 8 = 4 = 1 Bushel. 256 = 32 = 16 = 4 = 1 Coom. 512 = 64 = 32 = 8 = 2 = 1 Quarter. 2560 = 320 = 160 = 40 = 10 = 5 = 1 Wey. 5120 = 640 = 320 = 80 = 20 = 10 = 2 = 1 Last. Also, 268 4/5 Cubic Inches = 1 Gallon. and 36 Bushels of Coals = 1 Chaldron.
 8. Proportions of the Long Measures of several Nations to the English Foot. Thousandth Parts. Inches. Thousandth Parts. Inches. English foot 1000 12.000 Amsterdam ell 2269 27.228 Paris foot 1065 3/4 12.792 Antwerp ell 2273 27.276 Rynland, or Leyden foot 1033 12.396 Rynland, or Leyden ell 2260 27.120 Amsterdam foot 942 11.304 Frankfort ell 1826 21.912 Brill foot 1103 13.236 Hamburgh ell 1905 22.860 Antwerp foot 946 11.352 Leipsic ell 2260 27.120 Dort foot 1184 14.208 Lubeck ell 1908 22.896 Lorrain foot 958 11.496 Noremburgh ell 2227 26.724 Mechlin foot 919 11.028 Bavaria ell 954 11.448 Middleburgh foot 991 11.892 Vienna ell 1053 12.636 Strasburgh foot 920 11.040 Bononia ell 2147 25.764 Bremen foot 964 11.568 Dantzic ell 1903 22.836 Cologn foot 954 11.448 Florence Brace or ell 1913 22.956 Frankfort ad Mœnum foot 948 11.376 Spanish, or Castile palm 751 9.012 Spanish foot 1001 12.012 Spanish vare 3004 36.040 Toledo foot 899 10.788 Lisbon vare 2750 33.000 Roman foot 967 11.604 Gibraltar vare 2760 33.120 On the monument of Cestius Statilius} foot 972 11.664 Toledo vare 2685 32.220 palm 861 10.322 Bononia foot 1204 14.448 Naples brace 2100 25.200 Mantua foot 1569 18.838 6880 82.560 Venice foot 1162 13.944 Genoa palm 830 9.960 Dantzic foot 944 11.328 Milan calamus 6544 78.528 Copenhagen foot 965 11.580 Parma cubit 1866 22.392 Prague foot 1026 12.312 China cubit 1016 12.192 Riga foot 1831 21.972 Cairo cubit 1824 21.888 Turin foot 1062 12.744 Old Babylonian cubit 1520 18.240 The Greek foot 1007 12.084 Old Greek cubit 1511 18.132 Old Roman foot 970 11.640 Old Roman cubit 1458 17.496 Lyons ell 3967 47.604 Turkish pike 2200 26.400 Bologna ell 2076 24.912 Persian arash 3197 38.364

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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