# 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 A*b.*

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 = 10^{2}, 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 = 10^{3},
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:

*Englisb Long Measure.*

*Cloth Measure.*

*Square Measure.*

*Solid,*or

*Cubical Measure.*

*Wine Measure.*

*Ale and Beer Measure.*

Note, The Ale gallon contains 282 cubic inches.

*Dry Measure.*

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 |