Part 99
The following examples will shew in what manner the proportion between the measures of any two given countries may be ascertained.
_Examples._
Let it be required to reduce 100 archines of Russia into varas of Spain.
The archine measuring 336 English lines, and the vara 395,25, according to the table prefixed, I state the following equation:
100 archines = _x_ 1 archine = 336 lines 395,25 lines = 1 vara Result 85,01 varas.
Reduce 100 varas into archines.
100 varas = _x_ 1 vara = 395,25 lines 336 lines = 1 archine Result 117,63 archines.
English _Long_ MEASURE.
|inch | +-----+ | 3|palm | +-----+-----+ | 9| 3|span| +-----+-----+----+ | 12| 4|1¹⁄₄|foot | +-----+-----+----+-----+ | 18| 6| 2| 1¹⁄₂|cubit| +-----+-----+----+-----+----++ | 36| 12| 4| 3| 2|yard| +-----+-----+----+-----+----+----+ | 45| 15| 5| 3³⁄₄|2¹⁄₂|1¹⁄₄|ell | +-----+-----+----+-----+----+----+----+ | 60| 20|6²⁄₃| 5|3¹⁄₂|1³⁄₄|1¹⁄₄|pace | +-----+-----+----+-----+----+----+----+-----+ | 72| 24| 8| 6| 4| 2|1³⁄₄| 1¹⁄₅|fathom| +-----+-----+----+-----+----+----+----+-----+----+-+ | 198| 66| 22|16¹⁄₂| 11|5¹⁄₂| 4|3¹⁄₁₀|2³⁄₄|pole| +-----+-----+----+-----+----+----+----+-----+----+---++ | 7920| 2640| 880| 660| 440| 220| 176| 132| 110| 40|furlong| +-----+-----+----+-----+----+----+----+-----+----+---+-+-----+ |63360|21120|7040| 5280|3520|1760|1408| 1056| 880|320|8|mile | +-----+-----+----+-----+----+----+----+-----+----+---+-+-----+
Jewish _Long or Itinerary_ MEASURE.
_Eng._ _feet._ _miles._ _paces._ _dec._ |cubit 0 0 1.824 +-----+ | 400|stadium 0 145 4.6 +-----+---+ | 2000| 5|Sab. day’s journey 0 729 3.0 +-----+---+--+ | 4000| 10| 2|eastern mile 1 403 1.0 +-----+---+--+--+ |12000| 30| 6| 3|parasang 4 153 3.0 +-----+---+--+--+-+ |96000|240|48|24|8|a day’s journey 33 172 4.0 +-----+---+--+--+-+
Roman _long_ MEASURE, _reduced to_ English.
_Eng._ _dec._ _paces._ _ft._ _inch_ |digitus transversus 0 0 0.725¹⁄₄ +-----+ | 1³⁄₄|uncia 0 0 0.967 +-----+-----+ | 4| 3|palmus minor 0 0 2.901 +-----+-----+-----+ | 16| 12| 4|pes 0 0 11.604 +-----+-----+-----+----+ | 20| 15| 5|1¹⁄₄|palmipes 0 1 2.505 +-----+-----+-----+----+----+ | 24| 18| 6|1¹⁄₂|1¹⁄₅|cubitus 0 1 5.406 +-----+-----+-----+----+----+-------+ | 40| 30| 10|2¹⁄₂| 2| 1²⁄₃|gradus 0 1 5.01 +-----+-----+-----+----+----+-------+----+ | 80| 60| 20| 5| 4| 3¹⁄₂| 2|passus 0 4 10.02 +-----+-----+-----+----+----+-------+----+----+ |10000| 7500| 2500| 625| 500| 416²⁄₃| 250| 215|sta- 120 4 4.5 | | | | | | | | |dium +-----+-----+-----+----+----+-------+----+----+-+ |80000|60000|20000|5000|4000|3333¹⁄₃|2000|1000|8|mil- 967 0 0 | | | | | | | | | |liare +-----+-----+-----+----+----+-------+----+----+-+-----
_English square or superficial_ MEASURES, are raised from the yard of 36 inches multiplied into itself; and this producing 1296 square inches in the square yard, the divisions of this are square feet and inches, and the multipliers, poles, roods, and acres.
English _square_ MEASURE.
|inches +-------+ | 144|feet +-------+--------+ | 1296| 9 |yards +-------+--------+-------+ | 3600| 25 | 2 |paces +-------+--------+-------+-------+ | 39204| 272¹⁄₄| 30¹⁄₄| 10,89|poles +-------+--------+-------+-------+---+ |1568160|10890 |1210 | 435,6 | 40|roods +-------+--------+-------+-------+---+-+ |6272640|43560 |4840 |1743,6 |160|4|acres +-------+--------+-------+-------+---+-+-----
_Long Measure._
12 Inches make 1 Foot. 3 Feet ---- 1 Yard. 5¹⁄₂ Yards ---- 1 Pole, or perch. 40 Poles ---- 1 Furlong. 8 Furlongs ---- 1 Mile. 4 Inches ---- 1 Hand. 6 Feet ---- 1 Fathom, or toise. 3 Miles ---- 1 League. 60 Nautical, or geographical miles, or 69¹⁄₂ statute miles ---- 1 Degree.
_Square Measure._
144 Square inches make 1 Square foot. 9 Square feet ---- 1 Square yard. 30¹⁄₄ Square yards ---- 1 Square pole. 40 Square poles ---- 1 Square rood. 4 Square roods ---- 1 Square acre.
_Solid, or Cubic Measure._
1728 Cubic in. make 1 Cubic foot. 27 Cubic feet ---- 1 Cubic yard. 251 Cubic in. ---- 1 Gal. wine measure. 281 do. ---- 1 Gal. beer measure. 168³⁄₅ do. ---- 1 Gal. dry measure.
_Dry Measure._
8 Pints make 1 Gallon. 2 Gallons ---- 1 Peck. 4 Pecks ---- 1 Bushel. 4 Bushels ---- 1 Coom. 2 Cooms ---- 1 Quarter. 5 Quarters ---- 1 Wey. 2 Weys ---- 1 Last.
_Avoirdupois Weight._
16 Drams make 1 Ounce. 16 Ounces ---- 1 Pound. 28 Pounds ---- ¹⁄₄ of a Hundred. 4 Quarters ---- 1 Hundred. 20 Hundred ---- 1 Ton. 14 Pounds ---- 1 Stone.
_French square_ MEASURES, are regulated by 12 square lines in the inch square, 12 inches in the foot, 22 feet in the perch, and 100 perches in the arpent or acre.
_French liquid_ MEASURES. At Paris, and in a great part of the kingdom, the smallest measure is the possou, which contains six cubic inches; 2 possous make the demi-septier; 2 demi-septiers the chopine; 2 chopines a pint; 2 pints a quart or pot; 4 quarts the gallon, or septier of estimation; 36 septiers the muid; which is subdivided into 2 demi-muids, 4 quarter muids, and 8 half quarter muids. The queue in Orleans, Blois, &c. contains a Paris muid and a half. The tun used at Bayonne and Bourdeaux, consists of 4 bariques, and equal to 3 Paris muids; at Orleans to 2: so that the first tun contains 864 pint, and the second 576. The demi-queue in Champagne, 96 quarts; the pipe in Anjou and Poictou, 2 bussards, equal to a demi-queues of Orleans, &c. or a muid and a half of Paris. The millerolle used in Provence, contains 66 Paris pints; and the poincon at Nantz, in Touraine, and the Blessois, equal to half the Orleans tun. The poincou at Paris is the same with the demi-queue.
_French Weights and Measures._
The toise is commonly used in France for military purposes, and is divided into 6 feet: each foot 12 inches; each inch 12 lines; each line 12 points. The pace is usually reckoned at 2¹⁄₂ feet.
_Poids de Marc, ou de Paris._
24 Grains make 1 Den’r. 3 Den’rs. ---- 1 Gros. 8 Gros ---- 1 Ounce. 8 Ounces ---- 1 Marc. 2 Marcs ---- 1 Pound.
The French have lately formed an entire new system of weights and measures: the following short account of them, and their proportion to the old weights and measures of France, and those of English standard, is extracted from _Nicholson’s Natural Philosophy_.
+------------------+-----------------+-------------------------------+ |Proportions of the|First part of the| | |measures of each |name which indi- | | |species to its |cates the propor-| | |principal measure |tion to the prin-|PRINCIPAL MEASURES, OR UNITIES.| |or unity. |cipal measure or +---------------+---------------+ | |unity. |Length. |Capacity. | +------------------+-----------------+---------------+---------------+ |10,000 |Myria} | | | | 1,000 |Kilo } | | | | 100 |Hecto} | | | | 10 |Deca } | | | | 0 |---- } |Metre. |Litre. | | 0.1 |Deci } | | | | 0.01 |Centi} | | | | 0.001 |Milli} | | | +------------------------------------+---------------+---------------+ |Proportion of the principal measures|10,000,000th |A Decimetre | |between themselves, and the length |part of the |cube. | |of the Meridian. |dist. from the | | | |Pole to the | | | |Equator. | | +------------------------------------+---------------+---------------+ |Value of the principal measures in |3 feet 11 lines|1 pint and ¹⁄₂₀| |the ancient French measures. |and ¹⁄₂ nearly.|or 1 litron and| | | |¹⁄₄ nearly. | | | | | +------------------------------------+---------------+---------------+ |Value in English measures. |Inches 39·383. |61.083 inch, | | | |which is more | | | |than the wine | | | |and less than | | | |the beer quart.| +------------------------------------+---------------+---------------+
+------------------+-----------------+-------------------------------+ |Proportions of the|First part of the| | |measures of each |name which indi- | | |species to its |cates the propor-| | |principal measure |tion to the prin-|PRINCIPAL MEASURES, OR UNITIES.| |or unity. |cipal measure or +---------------+---------------+ | |unity. |Weight. |Agrarian. | +------------------+-----------------+---------------+---------------+ |10,000 |Myria} | | | | 1,000 |Kilo } | | | | 100 |Hecto} | | | | 10 |Deca } | | | | 0 |---- } |Gramme. |Are. | | 0.1 |Deci } | | | | 0.01 |Centi} | | | | 0.001 |Milli} | | | +------------------------------------+---------------+---------------+ |Proportion of the principal measures|Weight of a |100 square | |between themselves, and the length |centimetre cube|metres. | |of the Meridian. |of distilled | | | |Water. | | | | | | +------------------------------------+---------------+---------------+ |Value of the principal measures in |18 grains and |Two square | |the ancient French measures. |841,000 parts. |perches des | | | |eaux et foret. | | | | | +------------------------------------+---------------+---------------+ |Value in English measures. |22·966 grains. |11·968 square | | | |yards. | | | | | | | | | | | | | +------------------------------------+---------------+---------------+
+------------------+-----------------+---------------+ |Proportions of the|First part of the| PRINCIPAL | |measures of each |name which indi- | MEASURES, | |species to its |cates the propor-| OR | |principal measure |tion to the prin-| UNITIES. | |or unity. |cipal measure or +---------------+ | |unity. |For Firewood. | +------------------+-----------------+---------------+ |10,000 |Myria} | | | 1,000 |Kilo } | | | 100 |Hecto} | | | 10 |Deca } | | | 0 |---- } |Stere. | | 0.1 |Deci } | | | 0.01 |Centi} | | | 0.001 |Milli} | | +------------------------------------+---------------+ |Proportion of the principal measures|One cubic | |between themselves, and the length |metre. | |of the Meridian. | | | | | | | | +------------------------------------+---------------+ |Value of the principal measures in |1 demi voie or | |the ancient French measures. |¹⁄₄ of a cord | | |des eaux et | | |foret. | +------------------------------------+---------------+ |Value in English measures. | | | | | | | | | | | | | | +------------------------------------+---------------+
By the new metrical system of the French, the geometrical circle used in astronomical, geographical, and topographical calculations, is divided instead of 360, into 400 equal parts, which are called _grades_: each grade is divided into 100 equal parts which are called _minutes_ of _grades_: and each minute into 100 _seconds_, of _grades_. The proportion of the new to the old degree is 0.9; and the next proportion or minute is 54′ of the old division; and the new second is 32″.4 of the ancient.
_Reduction of the old French Weights and measures to English; and the contrary._
1st. To reduce English Avoirdupois to Paris weight:
The avoirdupois pound of 16} ounces, or 7000 troy grains} = 8538 Paris grains The ounce = 533.6250}
2d. To reduce Paris running feet or inches into English,} multiply by }1.065977 ---- English running feet or inches into Paris divide by }
3d. To reduce Paris cubic feet or inches into English, } multiply by }1.211278 ---- English cubic feet or inches into Paris, divide by }
4th. To reduce the Paris pint to the English, multiply by}2.0171082 ---- To reduce the English pint to the Paris, divide by }
_German_ MEASURES. The Rhinland rood is the measure commonly used in Germany and Holland, and in most of the northern states, for all military purposes.
It is divided into 12 feet. The Rhinland rood is sometimes divided into tenths, or decimal feet, and the pace is made equal to 2 decimal feet, or ²⁄₁₀ of a rood.
_Proportions between the English Weights and Measures, and those of the principal Places in Europe._
+-------+-------- |Foot in|Pound in Places. | Parts.| Parts. -----------+-------+-------- London | 1000 | 100 Paris | 1068 | 108 Amsterdam | 942 | 93 Rhinland | 1033 | 96 Antwerp | 946 | 98 Lovaine | 958 | 98 Middleburgh| 991 | 98 Strasburgh | 920 | 93 Bremen | 964 | 94 Cologne | 954 | 97 Frankfort | 948 | 93 Leipsig | -- | 117 Hamburg | -- | 95 Venice | 1153 | 151 Prague | 1026 | 106 Copenhagen | 965 | 94 Nuremburgh | 1006 | 94 Bavaria | 954 | 40 Vienna | 1053 | 83 Madrid | 1001 | 99 Toledo | 899 | 100 Bologne | 1204 | 127 Naples | 861 | -- Florence | -- | 123 Genoa | -- | 142 Mantua | 1569 | 143 Turin | 1062 | -- Dantzig | 944 | 119 -----------+-------+--------
_Cubical_ MEASURES, or measures of capacity for liquors. English liquid measures were originally raised from troy weight, it being ordained that pounds troy of wheat, gathered from the middle of the ear, and well dried, should weigh a gallon of wine measure; yet a new weight, viz. the avoirdupois weight, had been introduced, to which a second standard gallon was adjusted, exceeding the former in the proportion of the avoirdupois weight to the troy weight. From this latter standard were raised two measures, the one for ale, the other for beer.
The sealed gallon at Guildhall, London, which is the English standard for wine, spirits, oil, &c. is supposed to contain 231 cubic inches; yet by actual experiment made in 1688, before the lord mayor and commissioners of excise, it only contains 224 cubic inches. It was however agreed to continue the common supposed contents of 231: hence, as 12 : 231 ∷ 14¹²⁄₂₀ : 281¹⁄₂ the cubic inches in an ale gallon; but in effect, the ale quart contains 70¹⁄₂ cubic inches; on which principles the ale and beer gallon will be 282 cubic inches.
_Dry_ MEASURE, is different from both the ale and wine measure, being nearly a mean between both.
According to a British act of parliament, passed in 1697, every round bushel with a plain and even bottom, being 18¹⁄₂ inches throughout, and eight inches deep, is to be accounted a legal Winchester bushel, according to the standard in the exchequer; consequently a corn gallon will contain 268.8 inches, as in the following table.
|inches +------+ | 2688|gallons +------+--+ | 5376| 2|pecks +------+--+-----+ | 21504| 8| 4¹⁄₂|bushels +------+--+-----+-+ |172032|64|32 |8|quarters +------+--+-----+-+--------
_Winchester Measure._
2 Pints make 1 Quart. 4 Quarts ---- 1 Gallon. 9 Gallons ---- 1 Firkin. 2 Firkins, or 18 Gallon ---- 1 Kilderkin. 2 Kilderkins, or 36 Gallons ---- 1 Barrel. 1 Barrel and half, or 54 Gallons ---- 1 Hogshead. 2 Hogsheads or 3 barrels, or 108 Gallons ---- 1 Butt. 2 Butts, or 216 Gallons ---- 1 Tun.
_Table Cloth Measure._
2 Inches and a Quarter make 1 Nail. 4 Nails ---- ¹⁄₄ of a Yard. 4 Quarters ---- 1 Yard. ³⁄₄ of a Yard ---- 1 Ell Flemish. 5 Quarters, or 1 Yard 1 Quarter ---- 1 Ell English. 6 Quarters ---- 1 French Ell.
MEASURE _of wood for firing_, is the cord, being four feet high, as many broad, and the length of the wood is as by law established, it is divided into two half cords.
MEASURE _for horses_, is the hand, which by statute contains 4 inches.
_Powder_ MEASURES, made of copper, holding from an ounce to 12 pounds, are very convenient in a siege, when guns or mortars are to be loaded with loose powder, especially in ricochet-firing, &c.
The French recommend measures that are made of block tin, such as are used for measuring out salt, viz. 1 ounce, 2, 3, 4, 8, which make the half pound; and lastly, of 16, which make the pound. These quantities answer every sort of ordnance.
_Diameters and Heights of Cylindric Powder Measures, holding from 1 to 15 Ounces._
+------+-----+-----+-----+-----+-----+-----+ |Ounces| 0 | 1 | 2 | 3 | 4 | 5 | +------+-----+-----+-----+-----+-----+-----+ | 0 | 0 |1·256|1·583|1·811|1·994|2·148| +------+-----+-----+-----+-----+-----+-----+ | 1 |2·706|2·793|2·876|2·953|3·027|3·098| +------+-----+-----+-----+-----+-----+-----+
_Diameters and Heights of Cylindric Powder Measures, holding from 1 to 15 Pounds._
+------+-----+-----+-----+-----+-----+-----+ |Pounds| 0 | 1 | 2 | 3 | 4 | 5 | +------+-----+-----+-----+-----+-----+-----+ | 0 | 0 |3·165|3·988|4·565|5·024|5·412| +------+-----+-----+-----+-----+-----+-----+ | 1 |6·890|7·039|7·245|7·442|7·628|7·805| +------+-----+-----+-----+-----+-----+-----+
The above are in inches and decimals.
MEASURE-_angle_, a brass instrument to measure angles, either saliant or rentrant, for exactly ascertaining the number of degrees and minutes, to delineate them on paper.
MEASURING, MENSURATION, in _military mathematics_, the assuming any certain quantity, and expressing the proportion of other similar quantities to the same; or the determining, by a certain known measure, the precise extent, quantity, or capacity of any thing.
MEASURING, in _general_, constitutes the practical part of geometry; and from the various subjects which it embraces, it acquires various names, and constitutes various arts, viz.
LONGIMETRY, ALTIMETRY, LEVELLING, GEODESIA, or SURVEYING, STEREOMETRY, SUPERFICIES, and SOLIDS, &c. which see.
MEASURING. See CHAIN.
MECHANICS, a mixed mathematical science, which considers motion and moving powers, their nature and laws, with the effects thereof, in machines, &c. The word is derived from the Greek. That part which considers motion arising from gravity, is sometimes called statics, in contradistinction from that part which considers the mechanical powers and their application, properly called mechanics: it is, in fine, the geometry of motion.
MECHANICS. The whole momentum or quantity of force of a moving body, is the result of the quantity of matter, multiplied by the velocity with which it is moved; and when the product arising from the multiplication of the particular quantities of matter in any two bodies, by their respective velocities are equal, their momentum will be so too. Upon this easy principle depends the whole of mechanics; and it holds universally true, that when two bodies are suspended on any machine, so as to act contrary to each other; if the machine be put in motion, and the perpendicular ascent of one body multiplied into its weight, be equal to the perpendicular descent of the other, multiplied into its weight, those bodies, how unequal soever in their weights, will balance each other in all situations: for, as the whole ascent of the one is performed in the same time as the whole descent of the other, their respective velocities must be as the spaces they move through; and the excess of weight in one is compensated by the excess of velocity in the other. Upon this principle it is easy to compute the power of any engine, either simple or compound; for it is only finding how much swifter the power moves than the weight does, (_i. e._ how much further in the same time,) and just so much is the power increased by the help of the engine.
The simple machines usually called mechanic powers, are six in number, _viz._ the _lever_, the _wheel and axle_, the _pulley_, the _inclined plane_, the _wedge_, and the _screw_.
There are four kinds of _levers_: 1st, where the prop is placed between the weight and the power. 2d, where the prop is at one end of the lever, the power at the other, and the weight between them. 3d, where the prop is at one end, the weight at the other, and the power applied between them. 4th, the bended lever, which differs from the first in form, but not in property.