Page images
PDF
EPUB

hand and minute hand had exactly changed places with each other. What was the precise time when the hands were in the first position? Ans. 2h. 15m. 569 sec.

39. Required the contents of a cube, that will contain a globe 20 inches in diameter; also of a cube, that may be inscribed in said globe.

Ans. Larger cube 8000 cub. in.; smaller, 1539 cub. in. 40. If in a pair of scales a body weigh 90 pounds in one scale, and only 40 pounds in the other, required the true weight, and the proportion of the lengths of the two arms of the balancebeam on each side of the point of suspension.

Ans. the weight 60lbs., and the proportions 3 to 2. 41. In turning a one-horse chaise within a ring of a certain diameter, it was observed that the outer wheel made two turns, while the inner wheel made but one; the wheels were each 4 feet high; and supposing them fixed at the distance of 5 feet asunder on the axletree, what was the circumference of the track described by the outer wheel? Ans. 62.83+ feet.

42. The ball on the top of St. Paul's church is 6 feet in diameter. What did the gilding of it cost, at 31d. per square Ans. 237 £. 10s. 1d.

inch?

43. There is a conical glass, 6 inches high, 5 inches wide at the top, and which is part filled with water. What must be the diameter of a ball, let fall into the water, that shall be immersed by it? Ans. 2.445+in.

44. A certain lady, the mother of three daughters, had a farm of 500 acres, in a circular form, with her dwelling-house in the centre. Being desirous of having her daughters settled near her, she gave to them three equal parcels, as large as could be made in three equal circles, included within the periphery of her farm, one to each, with a dwelling-house in the centre of each; that is, there were to be three equal circles, as large as could be made within a circle that contained 500 acres. How many acres did the farm of each daughter contain, how many acres did the mother retain, how far apart were the dwelling-houses of the daughters, and how far was the dwelling-house of each daughter from that of the mother?

Ans. Each daughter's farm contained 107 acres 2 roods 31.22+ rods. The mother retained 176 acres 3 roods 26.34+ rods. The distance from one daughter's house to the other was 148.119817+ rods. The mother's dwelling-house was distant from her daughters' 85.51+ rods.

more than an inch square, and 39.06 inches long. At about an inch and a half from each end, there was inserted a gold pin or stud, and in these pins, at the distance of 36 inches from each other, are two points, which are intended to designate the exact length of the yard. The subject was further considered by another committee, and a second rod made by the same man, and as an exact copy of the above, which is known as the "Standard Yard of 1760," and which was declared by Parliament in the "Act of Uniformity," in 1824, which took effect January 1, 1826, to be the legal standard of measure for Great Britain. As the distance between the two fixed points will vary with the temperature of the rod, the Act provides that it shall be at the temperature of 62° Fahrenheit.

This standard yard, which was to be denominated the "Imperial Yard," was intended to afford a fixed standard of measure, which could only be lost with the destruction or mutilation of the standard rod. But this, it was foreseen, might easily occur, as in fact it did happen in 1834, at the burning of the two'Houses of Parliament, when the imperial model shared the fate of the other valuable relics which were consumed in that ancient pile; and to provide against such an accident, it was declared that the imperial or standard yard, as compared with a pendulum vibrating seconds in the latitude of London, should bear the proportion of 36 to 39.1393 inches. To procure further accuracy, this pendulum was to move in a vacuum, at the level of the sea, and at the temperature of 62° Fahrenheit. And thus was fixed an absolute and invariable standard of linear measure, by which, according to the Act above named, all measures of extension are determined, whether the same be lineal, superficial, or solid. A third part of this standard yard is a legal foot, a twelfth part of the foot a legal inch, 5 such yards a pole, 220 a furlong, and 1760 a mile. A legal rood of land contains 1210 square yards, and an acre 4840 square yards, or 160 square poles.

By the same Act, all measures of capacity are determined by the imperial gallon, which contains 277.274 cubic inches. Two such gallons make a peck, one fourth of a gallon a quart, &c. As this standard gallon is determined by cubic inches, we see that it is ultimately referred to the standard yard as the basis on which it is founded. The Act provides, however, that it may also be determined by weight, in which case the measure to contain a gallon must be of a capacity to hold 10 pounds, avoirdupois weight, of distilled water, weighed in air,

at the temperature of 62° Fahrenheit, the barometer being at 30 inches.

For a standard of weights, the law of England makes the pound Troy* to contain 5760 grains, one cubic inch of distilled water weighed as above, weighing 252.458 such grains,

and the pound Avoirdupois to contain 7000 such grains.

The Act of Parliament which brought the standards of English weights and measures to their present state of comparative perfection was passed in 1835. This Act prohibits the use of the well-known Winchester bushel, and also of heaped measure. The subject of weights and measures is still under consideration by scientific men in England, and further improvements have been proposed, and will probably be introduced. It has even been suggested by commissioners appointed by government, that the system of coinage be changed, and one having decimal proportions adopted.

The system of weights and measures established by law in the United States is essentially the same as the English; but there is not, even at this day, that uniformity of practice in this country, which the interests of extensive trade require. At the organization of the Federal Government, authority was given to Congress to regulate this important matter, but no laws have as yet been enacted by that body to secure a uniform system through all the States. By an order of Congress, in June, 1836, a set of standard weights and measures was prepared for the use of each custom-house, and for each State, and these constitute the legal standards of the nation, so far as any national standard can be said to exist. The standards thus provided were similar to those used in England prior to the Act of 1824, and they lack that accuracy and scientific character which are exceedingly desirable in a country so extensive and so commercial as the United States. Many of the States of the Union have attempted to reduce their weights and measures to a uniform system, and not a little legislation has been directed to this end; but generally with very little effect. And until Congress shall take up the matter in good earnest, and with the aid of scientific men, but little can be done to secure a result so important.

* The origin of the words Troy and Avoirdupois has been variously given, but the most probable explanation is this: that the latter is derived from avoirs (averia), the ancient name for goods or chattels, and poids (weight.) The word Troy has probably no reference to a town in France, as was formerly supposed, but, as applied to weight, originated in › monkish name of Troy Novant, which was given to London, and ed on an ancient legend; so that Troy weight is properly London

To France belongs the credit of having established a system of weights and measures more simple and uniform than that possessed by any other nation. This system, which was insti tuted in 1795, is based upon the length of a quadrant of a me ridian, or the distance from the equator to the poles of the earth. This distance being ascertained with the greatest care and exactness, a ten-millionth part of it was assumed as the mètre or unit of length, and this is the standard for all lineal measures. The mètre was found to correspond very nearly with the old French yard, being equal to 3.07844 French feet, or 3.281 English feet, and by accidental similarity is very nearly equal to the length of the pendulum vibrating seconds.

The unit of the French WEIGHT is the gramme, which is equal in weight to a cubic centimètre, that is, the 100th part of a mètre of pure water, at the temperature of melting ice, which is equal to 15.434 English Troy grains.

One object which was kept in view in the formation of the French metrical system was, that all quantities might be expressed by whole numbers and decimals, without the necessity of separating them into classes of units distinct from the local values which the numeral figures have in the ordinary arithmetical notation; and this was accomplished by forming the classes of units of weight and measure according to the decimal scale. Thus, the mètre being the original unit, the next superior unit is the decamètre, which is equal to 10 mètres; the next above this is the hectomètre, equal to 100 mètres, &c., as will be seen in the table of French weights and measures. This rise of successive units in a decuple progression is generally expressed by Greek prefixes, as above, deca (Greek deka), meaning ten, and hecto (Greek hekaton), one hundred, while to express the classes of units inferior to the mètre, Latin pref xes are adopted, as décimètre, the 10th part of a mètre, centimètre, the 100th part, &c., decem and centum being the Latin words for ten and a hundred.

Besides the metrical system, which is thus accurate and convenient, there is in France what is called the Système Usuel, or common system, which was established in 1812 for the purposes of retail trade, on account of the aversion of the common people to the innovation of the metrical system. This latter system" tolerates the names of the old measures necessary in the inferior departments of trade, while, by a slight alteration, the value of these measures is so fixed as to have certain definite proportions to the metrical system." Its divisions are not decimal, but chiefly binary, from the convenience of the latter scale in small business transactions.

The following tables express the French measures of length, and also the French weights, according to both the metrical and common systems

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

Décagramme 154.3402 =

Hectogramme

Kilogramme
Myriagramme:
Quintal

Millier, or Bar:

=

=

=

=

=

"6 or 5.64 drams Avoirdupois. 3.2134oz. Troy, or 3.527oz. Avoirdupois. 2lb. 8oz. 3dwt. 2gr. Troy, or 2lb. 3oz. 4.428dr. Avoirdupois. 26.795lb. Troy, or 22.0485lb. Avoirdupois. 1cwt. 3qr. 25lb. nearly. 9 tons 16cwt. 3qr. 12ĺb.

[subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][merged small][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][subsumed][ocr errors]
« PreviousContinue »