Online Encyclopedia

Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.

WEIGHT

Online Encyclopedia
Originally appearing in Volume V02, Page 542 of the 1911 Encyclopedia Britannica.
» Make a correction to this article.
» Add information or comments to this article.
Spread the word: del.icio.us del.icio.us it!

WEIGHT (See also:

AVOIRDUPOIS) See also:Ounce. See also:Pound. See also:Stone. See also:Quarter. See also:Hundred- Ton. weight. I is six T48 iAs See also:sax-6 r6 i rx ~'a iii a3 a 224 14 I 2 a SBII 448 28 2 1 s's 1792 See also:II2 8 4 35840 2240 16o 8o 20 I (Also 7000 grains = See also:lib avoirdupois.) 120. See also:Change of See also:System.—It is sometimes necessary, when a quantity is expressed in one system, to See also:express it in another, 1 See also WEIGHTS AND See also:MEASURES. I convergents are L, q , 4 , ... the number can be expressed in the See also:form pl (I+p Q2) (1--Q2) (I -{-pQ) . . . , and that if we go up to the See also:factor 1 5"090+1 the product of these factors differs from the true value of the number by less than t 1 gngn tl The following are the ratios of some of the See also:units; each unit is expressed approximately as a decimal of the other, and their ratio is shown as a continued product (§ 116), a few of the corresponding convergents to the continued fraction (§ 117) being added in brackets. It must be remembered that the number expressing any quantity in terms of a unit is inversely proportional to the magnitude of the unit, i.e. the number of new units is to be found by multiplying the number of old units by the ratio of the old unit to the new unit. gg~ qq y d~ Yard See also:Metre -790000 =10039= 12'3 84 '83 94-"(1 1 ,ii- 42J • C I entimnchet re 2 1 5.402- - 730093 _ 5, 62- I 1 6&gi (, 3 ., 15-29 0000— 7 — 6~5 955 2 3 333 520 ).

Mile Kilometre _ — 16093 1 62 90.1 4 0=.Q.. 1-84-•23-G-9.. • (9f 23, 1SI$). 1 0 0 0 0 _— 0 Square yard =1 ss1 -0000_,.9_os,1_e s_. s si_ 2s_o. Square metre 0000—Y1900—6 305 15249 • • • (0, 61, 299)• See also:

Acre Hectare Quart Litre Pound Kilogramme _4 36_ — _I_0 52 0.00 _12, 11.01 ,I3 4,22 11 (1 1, T5r,9744 ,53' 500 T~00004"6—85 29392 • (ii.) See also:Special Applications._ 121. Commercial See also:Arithmetic.—This See also:term covers practically all dealings with See also:money which involve the application of the principle of proportion. A See also:simple class of cases is that which deals with equivalence of sums of money in different currencies; these cases really come under § 120. In other cases we are concerned with a proportion stated as a numerical percentage, or as a money percentage (i.e. a sum of money per See also:loo), or as a See also:rate in the £ or the See also:shilling. The following are some examples. Percentage: Brokerage, See also:commission, See also:discount, See also:dividend, See also:interest, investment, profit and loss. Rate in the £: Discount, dividend, rates, taxes. Rate in the shilling: Discount.

See also:

Text-books on arithmetic usually contain explanations of the See also:chief commercial transactions in which arithmetical calculations arise; it will be sufficient in the See also:present See also:article to See also:deal with interest and discount, and to give some notes on percentages and rates in the £. See also:Insurance and Annuities are matters of See also:general importance, which are dealt with elsewhere under their own headings. 122. Percentages and Rates in the £.—In dealing with percent-ages and rates it is important to See also:notice whether the sum which is expressed as a percentage of a rate on another sum is a See also:part of or an addition to that sum, or whether they are See also:independent of one another. Income tax, for instance, is calculated on income, and is in the nature of a See also:deduction from the income; but See also:local rates are calculated in proportion to certain other payments, actual or potential, and could without absurdity exceed 20S. in the £. It is also important to See also:note that if the increase or decrease of an amount A by a certain percentage produces B, it will require a different percentage to decrease or increase B to A. Thus, if B is 20% less than A, A is 25% greater than B. 123. Interest is usually calculated yearly or See also:half-yearly, at a certain rate per cent. on the See also:principal. In legal documents the rate is sometimes expressed as a certain sum of money " per centum per annum "; here " centum " must be taken to mean " £loo.,, Simple interest arises where unpaid interest accumulates as a See also:debt not itself bearing interest; but, if this debt bears interest, the See also:total, i.e. interest and interest on interest, is called See also:compound interest. If roor is the rate per cent. per annum, the simple interest on D. for n years is £nrA, and the compound interest (supposing interest payable yearly) is £[(1+r)°-1]A. If n is large, the compound interest is most easily calculated by means of logarithms.

124. Discount is of various kinds. Tradesmen allow discount for ready money, this being usually at so much in the shilling or £. Discount may be allowed twice in See also:

succession off quoted prices; in such cases the second discount is off the reduced See also:price, and there-fore it is not correct to add the two rates of discount together. Thus a discount of 20%, followed by a further discount of 25%,gives a total discount of 40 %, not 45 %°, off the See also:original amount. When an amount will fall due at some future date, the present value of the debt is found by deducting discount at some rate per cent. for the intervening See also:period, in the same way as interest to be added is calculated. This discount, of course, is not equal to the interest which the present value would produce at that rate of interest, but is rather greater, so that the present value as calculated in this way is less than the theoretical present value. 125. Applications to Physics are numerous, but are usually only of special interest. A See also:case of general interest is the measurement of temperature. The See also:graduation of a thermometer is determined by the freezing-point and the boiling-point of See also:water, the See also:interval between these being divided into a certain number of degrees, representing equal increases of temperature. On the See also:Fahrenheit See also:scale the points are respectively 32° and 212°; on the Centigrade scale they are o° and loo°; and on the See also:Reaumur they are o° and 8o°.

From these data a temperature as measured on one scale can be expressed on either of the other two scales. 126. Averages occur in See also:

statistics, See also:economics, &c. An See also:average is found by adding together several measurements of the same See also:kind and dividing by the number of measurements. In calculating an average it should be observed that the addition of any numerical quantity (See also:positive or negative) to each of the measurements produces the addition of the same quantity to the average, so that the calculation may often be simplified by taking some particular measurement as a new zero from which to measure.

End of Article: WEIGHT

Additional information and Comments

There are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML.
Site content, images, and layout Copyright © 2006 - Net Industries, worldwide.
Do not copy, download, transfer, or otherwise replicate the site content in whole or in part.

Links to articles and home page are always encouraged.

[back]
WEIGHING MACHINES 		[next]
WEIGHTS AND MEASURES

Site © 2006 - Net Industries