WEIGHTS AND MEASURES.] 



APPLIED MECHANICS. 



905 



We must presume that the mechanic is tolerably in- 

 timate with the ordinary operations of arithmetic Ad- 

 dition, Subtraction, Multiplication, and Division ; and 

 that he will bear in mind the following symbols, as a kind 

 of arithmetical short-hand, oftea useful in expressing 

 rules and modes of operation. 



+ placed before a quantity, means that it is to be 

 added to the quantity preceding it. 



placed before a quantity, means that it is to be 

 subtracted from the quantity preceding it. 



X placed between two quantities, means that the first 

 is to be multiplied by the other. 



-:- placed between two quantities, means that the first 

 is to be divided by the last. 



When instead of two dots in this symbol of division, 

 one quantity is written above the line and the other 

 below it, the upper is to bo divided by the lower. Thus 



12 

 12-:-4 may be written^-, which means that 12 is to be 



divided by 4. 



= placed between two quantities, means that the one 

 is equal to the other. 



Example 1. Power = weight X velocity,' means that 

 the power of any machine is equal to the weight raised 

 by it, multiplied by the velocity with which it is raised. 

 Tims, if an engine raise 330 Ibs. at the rate or velocity of 

 100 feet per minute, we should say its power is equiva- 

 to 330 Ibs. X 100 feet = 33,000 Ibs. at the rate of 1 

 foot per minute. 



weight (Ibs ) X velocity (ft. per min.) 



2. Horse-pouer = 330 00 



means that the power of a machine reduced to the 

 standard of horse-power, is equivalent to the weight in 

 Ibs. multiplied by the velocity in feet per minute, and 

 divided by 33000. Thus, if an engine raise 330 Ibs. 100 



feet high per minute, its horse-power is 





= 1 ; 



that is to say, one-horse power. 



WEIGHTS AND MEASURES. The table of weights 

 and measures most necessary in computations connected 

 with Practical Mechanics, are those of Avoirdupois 

 Weight, Lineal, Superficial, and Solid Measure, Time, 

 1 emperature, and the Division of the Circle. Unfortu- 

 nately for ease of recollection and computation, the 

 English Tables of measures have no regular system, and, 

 therefore, require to be remembered separately, or to 

 be constantly referred to. The French have adopted a 

 regular and simple system, both in the names and in the 

 relations of their different denominations. As their 

 measures are frequently referred to in scientific works, 

 we subjoin tables of them along with the English tables ; 

 and short rules for the reduction of quantities given in 

 the one, to their corresponding values in the other. 



TKOY WEIGHT. 

 Used for the precious metals and for chemical analysis. 



Contracted. 



24 Grains = 1 Pennyweight . 24 gr. =1 dwt. 



20 Pennyweights = 1 Ounce ... 20 dwt. = 1 oz. 

 12 Ounces = 1 Pound . . . 12 oz. = 1 Ib. 



1 pound troy therefore contains 5760 grains. 



1 pound avoirdupois contains 7000 troy grains. 



AVOIRDUPOIS WEIGHT. 



Used for weighing all materials except those to which 

 troy weight is confined. 



Contracted. 



1C Drachms => 1 Ounce . . . 16 dr. = 1 oz. 



16 Ounces = 1 Pound . . . 16 oz. =llb. 



28 Pounds = 1 Quarter . . 23 Ibs. = 1 qr. 



4 Quarters = 1 Hundredweight 4 qrs. = 1 cwt. 



20 Hundredweights = 1 Ton .... 20 cwt. = 1 ton. 



FBENCH DECIMAL SYSTEM OP WEIGHT. 



10 Milligrammes = 1 Centigramme 

 10 Centigrammes = 1 Decigramme. 

 10 Decigrammes = 1 Gramme = 15 '434 troy grains. 

 VOL. L 



10 Grammes = 1 Decagramme. 



10 Decagrammes = 1 Hectogramme. 



10 Hectogrammes = 1 Kilogramme = 2 20486 Ibs. 



avoirdupois. 



10 Kilogrammes = 1 Myriagramme. 

 10 Myriagrammes = 1 Quintal = 1 cwt. 3 qrs. 25 Ibs. , 



nearly. 

 100 Quintals = 1 Millier or Bar = 9 tons. 16 



cwt. 3 qrs. 12 Ibs 



The general principle adopted in the French system, 

 is that of the decimal scale. They settle on some unit of 

 weight or measure as the gramme for weight, and the 

 metre for measure. For the names of all fractious of that 

 unit, proceeding by tenths, hundred ths, and thousandths, 

 downwards, they prefix the Latin numerals deci for 

 tenth, centi for hundredth, milli for thousandth, to th 

 name of the unit. Thus, a centigramme is the hundredth 

 part of a gramme, and would be written in figures 0-01 

 gramme ; a millimetre is a thousandth part of a metre, 

 and would be written O'OOl metre. Again, for the names 

 of all multiples of the unit, proceeding by tens, hun- 

 dreds, thousands, and ten thousands upwards, they use 

 the Greek numerals deca, ten ; hecto, hundred ; kilo, 

 thousand ; myria, ten thousand, prefixed to the unit. 

 Thus, for a thousand metres, they say a kilometre, writ- 

 ten 1000 metres; for ten thousand grammes, they say 

 myriagramme, written 10,000 grammes. There are a 

 few exceptions for the larger denominations in the scale 

 of weights, which we have given in full. According to 

 this system, each denomination finds its place in the 

 ordinary decimal scale of notation, and arithmetical 

 operations are reduced to the simple rules, without the 

 necessities of complicated reduction. 



For example, if we wished to ascertain the cost of 7 

 myriagrammes, 3 kilogrammes, 4 hectogrammes, 6 deca- 

 grammes, 5 grammes, 3 centigrammes, of a material at 

 2 francs 20 cents per kilogramme, 

 we should write the quantity . 7346503 grammes 

 which is equivalent to ... 73 46503 kilogrammes, 



pointing otf 3 figures. 

 Multiply by the price per kilo. . 2-2 



14093006 

 14003006 



161-623066 francs. 



Or, 161 francs, 62 cents. 



In the English system, on the other hand, a similar 

 question as, for instance, the cost of 17 tons 4 cwt. 3 qrs. 

 and 18 Ibs., at 12s. 9d. per cwt. would involve the 

 necessity of reducing the several denominations, or of 

 artifices for employing fractional parts as in the ordinary 

 arithmetical rule of Practice. 



To reduce kilogrammes to Ibs. avoirdupois. 



Hide. Multiply by 2-20480. 



Example 1. To reduce 17 kilogrammes to Ibs. 

 Multiply by 2-204SG 



37 -48262 Ibs. 



For general practical computations, the decimal frac- 

 tion, after its first figure, may be neglected, and the 

 multiplier may be taken as 2 2 simply. 



Example 2. To reduce 23 kilogrammes to Ibs. 



23 X 2-2 = 50-6 Ibs. 



For closer approximation, after multiplying the num- 

 ber of kilogrammes by 2 '2, add to the result the 200th 

 part of the number, or the half with two decimal places 

 pointed off. 



Thus, 23 x 2-2=50-6 



add ^th of 23 -115 



50-715 Ibs. 



The accurate number 50 '71178 

 To reduce Ibs. avoirdupois to kilogrammes. 

 Ride. Divide by 2-20486, or multiply by its reci- 

 procal -45355. 



5 z 



