MENSURATION OF ARTIFICERS' WORFCS. All such works, whether superficial or solid, are computed by the rules proper for the figure of them.
The most common instruments for taking the measures are, a five-feet rod, divided into feet and quarters of a foot ; and a rule, either divided into inches, or twelfth parts, and each twelfth part into twelve others ; a fractional part beyond this division, measurers seldom, or never, take any account of.
When the dimensions are taken by a rule divided in this manner, the best methods to square the dimensions will then be by duodecimals, by the rule of practice, or by the multi plication of vulgar fractions ; but, in the opinion of some, the best method of taking dimensions is with a rule, when each lbot is divided into ten parts, and each part into ten other parts, or seconds, because the dimensions may be then squared by the rules of multiplication of decimals, which is by far the shortest and readiest method. Those who con tend that duodecimals, or cross multiplication, is the easiest method of squaring dimensions, as well as the most exact, are very much mistaken; for if the dimensions are taken in duodecimals, and reduced to decimals, and then squared, the operation, in this case, will certainly be much longer than if it had been done at once by duodecimals, and sometimes not so exact : but if the dimensions are taken in feet, tenths, &c.
the operation will not only be easier and shorter, but in many cases will be much more exact than by duodecimals: the rea son is obvious to those who consider that there are many cases in which it will be impossible to express, truly, a deci mal scale equal to a duodecimal one ; neither will it, in many cases, be possible to express accurately, a duodecimal scale equal to a decimal one; duodeehnals have the same property with regard to twelfth parts, as decimals have to tenth parts; therefore, in many eases, duodecimals will sometimes circulate and run on, ad infinitum, when reduced from decimals, as deci mals will, when reduced from duodecimals; and farther, since duodecimals are expressed by a series of twelfth parts, and decimals by a series of tenth parts, in multiplying each of the parts of the former, the trouble of dividing by twelve will then be unavoidable, and more burdensome to the mind than if the operation had been done by the latter, where there is no such division to be made, but merely to multiply as in common mutiplication, and point off the decimal places in the product.
This last method is always to be preferred, as the most natural, as well as the most easy of the two.