ON DRAWITffO, WRITING, AND MEASURING. lOT 



according to the properties of similar triangles, in the computation of propor- 

 tions. The same purpose is answered by Gunter's scale, by the sliding rule, 

 and by the logarithmic circles of Clairaut and of Nicholson, which are cm- 

 ployed mechanically in the same manner as a table of logarithms is used arith- 

 metically, the proportion of any two numbers to each other being determined 

 by the distance of the corresponding divisions on the scale; so that if we wish 

 to double or to halve a number, we have only to find the distance from 1 to 2, 

 and to lay it off from the given number either way. (Plate VII. Fig. 93, 94.) 



The measurement of angles is at once applied to the estimation of distances 

 in the dendrometer or engymeter; a part of the instrument forms a base of 

 known dimensions, and the angle at each extremity of this base being mea- 

 sured with great accuracy, the distance of the object may be inferred from an 

 easy calculation, or from a table. The most complete instruments of this 

 kind have two speculums for measuring the difference of the angles at once, 

 in the manner of Hadley's quadrant. Telescopic scales or micrometers are 

 also sometimes used for measuring angles subtended by distant objects, of^ 

 which the magnitude is known or may be estimated, for example, by the 

 height of a rank of soldiers, and inferring at once the distance at which they 

 stand. ' 



Arithmetical and even algebraical machines, of a much more complicated na- 

 ture, have been invented and constructed with great labour and ingenuity; but 

 they are rather to be considered as mathematical toys, than as instruments 

 capable of any useful application. 



An angle, when once measured, can be verbally and numerically described, 

 by reference to the whole circle as a unit : but for the identification of the 

 measure of a right line, we have no natural unit of this kind, and it is there- 

 fore necessary to establisli some arbitrary standard with which any given 

 lengths and surfaces may be compared. It might be of advantage in the com- 

 munication between different countries to fix one single standard to be em- 

 ployed throughout the world, but this does not appear to be practically pos- 

 sible, even if it were determined what the standard ought to be. " The ob- 

 servation of the isochronism of the small vibrations of a pendulum, and the 

 ease and certainty with which the length of a pendulum vibrating secomls- 



