for Engineering and other Purposes. 35 



The line B, therefore, the basis of the instrument, is a line 

 of inches and tenths, marked 10, 20, 30, &c. Now as the 

 cubic yard contains ^7 cubic feet, the unit of the line A is 

 B X 27 or 2*7 inches decimally subdivided. 



The line C for cubic inches is so proportioned that 1728 

 of its nominal divisions, (the number of cubic inches con- 

 tained in one cubic foot,) are equivalent to one tenth of an 

 inch ; but as we could not graduate such a scale, nor employ 

 it when done, our purpose is equally well served by the nu- 

 merals annexed to the divisions. 



Ten inches denotes 100 cubic feet on B, that space must 

 also denote 1728x100 or 172,800 cubic inches on C, 10 

 inches is therefore divided into 17 great divisions, numbered 

 respectively 10,000, 2, 3, 4, 50,000, 6, 7, 8, 9, 100,000, and 

 so on, each fifth numerical being the true number of cubic 

 inches, the ciphers being omitted in the intermediate places to 

 avoid confusion. 



The line D for spherical inches is C multiplied by "5236 

 the constant multiplier for giving the value of the sphere en- 

 closed in any given cube, or as expressed at the end of the 

 scale itself C x '5236 = 3'030. In this simple manner all the 

 values are worked out and graduated, the formula for con- 

 structing each being marked at the terminations of the several 

 lines. 



It only remains to observe that the group for superficial 

 measures is calculated for areas and columns of the common 

 height of one foot; the group for weights, which refer to 

 water, from the cubic foot of water weighing 62*5 pounds 

 avoirdupois, therefore 10 inches represents 6250 pounds avoir- 

 dupois ; the group for measures of capacity, from the gallon 

 being equivalent to 10 pounds of water, and so on. 



The scales of the instrument being therefore proportionals as explained, 

 we may read off in groups the value of any one measure in any other: 

 it is desired, for example, to know all the equivalent values of 33 cubic 

 feet, expressed upon the scale, (see diagram). Set the index to 33 on B. 

 cubic feet, and at one view the several answers appear, namely, on A. 

 1-22 cubic yards, on B. 33 cubic feet, on C. 67,000 cubic inches, (the 

 cube root of which from the tables or 38 to 39 will be the side in inches 

 of an equal cube,) on D. we read 1 09,000 spherical inches, (the cube root 

 of which 48 nearly is the diameter in inches of a sphere containing 33 

 cubic feet,) on E. 3-67 square yards, on F. 33 square feet, on G. 4750 

 square inches, (each area being supposed to be the base of a column one 

 foot high, and the square root of any of these will give the side of an 

 equal square column of the same height); on H. we read 6050 circular 

 inches, the square root of which is the diameter in inches of a circular 

 column or cylinder one foot high, (also containing 33 cubic feet) on I. 206 

 gallons, on J. 25*75 bushels, on K. 5*72 barrels, on L, -818 liquid tuns, 

 on M. 2500 pounds troy, that being the weight of 33 cubic feet of water, 



D 2 



