36 Mr. C. Holtzapffel on a Scale of Geometrical Equivalents 



on N. 2060 pounds avoirdupois, (multiplying either of these by the spe- 

 cific gravity of any substance, gives the weight of each, or it may be done 

 by inspection of the scales provided for that purpose p. 24 — 30,) on O. we 

 read 18'4 cwts., on P. 'OS tuns, on R. '932 cubic metres, on S. 3'06 super- 

 ficial mUres, as before extending to the height of one foot, and finally on 

 T. 932 kilogi-amvies, as the weight of 33 English cubic feet of water. 



It is not at all likely that the whole of these comparative 

 values would be wanted in any one inquiry, but all the mea- 

 sures are of frequent occurrence in calculations. To render 

 the reading as simple as possible the numerals denote the 

 true values throughout, so that no reductions nor changes 

 have to be made, unless it be the calling 1, either 10, 100,1000, 

 &c. which is common to all decimal scales : it need scarcely 

 be said that when the value of any one scale is thus altered, 

 the same must be done with all employed at the same time. 

 It will be found the most convenient first to take down the 

 numbers denoted on the scale, and then to seek the true place 

 for the decimal point. 



The results given in the general example show the varied 

 nature of the transpositions which the scale effects : these need 

 not be extended by way of illustration ; but we may also read 

 and resolve decimals, and perform many of the calculations 

 in engineering, &c. which would otherwise require the employ- 

 ment of two or more constant multipliers. 



Required the value of the decimal -231 of a cubic foot, in cubic inches. 

 Employ B. and C. The answer is 399*2 inches. 



Convert the decimal '987 of a pound troy into the decimal of a kilo- 

 gramme. Employ N. and T. The answer is -3685. 



"What fraction of a liquid tun of water is 7^ cwts. of the same ? Employ 



0. and L. Answer -322. 



The diameter of a sphere of water containing 500 gallons? Seek 500 in 



1. and take the cube root of the number obtained in D (from the tables). 

 Answer 263,900, the cube root of which is 64 inches nearly. . 



Required the side of an equal cube. Read 64 the diameter of the given 

 sphere in D, and the answer 33'5 will be found in C ; the two lines C. 

 and D. performing the multiplication and division by '5236. 



And in the like manner the lines G. and H. effect the multiplication 

 and division by '7854. Required the diameter of a column 45 feet high to 

 contain 790 gallons. Divide the quantity by the height in feet for the 

 contents of one foot, for which height the scales are calculated; answer 

 ] 7'55 gallons : seek that number in I. and take the square root of the 

 number found in H., namely, 51 5-4, as the answer, or squared, 23 inches 

 nearly, as the diameter of the column. 



Required the contents of a cooling floor for a brewery 19 yards long by 

 20 yards wide, covered to the depth of 9 inches, in cubic feet, barrels, and 

 tuns avoirdupois. By arithmetic 19x20 = 380, the area of the floor in 

 square yards ; deduct ^th, 9 inches being |^ths of 1 foot, for which depth 

 the scales are calculated, 380 less ^th = 285. 



Seek 285 in E. and read the answers in B. 2565 cubic feet, in K. 445*^ 

 barrels, and in P. 71 '56 tuns. 



Required further how many times this quantity would be required to 



