Jor Engineering and other Purposes. 



41 



and dimensions of similar vessels, under all varieties of size 

 and form with considerable accuracy, whereas the complexity 

 of such calculations often cause them to be neglected, leaving 

 the results to the unassisted judgement, or in other words to 

 be guessed at. 



The scale of geometric equivalents being, as before ad- 

 verted to, rather an instrument for transposition, than calcu- 

 lation in the strict sense of the word, it will be found desi- 

 rable to estimate the dimensions of certain known forms of 



given areas for reference 



a few have been tabulated. 



They would be employed in the following manner : 

 Required the diameter of a circular gasometer to contain 60,000 cubic 

 feet when filled to the height of 20 feet. 1000 cubic feet would be con- 

 tained in a circle 35-68 feet diameter, 1 foot high ; the height being 20 feet, 

 would necessarily contain 20,000 feet, therefore the proportion would be 



2l)'.'ooo °'' ^ T' ^^^^ 35-68, the given diameter in the 3 quadratic scale, 

 and the new quantity 61-9 will be found in the denominator scale. 



Required the side of a hexagonal tank to contain 3600 cubic feet when 

 filled 5 feet high. The side of a hexagon containing 100 feet is 6-2, the 

 ratio is therefore '^f^^ or y/I-x6-2 = 16-45 : this quantity obtained from 

 the quadratic scales 7 and 1 would be one 35th too small, and might be 

 corrected to that amount by a second process if required; and if in the like 

 manner it were required to multiply any quantity by the factor ^, we 

 might arrive at the result at twice as ^ x f = j^ > and so on. 



It will, however, be found in general the most convenient 

 to bring the ratio within the series of fractions expressed by 

 the numbers 1 to 10, beginning with y^th, and ending with 

 LP, or ten times, which are tabulated ; but we may take cog- 

 nizance of ratios very much larger and smaller after the fol- 

 lowing manner. 



"We may employ any two terms indifferently provided they 

 are in the same proportion ; for example, the terms 1 and 

 2, — 2 and 4, — 3 and 6, — 4 and 8, are each as one to two : their 

 squares are 1 and 4, — 4 and 16, — 9 and 36, — 16 and 64, or 

 as 1 to 4 throughout; it follows therefore that -^^ being the 

 tenth part of 1, the 20th part of 2, the 30th of 3, and so on, 



