fw Engineering and other Purposes. 37 



fill a vat 30 feet diameter and 40 feet liigh, and also the pressure i gainst 

 the side of the vat at the bottom, and ] 0, 20, and 30 feet below the sur- 

 face. To find the contents of the vat square the diameter, and multiply 

 it by the depth, (by arithmetic) 30x30x40 = 36,000. Seek 36,000 in 

 H. and the contents will appear 28,280 in G. (Thus the scales G. and 

 H. although representing inches in the general scheme, have given the 

 product of 36,000x7854 = 28,280 cubic feet.) Seek 28,280 in B. the 

 proper scale for cubic feet, and the answers 4910 barrels will be found in 

 K. and 701 liquid tuns in L. 



It only remains to divide the entire contents of the vat 28,280 by 

 the contents of the floor 2565, the quotient 1 1 nearly will be seen on 

 inspection as the number of brewings required. 



To find the pressure against the bottom of the vat, &c. seek the depths 

 40, 30, 20, and 10, in G, and the pressures will be read respectively in M. 

 17"4, 13*1, 8'7, 4-35 pounds avoirdupois. 



The scales on the other side of the instrument are for the 

 quadratic and cubic relations of quantities. 



Scales are made up of two parts, the spaces which are geo- 

 metrical quantities or extents, and the numerals which are 

 arithmetical quantities. So likewise do they admit of two 

 modes of application, first to the measurement of spaces by 

 means of their spaces, as in making reduced and enlarged 

 drawings, -proportional spaces being then marked by equal 

 numerals; — and secondly, to the measurement of numbers, as 

 in the slide rule, the thermometer scales, &c., proportional 

 numbers in this case being marked by equal spaces. 



This will be rendered very clear by an example. Required 

 I of a line A B, and | of the number 8. Select two scales in 

 the proportion of the terms of the fraction, namely, 



012345678 



A b B 



The spaces of the three scale are each three tenths of an inch, 

 and those in the four scale four tenths. 



The line A B equals 3 spaces of the denominator scale, but 

 the three spaces of the numerator scale A b are only | of 

 A B, A B being divided into 4 parts on the three scale ; 

 therefore in drawing, we measure the object with the denomi- 

 nator scale, and we draw from corresponding numbers on the 

 numerator. But if we desire to know |ths of 8, we find that 

 as regards the numerals on the scales matters are reversed, 

 the greater spaces require fewer figures in the same extent, or 

 they are numerically of smaller value; therefore to read | of 

 8 by the above scales, we seek the given number in the nu- 

 merator, and we find the reply 6 over against it on the de- 

 nominator scale. 



