237 ^^ /7*;/^ the Capacity of Water Tanks* 



TO FIND THE CAPACITY OF WATER-TANKS. 



Containing vessels are usually made in the form the frustum of 

 a cone. Tubs and pails, kits and tanks, pans and coffee-pots, all 

 have the same general form, and are measured by the same gen- 

 eral rules. 



Especially in this country, where so many tanks are annually 

 builr, is the frustum of a cone seen on a grand scale. These tanks 

 are usually set on a high tower, and are supplied with water 

 pumped by a windmill. They are made of clear redwood lumber, 

 and are strongly hooped with iron. When properly built they 

 are water-tight, and they resist decay for many years. The top 

 is several inches smaller than the bottom, to allow the hoops to 

 bind firmly when they are driven downward. ■ 



Owing to their circular and tapering form, it is not so easy to 

 calculate their capacity as it would be to find that of an ordinary 

 box or bin. The rule of the arithmetics for finding the volume 

 of the frustum of a cone is quite complex, and involves finding the 

 area of two circles, the square root of the product of these areas, 

 and other minor operations. 



An examination of the principles involved has enabled me to 

 deduce the following simple rule, which I trust will be found use- 

 ful by all who have occasion to measure anything which has the 

 form of the frustum of a cone. Even a barrel or cask may be 

 considered as two tubs joined together, and the calculation will 

 vary but little from the true capacity of the cask. 



The following directions and rule should be observed: 



Measure the inside radius, (half the distance across), both of the 

 top and of the bottom of the tank or tub, and also find its perpen- 

 dicular depth. Reduce the measurements to inches 



Multiply each radius by itself, and one radius by the other. 



Add the three products and multiply their sum by the depth. 



Multiply this product by the decimal .0045^3, and the result is 

 the capacity of the tank in gallons and decimals of a gallon. 



For example: A tank measures 4 feet and 6 inches across the 

 top, 5 ieet and 4 inches across the bottom, and is 4 feet and 2 

 inches deep; how many gallons will it contain. 



Operation. 



Smaller radius=27 inches. 



Larger radius:=32 inches. 



Depth =50 inches, 



27X27= 729 



32X32=1024 



27X32= 864 



r Total=26i7 



2617X50=130850 

 1 30850 X. 0045 ^=593. 186 



867, Answer. ij-yy^ f'/f 







