APPENDIX. 



COLLECTIONS OF FACTS. 



MATHEMATICS AND PHYSICS. 



If the square of the diameter of a circle be multiplied 

 by .7854, the product is the area. If the diameter of a 

 sphere be cubed and multiplied by .6236, the product is 

 the solidity ; and the square of the diameter, multiplied by 

 3.14159, is the surface of the sphere. 



To find the contents of a cask, add double the square 

 of the bung diameter to the square of the head diameter, 

 and multiply this sum by the head of the cask ; then divide 

 the product by 1,077 for ale gallons of 280 cubic inches 

 each, or by 882 for wine gallons of 231 cubic inches each. 



Quincunx is one at each of four corners, and one in the 

 middle, thus, : • : 



The convexity of the earth interposes to prevent the 

 sight of distant bodies. Thus, at 600 yards, one inch 

 would be concealed, or an object one inch high would not 

 be seen in a straight line ; at 900 yards, two inches ; at 

 1,400 yards, five inches ; atone mile, eight inches ; three 

 miles, six feet , four miles, ten feet ; five miles, sixteen 

 feet ; six miles, twenty-four feet ; ten miles, sixty-six feet ; 

 twelve miles, ninety-five feet ; thirteen miles, one hundred 

 and twelve feet, and fourteen miles, one hundred and thir- 

 ty feet. 



The mechanical powers may be reduced to three, but they 

 are usually expressed as six — the lever, the wheel and axle, 

 the pulley, the inclined plane, the screw, and the wedge. 



In a single moveable pulley, the power gained is double. 

 In a continued combination, the power is twice the num- 

 ber of pulleys, less 1. 



In levers, the power is reciprocally as the lengths are 

 each side of the fulcrum or centre of motion, as illustrated 

 in the steelyard. 



