PROBLEM VII. To find the convex superficies of an annulus, or ring, whose thickness and inner diameters are known. METHOD I. To the thickness of the ring, add the inner diameter; multiply the sum by the thickness, and the product by 9869, will give the superficies required. METHOD II. Multiply the circumference of the generating circle by the circumference round the middle of the ring, or that line generated by the centre of the generating circle, and the product will be the area. Note. This last method will give the convex superficies of any part of an annulus, or ring, comprehended between two planes passing through the fixt axis. EXAMPLE. What is the convex superficies of an annulus, or ring, whose inner diameter is 8in. and the thickness 3in.? Then 38 X 3 X 9'869 325-677 the superficies required. OF OF SPECIFIC GRAVITY. DEFINITION. I. The specific gravity of a body, is the relation that the weight of a magnitude of that kind of body, has to the weight of an equal magnitude of another kind of body. II. In this comparison of the weights of bodies, it is convenient to consider one body as the standard or unit, to which the others are to be compared; and as rain water is nearly alike in all places, therefore this seems to be the most convenient for a standard. III. It has been found by repeated experiments, that a cubic foot of rain water weighed 62 pounds avoirdupoise ; 62.5 consequently, (225) 0-03616898lb. is the weight of one 1728 cubic inch of rain water. IV. The knowledge of the specific gravities of bodies, is of great use in computing the weights of such bodies, as are too heavy or too difficult to have their weight discovered by other means. |