To find the diameter of a shaft subject to twisting only, given the twisting moment in inch-lb. and the allowable stress in lb. per square inch. Set the stress in lb. per square inch on B to the twisting moment in inch-lb. on A, and bring cursor to 5·1 on B. Then move the slide until the same number is found on B under the cursor that is simultaneously found on D under the index of C. EX.—A steel shaft is subjected to a twisting moment of 2,700,000 inch-lb. Determine the diameter if the allowable stress is taken at 9000 lb. per square inch. Set 9000 on B to 2,700,000 on A, and bring the cursor to 5·1 on B. Moving the slide to the left, it is found that when 11·51 on the R.H. scale of B is under the cursor, the L.H. index of C is opposite 11·51 on D. This, then, is the required diameter of the shaft. (N.B.—The rules for the scales to be used in finding the cube root (page 42) must be carefully observed in working these examples.) MOMENTS OF INERTIA. To find the moment of inertia of a square section about an axis formed by one of its diagonals (I = (_s_^4)/(12)). Set index of C to the length of the side of square _s_ on D; bring cursor to _s_ on C, 12 on B to cursor, and over index of B read moment of inertia on A. To find the moment of inertia of a rectangular section about an axis parallel to one side and perpendicular to the plane of bending. Set index of C to the height or depth _h_ of the section, and bring cursor to _h_ on B. Set 12 on B to cursor, and over breadth _b_ of the section on B read moment of inertia on A. EX.—Find the moment of inertia of a rectangular section of which _h_ = 14 in. and _b_ = 7 in. Set index of C to 14 on D, and cursor to 14 on B. Bring 12 on B to cursor, and over 7 on B read 1600 on A. DISCHARGE FROM PUMPS, PIPES, ETC. To find the theoretical delivery of pumps, in gallons per stroke. Set 29·4 on B to the diameter of the plunger in inches on D, and over length of stroke in feet on B read theoretical delivery in gallons per stroke on A. (N.B.—A deduction of from 20 to 40 per cent. should be made to allow for slip.) To find loss of head of water in feet due to friction in pipes (Prony’s rule). Set diameter of pipe in feet on B to velocity of water in feet per second on D and bring cursor to 2·25 on B; bring 1 on B to cursor, and over length of pipe in miles on B, read loss of head of water in feet, on A. To find velocity in feet per second, of water in pipes (Blackwell’s rule). Set 2·3 on B to diameter of pipe in feet on A, and under inclination of pipe in feet per mile on B read velocity in feet per second on D. To find the discharge over weirs in cubic feet per minute and per foot of width. (Discharge = 214√(_h_^3)) Set 0·00467 on C to the head in feet _h_ on D, and under _h_ on B read discharge on D. To find the theoretical velocity of water flowing under a given head in feet.