This de-pends upon (1) the steam-pressure to which the valve is exposed; (2) the lift of the valve; (3) the quantity of steam that must be discharged in a given time, in order to prevent an increase of pressure. These quantities having been determined, it is necessary to calculate (1) the area of opening required in order to discharge the given quantity of steam; (2) the diameter of a valve that will afford the required area of opening with the given lift.

The method of making these calculations is explained below.

A. the area of opening, in square inches, required, in order that a safety-valve may prevent the increase of steam-pressure beyond a given point.

(a) For stationary and marine boilers with natural draft: Take the product of (1) the area of the grate-surface in square feet, and (2) 2.63, and divide this product by the steam-pressure as shown by gauge, increased by 14.7.

(b) For stationary and marine boilers with forced draft: Take the product of (1) the area of the grate surface in square feet, and (2) 4.08, and divide this product by the steam pressure as shown by gauge, increased by 11.7.

(c) For locomotive boilers: Take the product of (1) the area of the grate-surface in square feet, (2) 11.67, and divide this product by the steam pressure as shown by gauge, increased by 14.7

To illustrate the rules, suppose that the steam-pressure in a locomotive boiler is 150 lbs. by gauge; what is the proper area of opening for the escape of steam by the safety-valve, the grate-surface being 16 square feet?

The product of 16 and 11.67 is 186.72, and the quotient arising from dividing this by the sum of 150 and 14.7, or 164.7, is about 1-13/100 square inches, which is the required area of opening.

B. The diameter of valve, in inches, required, to afford the necessary area of opening with the given lift.

(a) When the lift of the valve is equal to or less than the depth of the seat: Diminish the required area of opening by the product of (1) the square of the lift, in inches; (2) the square of the sine of the angle of bevel of the valve; (3) the cosine of the angle of bevel of the valve, and (4) 3.1416. Divide this difference by the product of (1) the lift in inches; (2) the sine of the angle of bevel of the valve, and (3) 3.1416.

(6) When the lift of the valve is greater than the depth of the seat: Diminish the required area of opening by the product of (1) the square of the depth of seat, in inches ; (2) the square of the sine of the angle of bevel of the valve ; (3) the cosine of the angle of bevel of the valve, and (4) 3.1416. Divide this difference by 3.1416 times the sum of (1) the depth of seat in inches, multiplied by the sine of the angle of bevel of the valve, and (2) the difference between the lift and the depth of seat, in inches.

A table of sines and cosines of angles from 20° to 50° will be found below, and an example is appended in illustration of the rules.

Example.-A safety-valve has a bevel of 33°, a depth of seat of inch, and is required to give an area of opening of 2 inches, with a lift of 1/2 inch. What should be its diameter?

Now 1.95 divided by 1.212 gives the diameter of valve, 1.61 inches, nearly. B.