tance between the fulcrum and the valve is lessened, so is the action or tendency of the lever to press down the valve increased.

27. When the required pressure upon the safety-valve is given, also the diameter of the valve, by what mode of calculation is the required amount of weight upon the valve or lever determined?

Square the diameter of the valve, that is, multiply the diameter by the diameter, which product being multiplied by the decimal number 7854, expresses the area of the valve in equal terms of unity; and if the weight be to act directly upon the valve, multiply the area by the pressure required; the product is the weight required, plus the weight of the valve: but if the pressure is to be effected through the intervention of a lever, then the weight required on the lever is less, equal to the number of times the distance between the fulcrum and the weight exceeds the distance between the fulcrum and the valve.

28. What is meant by the expression—“ area” of the valve?

The area is the amount of surface exposed to the action of the steam whereby to effect a raising

of the valve from its seating, and expressed in terms as the measurement of its diameter; for instance, if the diameter be inches, the area will be square inches; and so of other measure in

which the diameter is taken.

any

29. Why square the diameter of the valve and multiply by 7854, to find the area?

Because the area of a circle whose diameter is unity or 1, is to the area of a square whose side is unity, as 7854 to 1. If the pressure of steam on a square inch be multiplied by 7854, the product is the pressure on a circular inch, in equal terms of unity

30. If the pressure of steam be expressed by the circular inch in place of square inch, how is the amount of pressure on the square inch to be ascertained?

Divide the pressure on a circular inch by .7854; the quotient is the pressure on that of a square inch, in equal terms of unity; or, because 1.2733 is the reciprocal of 7854, multiply the pressure by that number, and an equal purpose will be effected.

31. If a square inch be made the unit of area, whereby to determine the amount of pressure on a safety-valve, and a pound the unit of weight, how many pounds must there be attached, directly, on a valve 7 inches diameter, to effect a pressure of eight pounds per square inch.

7.252 x 7854 =

41.282 inches, the area of the valve, and 41.282 x 8330-256 pounds, including the weight of the valve.

32. If, to effect the above purpose of pressure, a lever of 45 inches in length were applied, the distance between the fulcrum and the valve being six inches; what weight must be laid on the end of the lever, or what would be the indicated pressure by a spring balance?

neither case is the action of the lever taken into

account, and which ought to be deducted, as well as the weight of the valve.

33. Suppose a given diameter of valve is required to be replaced by two or more, and of diameters equal or unequal to each other, but in total amount of area equal to the first; by what mode of calculation is this to be effected?

All circles are in relation to each other as the squares of their diameters; hence, if the given diameter be squared and divided into the various required proportions, the square roots of the quotients give the various diameters required.

Thus, suppose it were required to form two safety-valves, whose united areas equal one of six inches in diameter, but, of the two, the area of the one to be twice that of the other: 62 36; but the one is to be twice that of the other; hence it must be divided into three parts; 36:3 12, and 12 x 224: consequently the one must contain 12, and the other 24 inches; then ✔ 12 3.464, and ✔24 = 4.899 inches diameter.

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34. Is there no other method adopted whereby to test the steam's elastic force in a boiler, than by means of a safety-valve?

Yes, by an inverted syphon containing mercury sufficient to overcome the pressure of the steam;

2.04 inches in height of the column being a counterpoise to a pressure of one pound; but as the syphon consists of two columns, a rise of about one inch, indicated by the mercury in the column open to the atmosphere, shows an increase of pressure equal to one pound per square inch in the boiler.

35. Is the indicated pressure of steam by a safety-valve, or otherwise, the total amount of effective force whereby to produce motion in a steamengine?

In those on the non-condensing principle it is; but in a condensing engine, if a perfect vacuum is obtained, fifteen pounds per square inch must be added; this, however, being unattainable in practice, through imperfect condensation, the proper amount to be added is fifteen pounds per square inch, minus the resisting vapour in the cylinder, as indicated by a barometer attached.

36. What is a barometer?

An instrument for measuring the density of vapour remaining in the condenser of a steamengine; it consists generally of a glass tube upward of thirty inches in length, placed vertically,