such equations. For example, as is well known to American students, these equations appear in the little Science Series Volume by M. Leon Pochet.

But it has never been deduced from these equations in plain terms, why the injector, which, under the law of momentum, may at first use steam to the full limit of expansive action, finally realizes a mechanical result of far less value than a pump which acts without expansive action. To illustrate :

If an injector works with steam of 100 pounds absolute pressure, the law of vis viva, which governs the flow of steam, requires that the work which the steam devotes to the action of the injector shall be the area ABCDEA* (Fig. 95), which is the same work

that a steam engine expanding 20 times would theoretically realize from an expenditure equal to the total heat of the weight of steam represented by the volume BC. On the other hand, a steam pump working without expansion would realize from the same expenditure of heat, simply the useful work represented by the area, ABCFA.

Now, assuming that in the pump there is neither loss by clearance nor cylinder condensation, the area, A'BCF'A', if BC represented a pound of steam, would be

=

(100 14.7) × 144 × 4.3 52632 foot-pounds,

4.3 cubic feet being the volume of a pound of steam at 100 pounds pressure per square inch.

On the other hand, the area ABCDEA, OA being 5 pounds pressure per square inch, is 156,542 foot-pounds, or fully three times as much effect as the pump for the same expenditure of heat.

* The diagram is slightly in error, as the point D should coincide with E.

But as a matter of fact the best practical duty* of an injector is about 2,000,000 foot-pounds, against 10,000,000 for a direct acting boiler feeding size of pump.

In other words the practical pumping effect of the pump is five times that of the injector. What then has become of the great superiority of the injector, which the equations of vis viva and of momentum indicated should be as 3 to 1?

It is not due to radiation, for this loss is greatest in the pump. It cannot be anything akin to cylinder condensation, for this exists only in the pump and there to the enormous extent of over of the total feed water. It is directly from this point of view, that Prof. Webb's deduction comes to our rescue, by showing us that, although the injector may and does initially endeavor to devote three times more of the heat in the steam to mechanical pumping effect, yet because such effect has to convey itself to the feed water by impact, not less than of the work represented by ABCDEA, can avoid being changed back from the form of mechanical work into heat, when the small mass of swiftly moving steam collides with a mass of water fifteen times as great, as is the case under the most usual conditions of the working of injectors.

=

Instead, therefore, of realizing 156,540 foot-pounds from the expansive area ABCDEA, we have only 15540 about 11,000 foot-pounds. Without the effect of cylinder condensation, we therefore have by Prof. Webb's theorem,

Useful effect of injector = 1889 = about of pump.

But as the cylinder condensation in the case of the pump is known to reduce its efficiency by at least, we have, by Prof. Webb's theorem, including cylinder condensation in the pump,

Useful effect of injector 2 x = of pump.

This result is now again inconsistent with practice, because we have stated that by experiment,

Useful effect of injector = of pump.

But Prof. Webb further points out that unless the directions of the particles of steam at the instant of striking the water are exactly parallel with the direction of the flow of the feed water, only

* By the term duty is here meant the popular measure of the efficiency of pumping machines, viz., number of foot-pounds of useful work per 100 pounds coal consumed.

a fraction of the part of area ABCDEA, Fig. 95, will remain as mechanical effect. Now, as a matter of fact, it is quite reasonable to suppose that many particles of steam rush from the steam pipe o, Fig. 96, in directions oa, oc oblique to the direction ob, and it is only necessary to suppose that about 50 per cent. of the weight of the steam does so act, in order to bring the theory

into harmony with experiment in assigning to the injector the useful effect of a pump, considering the injector as a pump only.

The following table* shows the actual ratio of the injector to the pump as a boiler feeder, giving it full credit as a feed-water heater as well as a pump.

TABLE I.

General Conditions.-Pressure of steam in boiler 80 pounds per square inch above the atmosphere, the boiler fed in one case by a direct acting steam pump, having a duty, when no feed-water heater is used, of 10,000,000 foot-pounds per 100 pounds of coal, and in the other by an injector which heats the feed water from 60 deg. to 150 deg. Fahr.

Temperature of feed water as delivered to the pump or to the injector, 60 deg. Fahr. Rate of evaporation of boiler, 10 pounds of water per pound of coal from and at 212 deg. Fahr.

* From article on "Efficiency of Pump vs. Injector," by Prof. D. S. Jacobus.—

See Stevens Indicator, April 15, 1888.

CONCLUSION.

By Prof. Webb's theorem, it appears that while the injector, considered as a pump, at first permits steam to work with the full advantage of expansive action and thereby transforms a greater per cent. of heat into work than a pump, yet all such advantage is lost by the retransformation of about of the expansive work into heat by oblique impact, thereby making the efficiency of an injector about of a non-expansive steam pump, notwithᄒ standing that such pumps, when of small size, waste over twice as much steam by cylinder condensation as is necessary to fill their cylinders.

Prof. Webb.-I gather from Mr. Kent's remarks, and the questions of others who are interested in my paper, that I have not been sufficiently explicit in the opening and closing paragraphs. I have, therefore, inserted a line in the former, to the effect that the pump works in connection with a heater, and will now endeavor to explain more thoroughly what I mean in the latter.

In this closing paragraph I would point out how the fact that the injector loses no heat is reconcilable with the other fact that it is not generally the most economical device for feeding a boiler; I say "generally," because if the injector is operated by exhaust steam, or if there is no exhaust steam available for heating the feed water, the injector is economical enough.

To see the matter clearly, it must be borne in mind that coal may be burned either (a) for the purpose of heating a quantity of water to be used as hot water, as, for example, where water is needed at, say, 212° for cooking purposes, or where it is to be used for dyeing and other purposes in the manufacture of cloth, or it might even be fed to a steam boiler as feed water; or (b) for the purpose of heating water from, say, 212° to some higher temperature so as to generate steam to be used in an engine for the production of mechanical power.

For the purpose (a), we may, if we please, generate steam in a boiler, and blow it into a tank of water to heat it, but steam at 130 pounds pressure is no better for this purpose than steam at 50 pounds, and the only economy possible is to avoid loss of heat.

On the other hand, for the purpose (b), the thing that we want is the steam, and steam at 130 pounds is about twice as valuable in a non-condensing engine as steam at 50 pounds; i. e., steam at 347° is twice as valuable in such an engine as steam at 280°, so

that we may economize not only by avoiding loss of heat, as in (a), but by avoiding loss of temperature.

For

An analogous case presents itself in the use of water. purposes of washing, water is no better drawn from a mill-pond than it is when taken from the tail-race, and the only economy possible is to avoid the loss of water; but for the generation of mechanical power, it is twice as valuable when taken from a mill-pond at an elevation of 20 feet as when it comes from one at but 10 feet elevation. In this case we may avoid not only the loss of water, but economy requires also that loss of head be avoided.

In feeding a steam boiler with water two things are necessary: First, there is a certain amount of mechanical work to be done in forcing the water in, which is equal to the volume of the entering water multiplied by the difference of pressure within and without the boiler, or more strictly by the difference between the pressure in the boiler where the water enters and the pressure in the tank from which the feed water is drawn plus the pressure corresponding to the height through which the water may be lifted; and, Second, the water is to be heated from the temperature of the water in the tank, to some higher temperature at which it is considered advisable to furnish it to the boiler. This will require a number of units of heat, equal to the weight of water furnished, multiplied by the rise in temperature. The first thing can only be accomplished by the expenditure of live steam or its equivalent, while for the second there is generally an abundance of exhaust steam available.

Now, to say that the injector wastes no heat is to a certain extent an evasion, because although it is literally true that it wastes none directly, it is equally true, that by warming the feed water with high pressure steam, it prevents the use of the exhaust steam for that purpose, and therefore indirectly causes the waste of as much heat in the exhaust steam as is needed to warm the water. Or, to put the thing otherwise, to say that the injector wastes no heat is to hide a defect; true it wastes no heat itself, but it wastes temperature, which is all that makes the heat valuable for generation of power.

Whatever steam the injector uses in doing the mechanical work of forcing in the feed water is no doubt well enough used, but the whole amount of steam drawn from the boiler is out of all proportion to the work done, say four times as much as a non