indeed. I think if this grid were made perhaps somewhat stronger than it is according to the model the great objection to an inequality in the rising of the pontoons would be got over.

Mr. LATIMER CLARK, C.E.: The first speaker is of opinion that the pontoons ought to have some appliance by which they could either be emptied simultaneously, or as Mr. Bramwell I think more properly stated it, be emptied to different levels in proportion to the load they have to sustain. Either of those arrangements may be readily introduced. As a matter of fact, the Russian engineers (and I must bear very high testimony to their skill and cleverness) have preferred that the pontoons should be emptied simultaneously; that is to say, that the pumps should act uniformly on a number of pipes all acting together, so that if there is any difference of level in any one pontoon over another, that one gives out more water, and they all flow naturally to a level. The simplest combination of pipes, however, enables you to empty 4, 6 or 8 pontoons-your pipes are numbered and under control-you can empty any series of them you like, and that series being all connected to one pipe, they all remain level. The operation is perfectly easy. Designs have been prepared for the introduction of indicators. The system is slightly complex, but I will not detain you more than two minutes in making it intelligible to you. A small air-pump is worked by the engine, and that pump communicates with an air-chamber and a number of pipes, one of which is carried to the bottom of each chamber in every part of the dock. Each pipe is in connection with a barometric column of mercury, and the whole of the upper end of each of these columns of mercury has a pressure upon it. The consequence is, that when this pressure is applied the mercury falls in the column below its natural level to an extent dependent on the height of the column of water in the pontoon below, at which point the excess of the air escapes under pressure; and therefore you can have inside the room a series of these columns indicating the height of water in each pontoon. If you have all the pumps working uniformly, all the pontoons will have level water, and the whole of these columns of mercury will range level. If you prefer any other distribution of the lifting power, you have a series of levels showing you the floating power of each pontoon. One man can guide the whole, and since the operation of raising would probably extend to an hour, he has very ample leisure to put any strain or adjustment he thinks necessary on the dock. Mr. Bramwell spoke of the necessity of rigidity in the dock, and I must say in designing this dock that has been one of the points we very much wished to obtain. I myself am not an advocate of the flexible docks or pontoons; I think a rigid dock is a very desirable thing, and we have great rigidity secured in this dock by the peculiar details of the construction of the side-which is really a very large box girder-and of the pontoons themselves, which being thoroughly braced (although the details are not shown here) are excessively rigid forms of girder, much stronger than an ordinary railway bridge. Therefore the whole structure is extremely rigid, and I think would satisfy the requirements even of Mr. Bramwell. He alluded to the shifting of vessels endways on the American system. That system has been and still is in use. I do not think it necessary

to detain the Meeting by pointing out some objections which there are to it, although the system is very pretty and ingenious. A vessel is brought in on a large pontoon, and hauled endways off that pontoon on to the land, and afterwards hauled back again. Referring again to the question of rigidity, the third speaker alluded to the use of the grid, and that of course gives-especially if it is supplied with the sideshoring frames which you see there any amount of stability, because the shoring frames may be as rigid as the vessel itself. Therefore I think the requirements of rigidity and the power of adjusting the burden to the weight which supports it are both provided for in this dock.

ON THE RATIO OF INDICATED TO EFFECTIVE HORSE-POWER AS ELUCIDATED

BY MR. DENNY'S M.M. TRIALS AT VARIED SPEEDS.*

By W. FROUDE, Esq., M.A., F.R.S., Vice-President.

[Read at the Seventeenth Session of the Institution of Naval Architects, 7th April, 1876; the Right Hon. LORD HAMPTON, G.C.B., D.C.L., President, in the Chair.]

MR. DENNY has taken the bold but well-considered step of discarding the conventional type of measured-mile trials which, as regards the speeds tried, have long been limited to full speed and half-boiler power. Mr. Denny now tries each of his ships at four or even at five speeds; and the result is that he obtains fair data for a complete curve of indicated horse-power from the lowest to the highest speeds; whereas with trials on the ordinary system we obtain merely two spots in the curve, and these at comparatively high speeds, the intermediate or lower portion of the curve being left uninvestigated.

No doubt the limited view of the proper range of the enquiry to which the trials are intended to supply an answer arose from the belief that resistance must be as the square of the speed, and horse-power as its cube; and this belief, incorporated into one or other of the well-known "constants," has survived more or less persistently in spite of attacks and misgivings, and has constituted a self-supported obstruction to new ideas. It is also true however that M.M. trials even as at present limited are costly experiments, and notions of economy have assisted to damp the ardour of those who have been on other grounds willing to become innovators. But no expenditure ostensibly encountered in the search for truth is really so uneconomical as that which, while it seems to furnish information, helps to support error and in fact "darkeneth counsel by words without knowledge;" and it is to Mr. Denny's honour that finding the so-called constants were invariably variable and inconsistent, he determined of himself to strike out a new line and find out by trial what is fact, instead of contenting himself with assuming what ought to be the relation between indicated horse-power and speed.

*Received 18th March, 1876.

A very interesting Paper which he read in the Mechanical Section of the British Association at Bristol, illustrated by instructive diagrams which gave the results of trials conducted on his system, at once showed how fruitful a field of investigation he had opened up. And as he was on the point of trying a new ship from which he expected good results, he kindly promised to furnish me with her lines and with the report of the M.M. trials; and with the sanction of the Director of Naval Construction it was arranged that I should test the performance of a model of the ship with the Admiralty apparatus, so as at once to see what was the relation between the ship's nett resistance at all speeds and the power expended in overcoming it. The results of the investigation were unusually interesting and instructive.

On the one hand Mr. Denny's horse-power results when closely scrutinised were found at once to supply most important information on the subject of engine friction, and on the other they have helped to corroborate and further elucidate certain general conclusions on the subject of the expenditure of power in propulsion, which other less crucial tests had enabled me to arrive at approximately. The method of analysis to which I subjected the results is one which I have long adopted with advantage.

I have always felt that the system of reducing the results of steam trials to indicated horse-power, though no doubt furnishing a true expression in a commercial sense of the relative merits of the ship under trial, tended nevertheless to cloud the real significance of the record, viewed as suggestive of those specialities of form or condition which have really governed the ship's performance; not only because indicated horsepower includes in one large term the merits of the ship, the engine, and the propeller, but because the term into which it groups these items is complicated by the introduction of the speed factor, instead of representing them under their more elementary form of force simply. With this view, ever since I have entered into such investigations I have invariably converted the horse-power term to a force term by simply dividing it by a speed factor; and, as shaping the reduction into its most natural and apposite form, I have adopted as the divisor the speed of the propeller, expressed not by its revolutions nakedly but by its revolutions × its pitch-that is to say, the virtual travel of the force delivered by the propeller. The result thus obtained from the indicated horse-power I have termed “indicated thrust;" it is in fact the thrust which the propeller would be exerting if the force of the steam were employed wholly in creating thrust, instead of partly in overcoming friction, driving the air pump, and overcoming other collateral resistances. Indicated thrust is simply a constant multiple of the mean steam pressure on the piston; and if this were given in the records of the trials, indicated thrust is mean piston pressure X total piston travel per revolution; when however (as is commonly pitch of propeller

the case) the indicated horse-power alone is given, then the expression for indicated 33,000 X I.H.P. thrust is

pitch × revolutions.

When decomposed into its constituent parts indicated thrust is resolved into several elements, which must be enumerated and kept in view.

These elements are: 1, the useful thrust or ship's true resistance; 2, the augment of resistance, which, as I have pointed out in many previous Papers, is due to the diminution which the action of the propeller creates in the pressure of the water against the stern end of the ship; 3, the equivalent of the friction of the screw blades in their edgeway motion through the water; 4, the equivalent of the friction due to the dead weight of the working parts, piston packings and the like, which constitute the initial or slow-speed friction of the engine; 5, the equivalent of friction of the engines due to the working load; 6, the equivalent of air pump and feed-pump duty.

In

116000

T

-12 000

FIG. 1.

It is probable that 2, 3, and 4 of the above list are all very nearly proportional to the useful thrust; 6 is probably nearly proportional to the square of the number of revolutions, and thus at least at the lower speeds approximately to the useful thrust ; 5 probably remains constant at all speeds, and for convenience it may be regarded as constant though perhaps in strict truth it should be termed "initial friction." If then we could separate the quasi-constant friction from the indicated thrust throughout, the remainder would be approximately proportional to the ship's true resistance. point of fact, the means of performing this separation have been furnished by the conversion of Mr. Denny's indicated horsepower record into a curve of indicated thrust. The determinations of the initial friction of the Merkara, the Taupo, the Hawea, and of the Greyhound appear in Figs. 1 and 2 (pp. 169 and 170) and Fig. 3 (Plate IX.) But the circumstance by which the separability of the initial friction from the other forces makes itself apparent, and the method by which the separation may be effected, will be more readily understood by referring to the accompanying hypothetical sketches rather than to the finished diagrams,

INDICATED THRUST IN LBS

-8 000

-4000

6

8

SPEED IN KNOTS

12

Assume that the ordinates at a, b, c, d, and e, Fig. 1, represent to scale the several indicated thrusts referred to the appropriate speeds; then a fair curve drawn through

Ꮓ

FIG. 2.

zero,

these points constitutes what I have called the "thrust curve." Now, on drawing the curve with the data supplied by Mr. Denny's trials, it becomes at once manifest in but every case that at its low-speed end the curve refuses to descend to the thrust tends towards a point representing a considerable amount of thrust, and it is impossible to doubt that this apparent thrust at the zero of speed when there can be no real thrust is the equivalent of what I have termed initial friction; so that if we could determine correctly the point at which the curve, if prolonged to the speed zero, would intersect the axis O Y, Fig. 2, and if we were to draw a line through the intersection parallel to the base, the height which would be thus cut off from the thrust ordinates

would represent the deduction to be made from them in respect of constant or initial friction, and the remainders of the ordinates between this new base and the curve would, as has been explained, be approximately proportional to the ship's true resistance.

Now the data do supply us with the means of fixing this intersection with considerable exactness in the following manner:-The curve as fixed by the data terminates at some moderate speed, say 3, 4, or 5 knots. It is well known now, that with tolerably wellshaped ships of such dimensions as those we are dealing with, the resistance due to such moderate speeds as these consists almost solely of surface friction, which-as our experiments have shown-varies nearly as the power 1.87 of the speed, with perhaps a very small residue or excess of resistance, apparently proportional to the square of the speed; and as this residue is very small indeed, we may without serious error assume that the whole resistance below 3 or 4 knots is as the power 1.87 of the speed. Hence on this assumption the lower end of the thrust curve when divested of the constant friction equivalent should be a parabola in which the ordinate is as the power 1.87 of the abscissa; and since, as we have seen, the entire thrust exclusive of the initial friction is proportionate at least at the slow speeds to the true resistance curve, the problem to be solved is the very simple geometrical one of so drawing a parabola of this order in connexion with the axis of co-ordinates of the diagram, that it shall meet or join the existing thrust curve with an identical tangential direction. The construction by which this is effected is extremely simple: at the point p, Fig. 2, near the lower end of the thrust curve draw the tangent p'p"; draw the vertical at h' so as to cut the space Oh into segments having the ratio indicated by the figured quantities, thus making Oh = 1·87 O h'; draw a line parallel to OX through the point where this vertical cuts the tangent; the point where this line cuts the thrust axis is the vertex of the required curve.