It will be obvious from these data that the resistance per square foot of midship section varies materially with the size of the vessel. The "Dwarf" and the "Rattler" have both about the same speed, but the "Dwarf" requires 4.9 horse-power per square foot of midship section to maintain this speed, whereas the "Rattler" only requires 1:56 horse-power. The "Fairy" and the "Himalaya" in like manner have nearly the same speed, but while the "Fairy" requires 5 horsepower per square foot of immersed section, the "Himalaya" only requires 36 horse-power per square foot of immersed section. The whole of these vessels are sharp vessels of good form, and the difference of resistance per square foot of section in the different cases shows that the co-efficient must vary, not only with the shape of the vessel, but also with the size.

When a vessel is propelled through the water at any considerable rate of speed, a film of water will be carried with it in the same manner that a film of water is carried round by a grindstone. To urge this water into motion, however, requires both power and time. At the very bow of the vessel the water which is encountered being in a state of rest, resists any sudden communication of motion by virtue of its inertia, and the consequence is that the vessel has to slide past this water, in which act much more power is consumed than if the water were put into motion by degrees. The water will naturally be moved in such a manner as to make the resistance a minimum, unless such motion is prevented by injudicious arrangements, and when a solid surface is moved through water, it may either move past the particles of water in the same manner as if it encountered a solid body, or it may move the contiguous particles of water with it, those particles in their turn moving others more remote with a slower velocity, so that there will be a number of films moving in the direction of the surface, of which that in contact with it will move with nearly the same velocity, and each succeeding film will move with a less velocity until that point is reached where the water is not moved at all. Now water which is moved in this manner requires much less power to move it than when the surface is compelled to rub upon the particles of water without being enabled to impart motion to them-as happens when the vessel gets into shallow water, or when from any cause the adhering film of water is rubbed off. The inertia of the water, however, when the bow first encounters it, prevents it from acquiring suddenly the motion of the vessel, and the water near the bow is therefore constrained to rub over the surface as a solid body would do, until by degrees it is enabled to acquire the motion of the vessel. The water thus put into motion is dismissed at the stern with the velocity it has acquired, carrying power with it, so that power is lost both by the necessity of moving the water without being able again to bring it to a state of quiescence, and also by the particular mode in which the motion is communicated, which is much as if one surface im

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pelling another by contact slipped through a great part of its course. A good deal of the power expended in communicating motion to the water will, in the case of screw vessels, be recovered if judicious proportions are employed. For as the friction of the vessel through the water causes a current of water to follow the vessel, and as the slip of the screw puts a column of water into motion in the opposite direction, these two forces may, by suitable arrangements, be made to balance one another so that the water at the stern of the vessel shall have no motion relatively with the water around it, but shall be left in the same state of quiescence with which it was at first encountered.

The difficulty of imparting motion to water increases with the height of the column above the point where the motion is produced. In a deep screw there will therefore be less slip than in a superficial screw. The water to which motion is given will always escape in the direction of least resistance, which is to the surface; and the length of the column of water to be moved will obviously depend upon the height of the surface above the point where the motion is imparted. Now in the case of water moved by friction, precisely the same action will take place as if it were moved by any other agency, and therefore the amount of power requisite for giving motion to the water encountered by the bottom of a vessel will vary somewhat with the depth of the immersion.

It appears from these considerations, that the resistance of a sharp vessel will increase-1st, as the wetted perimeter, or outline of the immersed section, as in the case of pipes and canals; 2nd, as the square of the velocity nearly, but in a less proportion than this in the case of high speeds; 3rd, as the length up to the point at which the velocity of the adhering film equals the velocity of the vessel, but after that point the length will not add proportionately to the resistance; 4th, as the depth of the immersion.

A diagram is given in Plate II., showing the rate at which the resistance of vessels increases with the velocity, and with the immersed midship section. This diagram was constructed by Messrs. Boulton and Watt about 1818, but has been extended by us so as to comprehend the dimensions of steam vessels at present in use. The figures along the top and bottom of the plate represent the number of square feet of immersed midship section of the vessel, and the figures in the vertical sides of the plate represent the speeds in miles per hour, while the diagonal lines represent the power in horses required to attain a given speed with a given section. If the space between 0 and 1 in the scale of speed in miles be made equal to a, and the number of any two consecutive divisions be respectively m and n, then n being always equal to m+1, any other space r which may be required to be found can be found by the following equation:

The efflux of air from vessels, and its flow through tubes, are governed by the same laws which apply in the case of water. When air escapes through an orifice in a thin plate, the effective diameter of the orifice is reduced, as in the case of water, by the action of the contracted vein; and when air passes through pipes, its velocity is diminished, as in the case of water, by the friction it suffers against the sides of the pipe. It appears from Koch's experiments, that with pressures of th to th of an atmosphere the actual discharge of air through an orifice in a thin plate is 0.58 of the theoretical discharge; but if a nozzle, like that of a bellows, is added, the actual discharge rises to 0.85 of the theoretical discharge. The theoretical velocity of air may easily be determined by finding the height of a column of air which would produce the pressure, and the velocity which a heavy body would acquire by falling from that height.

If H= the head of air necessary to overcome the friction of a pipe, the length of the pipe in feed, D the diameter of the pipe in feet, and V the velocity in feet per second:

V2 Then H024. X D 644.

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RESISTANCE OF RAILWAY TRAINS.

The resistance of railway trains at high speeds is partly made up of the back pressure caused by the blast pipe, of the concussions incident to the unevenness of the road, and of the wave of motion communicated to the earth, and partly of the resistance to high velocities offered by the atmosphere. So far as this last source of resistance is concerned, there is every reason to believe that it resembles the resistance which vessels experience in passing through water, and the considerations applicable to the one case are applicable to the other. A train moving with a high velocity carries a stratum of air with it, the thickness of which varies with the speed. This stratum usually reaches to the ground; and it sucks up the dust, and delivers it into the carriages to an inconvenient extent. This action is just the same as that which occurs when a vessel gets into shallow water; and it would diminish the resistance of railway trains if the carriages were to be set so high that the enveloping stratum of air did not rub upon the ground.

Mr. Bidder reckons the atmospheric resistance opposed to trains travelling at a rate of 30 miles an hour at 12 lbs. per ton, and he considers that the resistance increases at speeds above this rate, and decreases at speeds below this rate, as the square of the velocity. The experiments of Dr. Lardner first showed that the atmospheric resistance was an important element in the computation of the velocity which a railway train will achieve with a given amount of power. But although the total resistance varies nearly as the square of the velocity on rough lines, it is found on smooth lines to vary more nearly as the simple velocity.

A protracted controversy was at one time maintained between the respective advocates of the broad and narrow gauges as to the amount of atmospheric resistance experienced by the carriages of each gauge, from the different amounts of frontage they presented to the atmosphere. There seems no reason to doubt, however, that the wide train will present more resistance than the narrow train, just as a wide vessel would present more resistance than a narrow one in the water; and the first carriages of the train will experience more resistance than the last carriages, as the last carriages will come into the cylinder of air which the first carriages have put in motion.

The formula commonly accepted for determining the resistance of railway trains, and which is called the narrow gauge formula, was constructed by Mr. Scott Russell, from data furnished by Mr. Wyndham Harding, and is as follows:- Calling the frictions experienced by the train 6 lbs. per ton, and the resistance experienced by one square foot of frontage at one mile per hour, 0025 lbs., and T being the weight of the train in tons, V the velocity in miles per hour, N the number of square feet of frontage, and the resistance from concussions in lbs. per ton of the load at ten miles an hour and V over being taken equal to, then R being the resistance in lbs. per ton of the weight of the train,

Mr. Gooch made a number of experiments upon the Great Western Railway, the result of which goes to show that the resistance upon that line is less than what is given by Mr. Harding's formula; and if these experiments are to be accepted as conclusive, the natural inference is that Mr. Harding's formula represents the resistance as too great, since it cannot be doubted that the total resistance on the broad gauge will be somewhat greater than the total resistance on the narrow gauge with the same smoothness of rails.

The main conclusions of Mr. Gooch's experiments are shown graphically in Plate III., which contains diagrams indicative of the law of increased resistance with the speed, both according to Mr. Wyndham Harding's formula, and according to the experiments performed upon the Great Western Railway; and dynamometer diagrams are also introduced, showing the tractive force exerted at different rates of speed. The differences in the amount of tractive force at different times with the same velocity are mainly owing to the action of the wind.

ON BALANCING THE MOMENTUM OF ENGINES.

In all reciprocating engines the piston, piston-rod, and connectingrod, have to be brought to a state of rest at the end of the stroke, and to be urged again into motion at the beginning of the stroke. It is obvious, however, that in the case of large masses of matter in rapid motion, which have rapidly to be brought to a state of rest, and where consequently the whole momentum of the moving mass has to be rapidly surrendered, a larger thrust must at those times be communicated to the crank pin than what is due to the pressure of the steam, and the pressure against the end of the cylinder and the pressure against the crank pin will no longer balance one another, since the latter is increased by the amount of the thrust or pressure due to the arrested momentum. Now, since locomotive engines are constructed with two horizontal cylinders each operating at some distance from the central vertical plane of the machine, it follows that the thrust upon the crank pin at high speeds being different in amount from the thrust upon the end of the cylinder, induces a sinuous motion of the machine upon the rails, which may become so great as to be both injurious and dangerous. In consequence of this inconvenience, contrivances have been employed to balance locomotives in such a manner as to enable them to run steadily on the rails. The first movement in this direction appears to have been made by Mr. Heaton of Birmingham, who proposed to give steadiness to locomotives by attaching a revolving weight to the driving wheels. Braithwaite and Fernihough followed in the same direction, and subsequently Nollau and Le Chatelier, the latter of whom, in 1849, published a dissertation on the subject, entitled "Etude sur la Stabilité des Machines Locomotives en Mouvement." In some of the experiments made to determine the best arrangements for conferring steadiness, the locomotive was suspended by ropes or chains, and such an adjustment of the revolving weights was effected as would enable the engine to work without swinging about in any degree. The object of the whole of these measures of improvement, however, had reference not to the more smooth or efficient working of the