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would pass over 18 inches of the lower rail without touching it, describing in its fall a parabola modified by the effect of the springs on the engine.
This has been put to the test of experience by bending a rail nearly half an inch, and then painting it. An engine and train of carriages were then run over it, none of the wheels of which touched the paint for 22 inches. This affects a railway in three ways. First, when the engine has to fall, through a bad joint, the rail which it leaves being higher than the rail it is coming upon, the increased momentum from the fall will here occasion a larger deflection than ordinary, and a consequent inclined plane against the engine, from the time it comes on the rail till it passes the next chair. Secondly, when a rail is permanently bent, where the resistance on the second or rising part of the rail will be less than in the first case. And thirdly, when the rail is simply deflected by the weight of the engine, and restores itself to its original level when that weight has passed; here the effect will be least of all, the rail taking the form of a receding wave before the wheel and a following wave after it.
In the second case, where the rail is permanently bent, the formula for the space the engine would fall will be
where H is the height of the plane, and L its length, s and t being as before. For instance, if the bend is 1 of an inch in a 3 foot rail, we have
and s= 193
00125 of an inch, at 30 miles an hour,
00278 of an inch at 20 miles an hour, or to
of an inch at 20, and of an inch, at 30 miles an hour, would be descended by the engine by the effect of gravity, in the same time that steam and gravity together take it along 18 inches of the rail.
Let us next suppose we have steam enough to carry the engine along at a velocity so great, that gravity will not bring it down the 1 of an inch perpendicular, whilst steam carries it along the 18 inches horizontal, we shall find this velocity to be at and above 44 miles an hour, for it takes of a second for a body to fall one-tenth of an inch by the effect of gravity, and": 18 in. =3600": 44 miles; hence at 44 miles an hour, and at all velocities above it, the engine, after arriving on the rail, bent one-tenth of an inch in the middle, and forming two planes, will no longer touch the rail till after it has passed the middle of it, and velocities of 60 miles an hour have been attained.
(To be continued.)
ERIE CANAL ENLARGEMENT.-A series of articles on this subject, have been lately published in the Railroad Journal, under the signature of Fulton, which appear to us to be both timely and appropriate. Other numbers are yet to follow. The writer calculates the whole cost of the enlargement, including damage and loss of interest, at $40,000,000!! He shows from the annual Reports of the Comptroller, that in consequence of the gradual destruction of the forests in the neighborhood of the canals, the down tonnage has fallen off within the last five years to the extent of 140,000 tons, will not, for a long time to come, be made up by the increase of agricultural products; that even double locks are not now wanted; and that any enlargement beyond adding 12 or 18 inches to the banks, will be money thrown He complains of the impolicy and injustice of making private enterprise, as developed in railways along the line of the canal, tributary to the State, as a means of defraying the interest on the enlargement. He re
buts the doctrine heretofore maintained by some, that the effect of the enlargement will be to reduce transportation 50 per cent. Persons interested in the subject, as every citizen of the State is, either directly or indirectly, will do well to refer to the articles themselves. We perceive, as yet, no decisive movement in the Legislature, having for its object to arrest the enormous expenditure which is being entailed upon us. The subject will be thoroughly scanned by posterity-of that be assured. Forty million dollars, or twenty millions, if such a debt is incurred for the proposed enlargement, will be an incubus upon our credit and resources, which it will not be easy to shake off-Jour. of Commerce.
LOCOMOTIVE ENGINES.-The statement of the performance of the Locomotive Engine "Minerva," on the Philadelphia and Reading railroad which we take from the United States Gazette, will be found interesting and useful on account of the business like manner in which it is prepared.
More of the Philadelphia Engines-We have great pleasure in presenting our readers with the subjoined statement of the performance of the Minerva" Locomotive Engine, built by William Norris, Philadelphia, on the Philadelphia and Reading Railroad, with a train of 85 loaded cars, January 15, 1840.
Between Reading &
Pottstown, 54 2271 1 322 0.4 17.5 113.8 6.5 4.3 5.1 Wood
Phoenixville 62 261|0 56 329 0.65 13.0 40.2 3.1 2.5 7.4 do. do. do. Phoenixville
& inc. plane, 85 3502 47 886 1.14 24.0 59.5 2.5 9.1 15.3 Wood green Total, 4 44 1537 2.19 54 5213.5 3.92
Two quarts of oil only were used by the Engine and Tender in the trip, including oiling before starting. Nett weight of freight 216-3 tons gross weight, 350 tons or 784,000 lbs.
In the above statement the tons mentioned are gross of 2240 lbs.
Weather clear and cold, rails in good order.
Weight of engine, empty,
With water to second cock,
With water, fuel, and two men,
On four driving wheels,
On driving wheels, with water and fuel,
On driving wheels, with water, fuel and two men, or in run
Her tender holds 504 gallons water.
23,040 lbs. 25,730
The engine started the train of 85 cars three times on a level; and on one occasion in a curve of 955 feet radius, without any straining or difficulty, and at various times attained a speed of 14 miles per hour through some curves of the above radius on a level.
The quantity of steam generated, when common dry oak wood was used was more than sufficient to supply her cylinders; and from the surplus quantity which escaped from the safety valve, I have no doubt she could
have taken 20 more loaded cars, or 90 tons, had they been ready, and without any injury to her machinery. Signed, G. A. NICOLLS. Superintendant Transportation Phila. and Reading Railroad. Reading, Pa. January 18, 1840.
For the American Railroad Journal, and Mechanics' Magazine. METEOROLOGICAL RECORD FOR THE MONTHS OF NOV. and DEC., 1839. Kept on Red River, below Alexandria, La., (Lat. 31.10 N., Long., 91.59 W)
DESTRUCTION OF WOODEN BRIDGES BY ICE.-SUSPENSION BRIDGES.
The breaking up of the winter has caused a recurrence of a specie of accident which is far from being rare. We allude to the destruction of bridges by the combined force of a swollen stream and immense masses of ice. The liability to this kind of accident depends more upon the character of the stream nearer its source than at the location of the bridge itself. A river of any considerable size receiving the drainage of a large track of country, is of course apt to be speedily swollen by a sudden and heavy fall of rain or rapid thaw, and as one or the other of these circumstances are sure to accompany the breaking up of the ice, such streams must present locations badly adapted to ordinary wooden bridges. Shallow streams, from daming up the ice, are rather worse than others in this respect, yet they are the most frequently crossed by these insecure structures.
Bridges of a more durable construction, if not built in the most substantial manner, are likely to suffer from the same cause, if the water way has been too much diminished..
The proper substitute in such localities are suspension bridges of iron wire. These claim the preference of all others, whether we regard to economy of first cost, or their superior adaptation to the circumstances of the locality. Over a large portion of our country the character of the streams is altogether more favorable to this than any other specie of structure. The example of the new bridge at Fair Mount will, we hope, speedily be followed in many places.
For the American Railroad Journal and Mechanics' Magazine. THEORY OF THE CRANK, WITH REFERENCE TO DE PAMBOUR'S MODE OF CALCULATING THE PROPELLING POWER OF A LOCOMOTIVE ENGINE. BY JOHN A. ROEBLING, C. E.
The question, "Is the change of a straight motion in toa rotary motion, attended with any loss of useful power or not?" has been the subject of va
rious discussions among mathematicians, and has never been, to my knowledge, satisfactorily settled.
The Crank, by which that change of motion is effected, forms, in the present state of mechanics, a most conspicuous part of machinery, and the nature of its action should therefore be well understood.
The following demonstration, which the writer respectfully offers to the public, will prove, that if the amount of power actually expended is represented by 1, the application of the crank occasions a loss of useful effect equal to the expression, (« signifying the ratio of the circumference of the circle,)
and, it is believed, that the principle of the crank may now be considered as fully established.
Let the above diagram, a c b, represent a crank, moving around the fixed shaft c, in the direction from a to b, and let the power applied be represented by the solid frame e a d f, moving in a straight course, corresponding to the direction e c g.
When the frame or the power is pressing against the crank at a, which point is commonly called the dead point, it is obvious, that the whole pressure is transferred to the centre of the shaft, c. The centre, being an immoveable point, will press with the same force back; therefore, the crank at a, will remain at rest, and will have no tendency whatever to move the shaft around the centre.
On the other hand, when the crank is at b, then the direction of the power will be vertical to the crank, and will press in the direction of a tangent; therefore, the full pressure is usefully applied at b, and no part of it is transferred to the centre.
Let us presume that the motive power is applied steadily and uniformly, moving the same distance, in the same space of time, and in the same direction.
As the full pressure acts at b, in the direction of a tangent, its effect with respect to the centre of motion will be as the radius bc, or, as the length of the crank; and if we represent the motive power by 1, then
1. The effect of the crank or its momentum at b, will be R, the radius of the quadrant.