We now most unequivocally assert, that the remarks in question were written by the editor without any consultation, advice, or instigation from any person, that they were the result of his own convictions upon first reading the communication of Mr. Ward, and were seen by no one, save by his partner, the printer of the Journal, until printed.

We may likewise state, that the remarks by "an Engineer," in the last number of the Journal, (not yet published, when the above communication was received,) were written before our own notice could have been seen by the writer-before we had either seen him or spoken with him on the subject, and we were ourselves surprised with the coincidence of our viewsin several instances having turned to the same authority, in confirmation of our respective opinions.

This much being premised we proceed to notice the several objections taken to our criticisms. In the first instance, it will be seen, that the difficulty lies in the different value given to the estimated horse power. What we mean to assert is this, that the horse power estimated from the size of the cylinders, etc., is not in all cases the expression for the real and effective power of the engine, and that particularly where high velocities are aimed at, the consumption of fuel is far beyond that of the engine working at the highest useful velocity. In other words, and to illustrate our meaning the better, we mean to say, that of two boats precisely equal in all respects, the one obtaining the highest possible speed, will burn more fuel, in travelling a given distance, than the one travelling at a certain rate beneath that of the first. Is it not a well known fact, that in racing at the top of their speed, our steamboats consume more fuel than when going the same distance at their ordinary velocity?

We had considered this fact to be universally conceded, and it was to this we referred, when pointing out what to us seemed a deficiency in Mr. Ward's table. We conceive that a fair comparison cannot be made between the estimated horse power of the Great Western, etc., working at the most economical velocity, and that of our North river boats, working beyond the most economical velocity, and burning cords of wood to gain an extra mile per hour.

If authority in this case is needed, we refer to the experiments of Pambour, in which an engine working its maximum at a fixed pressure, (or nearly so,) uniformly decreased its velocity in inverse proportion to the increase of load, caused by a greater amount of ascent in the road. Pambour also adds a caution, that the velocity, among other things, be taken into account, in estimating the horse power of locomotive or any other sort of engines. In view of this very case, Mr. Stephenson estimates the horse power of one of the very boats named in the table in question, so high as to give quite a different result in the economy of fuel. (See the article in the last number of the Journal.)

It will therefore be granted, that if this is a correct view of the matter, the speed size and form of the vessels, are, one or all of them necessary el

ements in such a table. And that this is a correct view, we can hardly conceive will be questioned by any one.

In the next place Mr. W. admits the economy of working steam expansively, and disclaims any intention of doubting it, but adds, "that all its advantages may be obtained without resorting to the dangerous pressure of 57 pounds per square inch, or even venturing into the neighborhood." It will be found, by a careful examination of the authorities brought forward in our remarks, that the best effect, in point of economy, was found to result from using steam, certainly not far from a pressure of 57 pounds, if not in its immediate neighborhood. It is unnecessary to particularize, but it will be found that the pressure named varies from 45 or thereabouts, to 50 or more lbs. per square inch. The very nature of the laws of steam will point out the greatest economy to be derived from the use of steam of high pressure, the limit, of course to be dependent upon the strength of the boiler.

It appears that our criticism of the writer's misinterpretation of the word "mere," as used by Prof. Renwick, were unintelligible. We must confess that we did not render the matter more clear, by attempting to explain what was clearly self-evident. We meant to say, that the word mere was wrongly translated, and by a substitution of other words than those used in the passage quoted, to show that such interpretation, involved an absurdity.

As to the opinions of practical and well informed men, we have only to say, that we quoted such authority as we could find-papers sanctioned by the Institution of Civil Engineers-the appendix to a memorial signed by nearly all the gentlemen concerned in steaming on our waters. This, however, is matter of opinion, and every one has a right to his own; we wish, however, such a consideration of the facts in question, as shall bring about, at least an approximation of opinion, and we feel convinced that there must be some misapprehension in the mind of the writer of the foregoing communication, which has led him into an untenable position.

As we have said before, our sole object, is to get at the truth, and we have therefore devoted more time to the explanation of our remarks, in the hope that misapprehension may be removed, and the subject in dispute narrowed down to the true point in question.

To the Editors of the American Railroad Journal and Mechanics' Magazine.

GENTLEMEN :-I observe that three of your correspondents, have lately assumed positions respecting the crank, that if proved, would annihilate the whole theory of mechanics, and lead directly to a perpetual motion.

The first gentleman, vol. x, page 161, argues that when the power acts in parallel lines, 0-2146 of the power is lost by the use of the crank.

The second, vol. x, page 205, shows by a numerical calculation that this is not exactly correct, but that when we use a connecting rod "there is necessarily some loss, to obviate which, the connecting rod is made as long as possible."

The third, vol. x, page 241, says, that "the force in passing from its primitive direction, to its final direction in the tangent to the rotary circle of the crank must evidently lose two proportions," etc.

Now, there can be no expense where there is no motion. We may raise a weight by any of the mechanical agents, and the weight multiplied by its velocity, will at all times equal the power applied, multiplied by its velocity.

When the active power ceases, there is no more expense of power, however great may be the inert force that is required to retain the weight in its position.

Thus, in the crank, and in the combination of the crank and connecting rod, there is an inert resistance required of the guides and of the centre of the crank motion; but as these remain fixed, with respect to the rest of the machine, they cause no expense of power, but merely enable the power to be diverted from its original direction to that in the direction of the tangent. Consequently, the whole expense, (except friction) is caused by the direct resistance of the pin, multiplied by the distance through which it acts. This being the total effect, if it be less than the power expended, we may gain by reversing the action, and converting a circular into a rectilinear motion, and consequently construct a perpetual motion.

But since this " reductio ad absurdum" rests upon the basis, that a perpetual motion is a mechanical impossibility. And since this assumption may be denied, and the solution therefore rendered unsatisfactory, we will take a positive demonstration.

In the first case, where the power acts in parallel lines, we have precisely the condition of gravity causing the descent of a heavy body on a curved inclined plane. Here it has been generally conceded that no power is lost. But since this has also been disputed, we take another more conclusive mode of investigation.

Let P the original power, f=the force in the direction of the tangent, V the velocity of P when v=the velocity of f, and c=the angle included between the crank and the direction of P.

Take the first case where the power acts parallel.

PV=fv. But P V is the expense of power, and ƒ the effect, therefore we see that there is no loss.

Again, with the connecting rod as usually applied. Let d the angle of departure of the rod from the line of the original direction of the power, p=the force in the direction of the rod. Then, by the resolution of forces, we get p=Px sec. d=the force in the direction of the rod, and by resolving p, we get a force=P acting on the pin parallel to the original direction.

Since, then, it is both equal and parallel, we find that the rod merely transfers the power from the coupling box to the crank pin, without

loss, and we may there compound or resolve it in the same manner as if immediately applied at the pin; in which case, we have already seen that there is no loss of power. Therefore, there is no loss of power, either from the circular motion of the crank, or the diagonal action of the connecting rod.

Having thus reviewed the remarks of these gentlemen, I will present for their investigation the following formula, to suit all conditions of crank and connecting rod.

f=Px sec. dx sin. (cd)

The positive sign belongs to the 1st and 4th, and the negative sign, to the 2d and 3d quadrants.

E

Demonstration. Let C be the centre of the crank, P the position of the pin, and B the position of the coupling box. PE a tangent to the circle described by the pin, touching at P, and crossing BC the line of the diréction of the power, at D. BE perpendicular to PE, and P A perpendicular to BC. (The pin P being in the first or fourth quadrant.) Then if B A represent the power, B P will represent the force in the direction of the rod, and B P being resolved, gives E P in the direction of the tangent =f. Therefore, the power B A produces the force EP.

PC and BE are both at right angles to PE, and therefore parallel to each other, consequently

DBE PCA=c, BPE=DBE+DB P=c+d, calling B A radius, we have B P=secant d, consequently, the force B P= PX secant d.

When B P radius, then E P=f=sin (c+d) therefore,

Rad. Px sec. d:: sin. (c+d) : f=Px sec. d× sin. (c+d).

:

We have, thus, the first part of our formula, or that part for the first and fourth quadrants.

For the opposite semi-circle, use the same letters accented, to signify the same relative points.

Then, because E' B' and C P' are parallel, the angle E' B' A'=P′ C A', therefore E' B' P' P' CA-P'B'A'= (cd).

Then as in the former case, calling B' A'=radius, we get B' P' secant d, and when B' P'= radius then E' P'=f=sin. (c—d). Therefore,

Rad. Px sec. d:: sin. (c—d): f=Px sec, d× sin. (c—d). This gives us the second part of our formula, or that for the semi-circle opposite the power, and by combining the two, we get,

f=Px sec. dx sin. (c±d). Q. E. D.

Carollary I-If the length of the connecting rod be infinitely great, the power acts in parallel lines, the angle d becomes 0, and consequently when c is the same in each quadrant, ƒ is also the same, and therefore each quadrant receives an equal amount of force.

Corollary II-When the length of the rod is infinitely great, then f becomes a maximum when sin. c becomes a maximum=sin. 90°

=1, we have then f=Px1x1=P.

radius

Corollary III-When the length of the connecting rod is a maximum, equal the length of the crank, then c=d, and the formula becomes f=Px sec, cx sin. (cc). Hence, in the second semi-circle f=PX sec. cx sin. 0=0. Therefore no power is communicated during the second semi-circle, and consequently the intensity of the force during the revolution through the first semi-circle, is doubled by the connecting rod, and at the same time the piston moves through the diameter of the crank motion.

Corollary IV. The longer the connecting rod the more uniform will be the force, for the longer the rod the less the angle d, and consequently the less the force subtracted from the second semi-circle, and added to the first.

Corollary V-Since the effect is equal to the expense of power, we have under all these conditions v⇒

V P

f

Friction.--In all these cases, we have supposed a perfect machine, working without friction, and found that we neither lose power by the circular motion of the crank, nor yet by the diagonal action of the connecting rod. But when we introduce friction, the question assumes quite a different appearance, and we here discover the reason why the connecting rod should be made as long as the machine will admit, for the purpose of reducing the loss of power by friction. B A being the direction and intensity of the power, AP is the force with which the coupling box rubs against the guide. When the power acts in parallel lines, this loss does not occur, but when the rod is short it becomes very serious. AP being the tangent to the angle d, if the rod be a minimum the friction will become almost infinite as the box approaches the centre. Besides, during one revolution, this friction acts through twice the diameter of the crank circle, while the friction on the pin when the power is parallel, is not only less, but acts only through the circumference of the pin.

Again, the force B P being the secant of d, is always greater, than BA the radius, except at the dead points, and increases to infinity or nearly so, when the rod is a minimum.