BARROIV DYNANOMETRICAL
CURB.

(See Engiaving, front page.)

Almost every engineer who has applied the apparatus of Prony to measure the force of machinery, ha» found it extremely difficult, particularly with machines of great power, to keep it during the experiment in two horizontal position ; the irregularities produced by friction, cause it to jerk in a manner dangerous to the assistant, and also tend to vitiate the accuracy of the observation. Many mechanicians have attempted to obviate this serious inconvenience, by adapting a dynanometer to the extremity of the lever, instead of weights. M. Barrois justly considered, that in two machine of great power, it would be difficult to construct a dynanometrical instrument of equal truth and strength; and, having occasion to ascertain the power of an engine assumed to be equal to fifty horses, he employed the apparatus we Bre about to describe, which not only answered the purpose in every respect, but also spared the cost of a dynanometer. To the professional engineer, a cursory glance at the design will serve to show its mode of action; yet the number of processes that have been published on the power of machines, prove that the best method for measuring that force, is not distinctly developed; at all events, something is left to the judgment, where everything should be precise and definite. It is, therefore, with a view of diffusing the knowledge of these means among mechanicians imperfectly acquainted with mathemctical analysis, that we now insert a description, as well as the elementary theory of the simple, yet beautifully scientific apparatus, used by M. Barrois, and which he calls an Oblique Curb (F rein OUique).

In the engraving, a is a section of the revolving spindle of the machine, which receives motion from the prime-mover, whose force we wish to measure. This spindle is acted upon as directly as possible by the prime-mover.

A, B, are two strong pieces of wood, which may be tightened upon the neck a by means of screw-bolts, 4, 4; in these two pieces of wood, the semi-circular gaps c, c, are cut out, which encircle the neck, and are armed with collars of sheet-steel, to reduce the friction which is unavoidable. At the end of the longer piece B, the weights D are attached, and an index 7, which serves to mark upon the graduated quadrant VH. which is described upon a wall, the position which the curb is compelled to assume by the effect of friction.

It is clear, then, that if whilst the spindle a turns, we screw up the nuts 4, 4, the curb having remained a sufficient time, so that it cannot return to a horizontal position, will describe a certain angle, and support itself in an oblique position, such as is represented in the engraving. We will now examine how this position, and the velocity of the spindle, enable us to ascertain the force of the prime-mover. Previously to arranging the apparatus, it is necessary to weigh it with all its appurtenances, and this weight we designate by P (in kilogrammes) ; it is then hallanred upon an angular bar of iron, to find its centre of gravity; this we will suppose to be determined and indicated by G. We then measure, with great care, the distance G O, from the centre of gravity to the centre of rotation, and express by R, this length (in metres). This done, the curb is placed upon the spindle a, leaving it free in the first instance, so that the centre of gravity G, finds itself at G\ on the vertical line passing through the centre of rotation, and we adjust the index 7, in such a way that it points to V, the commencement of the graduated quadrant.

Suppose we have to measure the power of a steam-engine; in the first place, the engine is allowed to work during some time, the curb being restrained by a cord, and no observation made, so that the friction on the collars o, c, may be equalized; we then put it in gear, and, by means of the induction valve, let in the steam by degrees, until the ordinary rate of velocity is attained; we then screw up, little by little, the pins 4,4, at the same time that the volume of steam is increased through the induction valve. The friction causes the curb to retain an inclined position, and, when the induction valve is entirely opened, the engine has for some minutes a regular speed, in virtue of which, the piston travels about one metre every second of time. We now commence our observations in the following manner :—Whilst an assistant counts the number of turns that the spindle a, makes in each minute, another notes the angle indicated on the graduated quadrant by the index /. We now screw up the pins, b b, so that it may remain nearly at the same point; observing the corresponding angle of the mean of these small oscillations of the index, on the quadrant; this angle we shall designate a.

It is essential that the velocity of the machine be as nearly uniform as possible during the observation, otherwise we must take into consideration the force of inertia in the fly-wheel. The neglect of this precaution has, in many instances, entirely vitiated the whole proceeding, and given a much greater amount of power than the machine was capable of exerting; because the assistant who ordinarily attends to the screwing up of the pin* of the curb, takes care to do so at the moment when the machine attains a high velocity; this speed, then, gradually diminishes, and the force of inertia of the fly-wheel is added to that of the prime-mover, and thus pro duces oftentimes a greater effect than is due to the latter.

In the arrangement of M. Barrois, whenever the friction is accidentally increased, the curb rises, and produces the cross resistance in such a way that the equilibrium is soon restored; whenever the friction is reduced, the curb falls, and the equilibrium is similarly regaiued, and may, therefore, in almost every case, be considered equable. It is also worthy of remark, that the oscillations made by this dynanometrical curb are extremely small, and at an angle of 30°, are one-half less than when the curb was in a horizontal position, and for the time necessary to make the observation, the oscillations are scarcely appreciable. Indeed M. Barrois states, that he had easily kept his curb, during six minutes, at the same angle, when applied to an engine of fifty-horses power

According to the doctrine of the centre of gravity, this curb may be considered as having all its weight concentrated at one point G; from this point let us draw the vertical line (»#, which meets at g' the horizontal line drawn from the centre O, we may consider the friction upon the neck of the spindle, a, as operating upon an imaginary circle g' g', because the sum of the moments of all the friction remains the same, According to this supposition, this friction will be in the nature of forces tangential to the circumference 5' g'. which are capable of being united in one whole, equal to their sum, and directed according to the vertical Laii:t'iar/ G, Now since all the forces of the system may be reduced to two—viz, the resultants of the friction upon the imaginary circle g'g', and the weights of the entire apparatus—both subject to the same law, and both in equilibrium—they are equal, and directly opposed; and, therefore, since the friction in the one case depends upon the velocity given to g' g', —the friction upon the neck of the spindle o, will produce the same resisting effect, as if the machine ro»e by means of a cod, encircling the neck g' g , as upon an axis; to wit, a weight H, equal to that of the complete curb.

The quantity of action then produced by

the prime mover, in a certain time, is capable of raising the weight P, of the curb to a height equal to the space which would be passed over in the same time by the point g, if it were carried down by the movement of rotation of the axis O.

If we put a to represent the proportion of the circumference to the diameter, it is clear,

1. That Og = If .sin a;

2. That the circumference of the imaginary axis <i g' =i uj li. si n 11;

3. That 2 a R . v . sin a is the space which the point g passes through in a second, if it be carried down by the movement of the axis O

4. Thatg"'A^/>-8ina, expresses

CO

the number of kilogrammes which the machine is al lc to raise every second to the height of one metre—that is, without making any allowance for friction.

5. That as, according to the custom among engineers, we understand the power of one horse to be equal to 80 kilogrammes, raised one metre high in every second, the force given out by the primemover during the experiment, and transmitted to the spindle a a a, will be

THE SAFETY LAMP.

To the Editor of the Penny Mechanic and

Chemist. Sin,—Various are the suggestions which have, from time to time, been offered with a view to the improvement of the safetylamp of Sir Humphrey Davy; it having been found that, as originally proposed by that distinguished chemist, the lamp in question was open to some rather serious objections, one of the most prominent of which is, the extreme liability of the ironwire guage, which encircles the name, to become oxidized, or, popularly speaking, corroded, in which state, it is evident, the lamp can afford little or no protection to the miner; indeed many disastrous accidents have frequently arisen from the imprudent employment in mines of lamps in this deteriorated and insecure condition. As. then, the safety of the " Davy" is wholly dependent upon the integrity of the wire gauze, it has been considered advisable by Mr. Murray and many other scientific men, to dispense entirely with it, and, accordingly, that gentleman, in his improved lamp, has, in lieu of it, surrounded the flame with two concentric cylinders of glass, the space Between them being occupied by water. Messrs. Upton and Roberts have also followed a somewhat similar arrangement; but, for my own part, such is the confidence I entertain in the opinions advanced by Sir Humphrey with respect to the security of his lamp, that I am inclined to believe, if the rapid oxidation of the gauge could by any means be prevented, that the "Davy" would still be found by the miner one of the most valuable companions with which the discoveries of science have hitherto furnished him. With the view, then, of accomplishing the desirable object to which I have just referred—the protection of the gauge from oxidation—I beg to propose the following application of the electrotype—viz. the deposition upon the surface of a thin film or coating of platinum; the effect of such deposition being, first, to defend the gauge from the direct action of the humid atmosphere of the mine; thus, consequently, preventing all oxidation or corrosion; and, secondly, owing to the slowness with which platinum conducts heat, increasing, in some degree, the cooling influence which, according to the principle involved in the construction of Sir Humphrey's lamp, it is intended the gauge should exert upon the flame. And here it may be as well to observe, that the process above alluded to, which Mr. Smee appropriately terms platinating, is effected by employing a weak solution of the nitromuriate of platinum; the object to be coated—the gauge, for instance—after having been well cleaned with a feeble solution of potash, being connected with the zinc end of the battery, a platinum wire having been previously brought into connexion with the opposite extremity, the latter wire must, however, be only just immersed in the solution. The operation, when all these particulars are duly attend

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ed to, being completed in the course of a few minutes Mr. Smee recommended, moreover, "that the object should, from time to time, be withdrawn from the fluid, and rubbed over with two little whiting." (See " Elements of Electro-Metallurgy," by A. Smee, p. 94.)

It is evident that a coating of silver might, in a similar manner, be deposited upon the gauge; but platinum, on account of its extreme indestructibility, as well, too, as being a much less perfect conductor of caloric than silver, is certainly entitled to the preference. Electro-gilding might, however, be resorted to with advantage for infilming the gauge, although, I do not think, it would be found so durable ai platinating for this purpose.

In conclusion, it may not, perhaps, be inappropriate to observe, that the safetylamp of Davy might not only be preserved, but even a gauge suitable to it be made, by the aid of galvanic electricity; all that would be requisite with that view, being to select a piece of fine canvass or some similar fabric, and, after preparing it in the usual manner with plumbago, to precipitate upon it, by means of the battery, a copious covering from the sulphate, nitrate, or some other salt of copper.

Hoping that the above few hints, should they receive a practical application, may prove serviceable to that numerous and useful body of our countrymen, the miners, I have the honour to remain,

Your most obedient servant,

W. H. 0.

THE ELEMENTARY PRINCIPLES OF MECHANISM.

(Continued from page 180.) 35. To find the Velocity Ratio in Wrapping Connexions, —Let A and B, fig- l"' be the centres of motion, P Q the wrapping connector, touching the curves at P and Q, and let the point P be moved to p,

10.

ly. But, in the process of wrapping and unwrapping, the connector touches the curves in a series of consecutive points between q and S. or p and r, and, ultimately, q coincides with S, and p with r. So that the extremities of the connector may be considered, at any given moment, as if jointed to the two curves at the points of contact, and turning upon these points in the manner of a link. The relative velocities of the curves are, therefore, momentarily the same as if A P, B Q, were a pair of rods connected by a link P Q. Hence we infer that the angular velocities of the pieces are to each offer inversely as the segments into which the connector divides the line of centres.

M. If the line of direction of the link, in link-work; of the common normal to the curves in contact motion; and of the connector in wrapping motion, be severally termed the line of action, we can express the separate propositions which relate to the Velocity Ratio, by saying that the angular velocities of the two pieces are to each other inversely as the segments into which the line of action divides the line of centres, or inversely as the perpendiculars from the centres of motion upon the line of action.

The reader must bear in mind, that these investigations are, for the present, confined to motions in the same plane. Those cases in which the motions are in different planes, are more easily examined as the individual combinations which require them occur.

37. We have shown that the principal pieces which constitute a train of mechanism, are compelled to move each in a given path. For, all general purposes, this path may be considered as a circle, as, in fact, the pieces always either revolve or move in right lines; and the contrivances by which motion is communicated in a rectilinear path, are precisely the same as those by which it is given to a revolving piece, which, indeed, is sufficiently obvious, if we refer to the geometrical artifice, which considers a right line as the arc of a circle whose radius is infinite. By this means much complication is avoided—as, for example, a pinion driving a rack, is plainly the same contrivance as a pinion driving a toothed wheel, the rack being considered as a portion of a toothed wheel, whose radius is infinite.

It is true, that pieces in a train may be found which describe other paths—such as elliptical, epicycloidal, or sinuous lines; but, it must be remembered, that these are invariably produced, by a combination of various circular motions, consequently,

the motion of the piece is actually produced by pieces that travel in circular paths. Cases of this description come under the head of Aggregate Motions ; the consideration of which, as already stated, is deferred to a future opportunity.

33. The path of a revolving piece may be considered as unlimited in extent and in either direction. But a piece that travels in a right line is necessarily limited in its motion in either direction, to the length of that line.

It is clear that the method by which motion is communicated from one piece to another, may be of such a nature as to limit the motion of those pieces, although, considered apart from the connexion, they may be susceptible of unlimited motion. Thus, suppose the driver and follower to be a pair of revolving cylinders, and, therefore, capable of unlimited motion, now if the communication of motion be effected by a cord, whose extremities are attached one to each cylinder, and coiled round it, so that when the driver revolves it shall give motion to the follower, by winding the cord round its surface, and unwinding it from that of the follower, we see that the rotations of either cylinder are limited to the number of coils which its circumference contains, when that of the other is empty.

Thus it appears, that the motion of a pair of connected pieces, may be limited either by the figure of one or both of their paths, or by the nature of their connexion; and a limited connexion may be formed between unlimited paths, or vice versa; but if either the paths or the connexion he limited, then the motion of the pieces will be likewise limited.*

COMMUNICATION OF MOTION BY ROLLING CONTACT.

{Directional Relation, and Velocity Ratio constant.)

39. In rolling contact, we have seen that the point of contact is always in the line of centres; and that the angular velocities are inversely as the segments into which the point of contact divides that line. Consequently, if the velocity ratio be constant, the segments must also

* In classifying the communication of motion, the distinction between limited and unlimited methods of communication is of considerable importance; not so. however, the union of unlimited connexions with limited paths, which require but little attention, as the modifications to which they lead, are, in general, sufficiently obvious.