MR. IBBETSON'S GEOMETRIC CHUCK. Child for this 'offer; but if he will take the trouble to compare his curves with the specimens I have given of mine,-recollecting the fact that I had already copied two,—he cannot, I think, consider me illiberal in observing, that if his offer was not superfluous, it was, at least, uncalled for. Besides, Mr. Child should have considered that he had to redeem the character of his own instrument, before he proposed to me to prove the further powers of mine. Whether I can or cannot copy these other curves must remain to be proved; as I have not, for some time past, possessed a chuck, to enable me to make the trial, having disposed of the only one I had in a finished state. The moment I have one, I will furnish your pages with the result of my attempt. Admitting, however, that they should completely pose me, I nevertheless most unequivocally decline his offer; and I am decided not to allow myself to become acquainted, in any way whatever, with the mechanism of his apparatus. I do not say this in any bad feeling, or with the least intention to underrate the merit of Mr. Child's exertions: I say it, because the geometric chuck is, at present, all my own, and that I am firmly determined not to blend it with the unpublished contrivances of any other person. If Mr. Child's model was before the public, and I saw any principle in it that was new to me, and was pleased with the effect, I might, possibly, avail myself of it; avowing, at the same time, that I did so. I am at present, however, quite content to go on in my own way, and to leave Mr. Child to go on in his; and I certainly should never have thought it necessary to have said anything concerning his model, had he not addressed me on the subject of it, and competed its powers with those of my chuck. The geometric chuck has grown into its present state in the course of a period of ten years, under the labour of my own hands; and I do not yet know the extent of its powers. Almost every time I have 53 worked it, some fresh power has been developed; and I certainly have more pleasure, and derive more satisfaction, from one discovery that I make myself, than from fifty becoming known to me in any other way. I have lately devised the means of introducing a new principle, and have put it in practice,the effect of which will be, I expect, both novel and curious; and at this moment, no one but myself (excepting one gentleman) has the least hint of it. Whenever I have spoken of the powers of the geometric chuck, I have always said that it received them from pure circular motion,— thereby leaving it to be understood that it was not in its nature to produce cycloids, spirals, parabolas, byperbolas, nor any curve that requires, in its organical description, a direct right line motion. Every curve that has not the property of returning into itself depends on this motion; and a chuck to work on the lathe is not an instrument calculated to produce it. I did, at one time, introduce a reciprocating right line movement; but the action of it, and effect, did not please me, and I rejected it. This chuck works on the lathe with the greatest precision, and best possible effect. It may be worked as a common chuck, to prepare and face the material for further operation; it can then be adjusted to work as an oval chuck, as an eccentric chuck, or as an epicycloidal chuck; and it will, consequently, combine the effect produced by those chucks, and thereby produce the most beautiful and curious ornamental work imaginable. The finest hair-lines possible may be produced by it, and it will cut its work in as deep, and bring it up as sharp, as can possibly be effected in the art of turning and it will do this with the greatest possible rapidity. Engravings can be executed by it on wood, copper, or other material. Some of its productions in this way are to be seen in your pages. I presented to the Society of Arts, some years back, a collection of 54 MR. IBBETSON'S GEOMETRIC CHUCK, specimens which I printed in 1820; and I possess between four and five hundred engraved blocks and plates executed by it,-some of them with a diamond, on glass and hardened steel. It is not only susceptible of being used as a chuck on the lathe, but may be fixed in an horizontal position on a frame, and worked by hand; in this way, the curves are not limited as to size,-which they necessarily are when it works on the lathe. I have a contrivance for making it work on a wheel cutting and dividing machine I possess, which gives, in addition to the chuck, the power of that engine. Thus, when worked in an horizontal position, it becomes an instrument of amusement as well as of art, to a person who may know nothing whatever of turning, or to one who may not like the labour, or be able to work the lathe; and in this position it will produce, on the principle of drawing or engraving, all the figures it is capable of delineating when worked on the lathe. Mr. Child, in his communications to you, states, first, "that his model can do all that I bave exhibited, and, in his opinion, produce curves much more intricate;" and in his next communication, he says that he " con saw, when my specimens appeared, that my chuck was structed on the same principle as his model." Now, I don't exactly see by what mode of reasoning he arrives at either of these conclusions. If he was satisfied that our instruments were constructed on the same principle, the natural conclusion was, certainly, that they would perform with equal power; but it afforded no grounds for ascribing superior power to his model. My view of the case is, however, quite different. Judging from what Mr. Child says, and from the specimens he has produced, I am perfectly satisfied that our instruments are constructed upon quite opposite principles. In my chuck, the surface upon which the curves are delineated moves against a fixed tool or point. In his, it is evident, from the curves he says he can describe, that the de scribing point moves against the surface; it must do so, to produce cycloidal figures: they cannot be obtained by the rotation of a plane against a fixed point. These are direct opposite principles, and the effect of them is different, in almost every possible way. Any person who has an oval chuck, may go to his lathe, and satisfy himself of the fact in one moment. Let him first describe an ellipsis, in the usual way, on any surface of wood affixed to the chuck; then make a small hole anywhere on the line of the ellipsis, and fix a bit of slate pencil in it; hold a slate steadily in front of the chuck, so as just to touch the point of the pencil; then move the lathe round, and the pencil will, of course, draw a line on the slate. This line will not, however, be another ellipsis (viz. a curve of the second order), but a totally different curve(viz. a curve of the fourth order), denominated by the great English mathematician, John Landen,F.R.S. "the geometrical oval," and by the French mathematicians, "the car. dioid," because in one case it assumes the shape of a heart. Now, the motion of the oval chuck is precisely the same in both cases; and therefore the difference in the curves arises from the effect of a point moving against the surface being different from the effect of a surface moving against a fixed point. A person, therefore, who may possess a machine that describes ellipses, upon the principle of a point moving against a fixed surface, will find that he must proceed upon a totally different principle of construction, if he wish to make an instrument to produce ellipses by causing the surface to move against a fixed point. A machine that is constructed on the principle of causing the describing point to move, embraces, with the same quantum of mechanical contrivance, more power than the machine which gives motion to the surface against a fixed point; but the latter will have the superiority greatly in steadiness, precision, and correctness of execution. Ramsden's dividing machine was MR. IBBETSON'S GEOMETRIC CHUCK. constructed on this principle; and all other dividing machines have been the same,-adding a radial right line movement to the describing point, to mark the divisions. With regard to the division of the ellipsis, I will further observe, that whatever practical difficulty is found in dividing the periphery of a circle into equal parts, must exist in a much greater degree when we come to divide the periphery of an ellipsis. The correct motion of one circle is not, then, the only thing to be considered; the correct motion of other circles is to be added, and a method for the correct regulation of their angular velocity must be obtained. In my construction of the geometric chuck, I have fortunately hit upon a method by which the periphery of an ellipsis (whether the ellipsis be more or less eccentric) can be divided into equal parts upon a correct mathematical principle; and the instrument, when once set, will so divide it with the same facility and correctness as bas hitherto been accomplished with respect to the plain circle. This principle of motion can be added to a Ramsden's, or other dividing machine; or to a wheel-cutting apparatus; so that the means now exist of graduating an ellipsis, and of cutting elliptical wheels into any number of teeth, should such things be of any use in the arts. After what I have now said, it is scarcely necessary to add, that my curiosity has been considerably excited on the subject of Mr. Child's model possessing the power of dividing the periphery of an ellipsis into equal parts. It is, indeed, the only point on which I now feel the least interest, and am not perfectly satisfied. I shall, therefore, be greatly disappointed, if 1 do not very shortly see, in your pages, the specimens Mr. Child alludes to ;-a few specimens will set the matter at rest, which assertion and opinion can never do. The question, in my opinion, now is, not whether our instruments can copy each other's productions, but whether they are capable of executing the work ascribed to them. The following specimens,executed *55 by the geometric chuck, will throw some further light on this subject: No. 1 shows the effect of the natural inequality of elliptical motion. The looped figure is thrown into the figure of an ellipsis; and it will be perceived, that the loops are farthest apart at the extremes of the conjugate axis, and are nearest (in this pattern they intersect) at the extremes of the transverse axis. On considering this, the cause will be obvious; and the remedy becomes the desideratum. No. 2. In this specimen, the external set of loops arrange at equal distances; but not so with the internal sets. This proves the power of doing the thing, and shows that every different ratio between the transverse and conjugate, renders a different adjustment of the instrument necessary. No. 3 consists of circles only, arranged at equal distances, in the periphery of an ellipsis. This shows that eccentric work consisting of circles, or, instead of circles, radiating lines, may be thrown into elliptical figures; and it shows, also, the power of the instrument to divide the periphery of an ellipsis into equal parts. In this engraving there are three sets of circles, arranged elliptically one within the other; and in each, the adjustment of the instrument corresponded with the variation in the ratio between the conjugate and transverse diameters of the ellipsis. No. 4 is a one-lined figure, as on inspection may be perceived. This curved line is produced under the same combination of motion which produced the preceding figures, but under a different arrangement of the locality of the motions, and their angular velocity. Nos. 5, 6, and 7, are specimens, engraved on one block, of the plain or simple elliptical movement of the geometric chuck; and show that it is capable of combining the ellipsis in every possible way, and in every direction; and of producing it in every variety-from the line to the circle. No. 20. This is a true oval-shaped eurve. It is produced by the plain. MR. IBBETSON'S GEOMETRIC CHUCK. Note by the Editor. When we made the selections from Mr. Child's specimens, which we published in our 225th, 233d, and 245th Numbers, and added a classification and description of the remainder from the able pen of Mr. Jopling, we thought we had left in no doubt the reality of any of the powers which Mr. C. represented his apparatus to possess. But having been led by the preceding letters to review what had been formerly laid before our readers on the subject, we perceive that 57 the proof was defective in the point alluded to by Mr. Ibbetson-namely, in showing that Mr. Child's "model possesses the power of equalizing the motion of a point in the periphery of an ellipsis.". We have, therefore, examined again, with care, the packet of Mr. Child's specimens still in our possession, and though we have not met with any example of a perfectly equal divi sion of the periphery of an ellipsis, we observe several very close approximations to it, as in the following figures; |