In Fig. 1, then, we have a crank CI, whose radius is equal to CB, half the major axis, turning about a fixed center C. Upon the crank-pin I is hung, so as to turn freely, a rigid cross composed of a long slotted piece TT, in which slides a block, and two cylindrical arms at right angles to it and in line with each other, the axis EE passing through I. The arm on the right slides through a socket pivoted at the focus F; the one on the left slides through a similar socket, which is pivoted at G to a third socket longer than the others, which again is pivoted at the focus F'; the distance F'G being equal to AB. Through this long socket slides a rod KP, the end P being formed into an eye, by which this rod is pivoted to the block which slides in the long slot, and thus controls the motion of the block; and the pivot at P is centrally drilled to carry the pencil. It is thus apparent that the center line of the slot TT must in all positions be tangent to the hyperbola PBR, which will be traced by the pencil, whose motions are so restricted as always to satisfy the conditions explained in connection with Fig. 2. The apparatus as thus represented does not at first sight appear unduly complicated. But in order to render it adjustable, so that hyperbolas of varying eccentricities and on different scales may be drawn with it, several parts not here shown must be added. A frame must be provided, in which to arrange supports for the pivots at F and F', and these supports connected by a right and left handed screw, or equivalent means of altering the distance between the foci; the crank CI and the socket F'G must be of variable length, and these in each case would require to be carefully adjusted. So that, as we stated in the beginning, it is questionable whether a draughtsman of ordinary skill could draw the curve any more readily by the aid of such a piece of mechanism than he could without it; but it may claim a passing notice as a novel device, and the first one, we believe, for describing the hyperbola by a combination of rigid parts. * * * * * EXPERIMENTS WITH FIBERS. By Dr. THOMAS TAYLOR. As Microscopist of the United States Department of Agriculture, I am frequently called upon to make investigations as to the character of textile fibers and fabrics, not only for the public generally, but also for several departments of the Government. Textile fibers are presented both in the raw and as articles of manufacture. In the latter case they may have been dyed, stained, or painted. It is obvious that under these conditions the fibers should be subjected to chemical reaction to bring them as nearly as possible to their normal condition.