Cylinder (geometry)

“ If a cylinder move uniformly forward in the direction of its length, the resistance made thereto is not at all changed by augmenting or diminishing that length; and is therefore the same with the resistance of a circle, described with the same diameter, and moving forward with the same velocity in the direction, of a right line perpendicular to its plane. For the sides are not at all opposed to the motion; and a cylinder becomes a circle when its length is diminished in infinitum. ”

“ This shows that there are two branches of the curve; the upper one does not pass through a maximum, but the lower one does.
(7) A cylinder whose height is twice the radius of the base is increasing in volume, so that all its parts keep always in the same proportion to each other; that is, at any instant, the cylinder is similar to the original cylinder. When the radius of the base is feet, the surface area is increasing at the rate of square inches per second ”

“ Let a right line go from centre to centre, and it will be the axis. Then draw lines from circumference to circumference, and you have a cylinder. A piece of the funnel of a stove is a cylinder. A cylinder is, in fact, a prism whose bases are circles instead of polygons* The height of a cylinder is the length of the axis, or the distance from one base to the other. If the axis be perpendicular, the cylinder is said to be upright. ”

“ A B (fig. 4 of Plate 20) is a hollow cylinder, of a diameter proportioned to the effect wanted to be produced. C is a cylinder closed at both ends, which fills that just mentioned as far as the length goes, excepting a play of about 1⁄8 of an inch. This interior cylinder revolves in the former; but not on its own centre. It revolves on an axis E eccentric to itself, but exactly concentric with the outer cylinder A B. The centre therefore, of the inner cylinder C, describes a circle within the outer one, which is always parallel to its circumference. ”

“ We may suppose our original cylindrical cells to have spherical ends, which is their normal and symmetrical mode of termination; and, for closest packing, it is obvious that the end of any one cylinder will touch, and fit in between, the ends of three cylinders in the opposite row. It is just as when we pile round-shot in a heap; each sphere that we {328} set down fits into its nest between three others, and the four form a regular tetrahedral arrangement. ”

“ To Turn a Cylinder Cover.—A cylinder cover affords an example of chucking in which the work done at one chucking requires to be very true with that done at a subsequent chucking, thus the gland hole which is on one side requires to be quite true with the diameter that fits into the cylinder bore, this diameter being on the opposite side. ”

“ The large cylinder being put in motion, the form of types thereon, is—in succession—carried to four or more corresponding, horizontal, impression cylinders, arranged at proper distances around it, to give the impression to four or more sheets, introduced one by each impression cylinder. The fly and feed-boards of two of the impression cylinders are similar to those on the well-known double cylinder press ”

“ A second mode of generation is no less admirable: If we make the spiral of Archimedes the base of a right cylinder, and imagine a cone of revolution having for its axis the side of the cylinder passing through the initial point of the spiral, then this cone cuts the cylinder in a curve of double curvature. The perpendiculars to the axis drawn through every point in this curve form the surface of a screw which Pappus here calls the plectoidal surface. ”

“ Drying Cylinders.—These cylinders, by the same firm, for which patents were obtained in 1872 and 1887, are made with concave and convex ends, the latter type being shown in Fig. 44. The cylinder body is made [186] of hard cast-iron, turned and polished on outside surface. The ends and trunnions are of tough cast iron, turned to fit into their places, and there secured by bolts and nuts by a patented method, whereby no bolts (excepting for the manhole) are put through the metal, an unbroken surface is preserved, and the annoyance of leakage through the bolt-holes is avoided. ”

“ The motion for working the cylinder, if an independent one, should be rigid and strong; for if there is any spring in it, though the cylinder may be brought in sufficiently close when there is much cutting on the card, if a blank card or one with very little cutting on it comes on, the extra pressure on the needles, especially with a large machine, may prevent it from getting in sufficiently close to clear the hooks from the griffe. ”

“ The circumference is simply the curved line that is drawn with the compass. The diameter of a circle is any straight line that passes through the center of the circle and has its ends in the circumference. It is possible to draw any number of diameters in the same circle, but they will all have the same length. Value of .—The girth or distance around a cylinder can be found by wrapping a narrow strip of newspaper around it. The point where the strip overlaps the end should be marked before the paper is removed from the cylinder. ”

“ For the globe is to its circumscribed cylinder as two to three; and therefore the force which can destroy all the motion of the cylinder, while the same cylinder is describing the length of four of its diameters, will destroy all the motion of the globe, while the globe is describing two thirds of this length, that is, eight third parts of its own diameter. ”

“ Cylindrical Equal Area Projection.—Let us suppose a model of the earth to be enveloped by a cylinder in such a way that the cylinder touches the equator, and let the plane of each parallel such as PR be prolonged to intersect the cylinder in the circle pr. ”

“ Since my escape I have had several conversations on this subject with an old schoolmaster of the district; and it was from him that I learned the use of the words 'cylinder' and 'sphere.' He explained to me—although I have forgotten the explanation—how what I had observed was in fact the natural consequence of the forms of the floating fragments; and showed me how it happened that a cylinder, swimming in a vortex, offered more resistance to its suction, and was drawn in with greater difficulty, than an equally bulky body of any form whatever. ”

“ Suppose, for instance, the mirror were cylindrical, and convex, and the object a circle placed directly in front of it. It will easily be seen that that diameter of the circle, which is parallel to the axis of the cylinder, will not be altered in the reflexion, but that the diameter perpendicular to that axis with all chords parallel to it, will have for their images portions of conic sections of less breadth than themselves, so that the image will appear diminished in breadth, and distorted into a form like that of the bowl of a spoon. ”

“ This platform carrying an index, can be rotated independently of the large circle. When the platform index is clamped, the two circles rotate together.
The Refracting Substance.—For substances which can be cast, the molten mass is poured into a cylindrical mould with a thin partition in the middle. In this way two equal semi-cylinders are obtained at each casting. Substances like wood or stone are turned, and the cylinder sawn into two equal halves; In my experiments, different sized cylinders were used; I have successfully used small ones with a radius of 8 cm. only. ”

“ The trussed girders supporting the platform may be treated as rectangular surfaces.
The centre of gravity of the guys, sleepers, and jib will be at a point in the centre of their length.
The centre of gravity of the engine may be somewhat difficult to find, but it will be sufficient to treat it142 as a cylinder. The centre of gravity of a cylinder is the middle of its axis. ”

“ In the first place, I remark that a cylinder carrying only its own weight and having the maximum length, beyond which it will break, will, when supported either in the middle or at both ends, have twice the length of one which is mortised into a wall and supported only at one end. ”

“ Finally, a short, open cylinder with a vertical axis may be formed by curving a narrow plate or ribbon. It is not necessary to see the formula to recognize the fact that this cylinder must behave like a ribbon and a flat ring. The radius increasing, and the surface remaining constant, the resistance of the earth here likewise approaches zero.
As the resistance of the earth is inversely proportional to the diameter of the plates, the zero resistance can also be reached by dividing a plate ad infinitum. ”

“ When setting a cylinder which is to be bored it should, when the design will permit, be set true by the outside of the flange, or what is even better, by the outside of the cylinder itself, rather than by the rough bore, in order that the walls of the finished cylinder will have a uniform thickness. The position of very large cylinders, while they are being bored, is an important consideration. ”

“ The platform on which the cylinder rests, carries the usual index. Rotation of the cylinder in a left-handed direction gives a reading for total reflection. A second reading is obtained by rotation of the cylinder in the opposite direction, the receiver being now at R′. The difference between the first and the second reading is evidently equal to twice the critical angle. ”

“ It happens, however, that a cube and a cylinder are the only two figures upon which all the dimensions can be marked on one view of the piece, and as cylindrical pieces are much more common in machine work than cubes are, it is taken for granted that, where the pieces are cylindrical, but one view shall be used, and that where they are cubes either two views shall be given, or where they are square a cross shall be marked upon the parts that are square; thus, in Figure 122, is shown a cross formed by the lines A B across the face of the drawing, which saves making a second view. ”

“ We have now given minute instructions for drawing a cylinder escapement in all its details except the extent of the banking slot of the cylinder, which is usually made to embrace an angular extent of 270 degrees; consequently, the pillar of the cylinder will not measure more than ninety degrees of angular extent.
There is no escapement constructed where carefully-made drawings tend more to perfect knowledge of the action than the cylinder. ”

“ The small size of the cylinder allows the machine to be constructed in a very compact manner, so as to shorten the distance which the bed travels, thereby considerably increasing the number of impressions in a given time, beyond the single large cylinder press. ”

“ With regard to the pressure endwise, the area of a cylinder head 14 inches in diameter is 154 inches, and the strength of the 44 inches of circumference would be sufficient to sustain 352,000 lbs., which, divided by the area, is 2,275 lbs. per square inch. If the diameter is 56 inches, the circumference being 172, would sustain a pressure endwise of 555 lbs. per inch. Thus it will be seen that if the cylinder were even 20 feet in diameter, the iron would better sustain the pressure on the head that on the periphery. ”

“ It appears, therefore, that there is a constant force acting on the inner cylinder tending to draw it into that one of the outer cylinders from which its potential differs most.
If be numerically large and comparatively small, then the force is approximately
so that the difference of the potentials of the two cylinders can be measured if we can measure , and the delicacy of the measurement will be increased by raising , the potential of the inner cylinder. ”

“ Cylinder-printing is a much more rapid process, conducted by means of a brass cylinder with the pattern engraved on its surface, which is made to revolve against another cylinder covered with flannel, and charged with color from a trough into which its lower part is dipped. The calico is passed over a large cylinder made to revolve in contact with that on which the pattern is engraved, and which is charged with color from the one below it. Fig. 1 shows this arrangement, a being the large cylinder with the calico round it, b the engraved cylinder, c the color cylinder, and d the color trough. ”

“ In the cylinder, one radius of curvature has the finite and positive value R; but the other is infinite. Our formula becomes T ⁄ R, to which corresponds a positive pressure P, supplied by the surface-tension as in the case of the sphere, but evidently of just half the magnitude developed in the latter case for a given value of the radius R.
The catenoid has the remarkable property that its curvature in one direction is precisely equal and opposite to its curvature in the other, this property holding good for all points of the surface. ”