When the lathe is employed under the most advantageous circumstances to produce the various geometrical solids or figures, the tool is placed under the guidance of a ruler or rather of a slide, by which its path is strictly limited to a recti linear motion. Thus for a cylinder, the slide is placed exactly parallel with the rotary axis of the mandrel, and for a plain flat surface the tool is moved on a slide at right angles to the axis, Generally two slides fixed in these positions arc attached to the lathe to carry and guide the tool, the machine being known as the sliding rest; but mostly the one slide only is used as a traversing or directional slide for guiding the tool, the other as an adjusting or position slide, for regulating the penetration of the tool into the work.

Sometimes the two slides are moved simultaneously for the production of cones, but more generally the one slide is placed oblique and used alone. The lathe is employed with great effect in producing plane surfaces, but the more modern engine, the planing-machine, the offspring of the slide or traversing lathe recently adverted to, is now also very much employed for all kinds of rectilinear works.

The planing-machine being intended principally for rectilinear solids of all kinds, its movements are all rectilinear, and these are in general restricted to three, which are in the same relation to each other as the sides of a cube; namely, two are horizontal and at right angles to each other, and the third is vertical, and therefore perpendicular to the other two. The general outline of the machine will be conceived by imagining a horizontal railway to take the place of the revolving axis of the lathe, and the slide rest of the lathe to be fixed vertically against the face of a bridge stretching over the railway. In the general structure of this most invaluable machine, the railway is the cutting slide, upon which the work is slid to and fro. For producing a horizontal surface, the horizontal slide is employed traversing the tool across the face of the work, which is thus reduced by ploughing a series of parallel grooves, not exceeding in distance the width of the pointed tool, so that first the line, and then the surface arise, exactly as in the geome-tical suppositions. For vertical planes, the vertical is the traversing slide, the horizontal the adjusting; and for oblique planes, the vertical slide is swivelled round to the assigned angle, the imaginary railway being employed in all cases to the cutting motion.

To advance into greater detail would be to encroach on the subject of the succeeding chapters; although it may be added, that when we examine into almost any machine employed in cutting, it will be found that the end to be obtained is always a superficies, either plane or curved, and which superficies reduced to its elementary condition, presents length and breadth.

When, therefore, we have put on one side the mechanism required for connecting and disconnecting the engine with the prime mover, whether animal, steam, or other power; it will be found that when the superficies is produced by a pointed tool, the primary motions resolve themselves into two, which may be considered representative of length and breadth. The velocity of the one primary motion, is suited to the speed proper for cutting the material with the most productive effect, which for the metals is sometimes as low as ten or twenty feet per minute, measured at the tool, and for the woods, the speed is above ten or twenty times as great.* The velocity of the other primary motion is generally very small, and often intermittent; and it becomes a mere creep or traverse motion, by which the pointed tool is gradually moved in the second direction of the superficies, under formation.

In producing circular bodies, one of these primary motions becomes circulating or rotary, and in complex or irregular forms, an additional movement, making in all three, or sometimes four are compounded; and lastly, when linear or figured tools are employed, one of the motions is generally expunged.

* The principal limit of velocity in cutting machines, appears to be the greatest speed the tool will safely endure, without becoming so heated by the friction of separating the fibres, as to lose its temper or proper degree of hardness.

The cohesion of iron being very considerable, a velocity materially exceeding ten to twenty feet per minute, would soften and discolour the tool, whereas in general the tools for iron are left nearly or quite hard. Brass having much less cohesion than iron, allows a greater velocity to bo used, lead and tin admit of still more speed, and the fibrous cohesion of the soft woods is so small, that when the angles of the tools are favourable, there is hardly a limit to the velocity which may be used. Water, soap and water, oil, milk, and other fluids, are in many cases employed, and especially with the more fibrous metals, for the purpose of lubricating the cutting edges of the tools to keep down the temperature, the fluids reduce the friction of separating the fibres, and cool both the tool and work, thereby allowing an increase of velocity; and at the same time they lessen the deterioration of the instrument, and which when blunted, excites far more friction, and is likewise more exposed to being softened, than when keen and in perfect working order. There are, howover, various objections to the constant use of lubricating fluids with cutting tools.

The other. movements of cutting machines may be considered as secondary, and introduced either to effect the adjustment of position at starting, or the changes of position during the progress of the work; or the resettings by which the same superficies is repeated, as in the respective sides of a prism, or the teeth of a spur wheel, which may be viewed as a complex prism.

The above two or three movements may in general be im-pressed wholly upon the tool, wholly upon the work, or partly upon each; and which explains the very many ways which, in cases of simple forms, may be adopted to attain the same result.

In numerous instances likewise, all the movements are as it were linked together in a chain, so that they may recur at proper intervals, without the necessity for any other adjustment than that which is done prior to the first starting, such arc very appropriately called self-acting machines, and these, in many cases, give rise to very curious arrangements and combinations of parts, quite distinct from the movements abstractedly required to produce the various superficies and solids, in which the mathematician and mechanician from necessity exactly agree, when their respective speculations are sifted to their elementary Of primary laws, which are few, simple, and alike for all.

Mr. Nasmyth has written an interesting paper, entitled, "Remarks on the Introduction of the Slide Principle, in Tools and Machines employed in the production of Machinery." *

This principle, although known for a far greater period, has within less than half a century, and in many respects even within less than the fourth of a century, wrought most wonderful changes in the means of constructing mechanism, possessed of nearly mathematical accuracy. The whole of this is traced to the employment of the two, or the three slide movements, to which method Mr. Nasmyth has judiciously applied the term

"Slide Principle" but the object in this place is rather to examine in detail the principles and practices, than to refer to the influence thes have had on manufacturing industry, and thence on the general condition of mankind, and upon our own nation in particular.

* See Buchanan's Mill Work, by G. Rennie, F.R.S. 1841. Page 393.