The depth, or rather length, of the cutting face may be decreased, and the number of teeth increased, for the fibres to be cut cannot be more vertically than can be contained between 2 teeth. The operative length of the tool must also be taken into account, for the combined resistance of all the fibres resting within the teeth must be less than the power of the workman. It may be well to remark that this difficulty is generally met in practice by the workman so raising certain teeth out of cut as to leave only so many in operation as the circumstances enable him to work. One advantage results by so doing - the guide principle of a longer blade is gained than could be done had the length been limited by that of the operating teeth, or had there been a prolongation of metal without any teeth upon it. To avoid complicating an attempt to deal progressively with the action of the saw, this, and perhaps other considerations may for a while pass from notice. Considered as hitherto the teeth and tool are planned for operation in both tension and thrust. Now these are of so opposite a nature that a tool perfect under the one is likely to be imperfect under the other.

When the necessary thinness of the material and the tenacity of it are taken into account, tension seems the most suitable; but although the ancients and the workmen in Asia are of this way of thinking, yet in England the opposite practice is adopted. It may be well to give a few minutes to this branch of the subject.

The form of a saw must in one dimension at least be very thin, and that without any opportunity for strengthening any part by means of ribs. When a strengthening bar is introduced at the back as in dovetail saws, the depth of cut is limited. In order, then, to permit the guide principle to operate efficiently, this thin material must be so prolonged as under all circumstances to guide the cutting edge in a straight line. Of course we are dealing with saws to be used by hand, and not with ribbon or machine-driven saws.

If a light saw blade be hooked on an object, or placed against one, then tension causes this straight blade to be more and more straightened. On the contrary, if pressed forward by thrust, the weakness of the blade is evidenced by the bending. Now, formed as saw teeth are, either to cut in both directions, or in the forward direction only, then there is always one direction in which the work to be done is accomplished by a thrust upon this thin metal. Clearly the metal will bend. If, however, the teeth are such as to cut in one direction only, and that when the tension is on the metal, the work tends to preserve that straightness of blade upon which an important quality and use of the tool depends. That this tension system can be efficient with a very narrow blade is clear from the extensive use of ribbon saws. There is, however, a property in the breadth of the blade which applies equally to the tension and thrust systems - it is the guide principle. The breadth of the blade operates by touching the sides of the gateway opened by the teeth.

When it is desired to dispense with a straight guide for sawing purposes, it is done by narrowing the blade as in lock saws, tension frame saws, etc.

There is obviously a limit to the required breadth even for the most effectual guidance and movement: this guidance should be uniform through the entire cut; hence upon the guide principle alone, there is required a breadth of saw beyond what is requisite for the teeth. The reasoning hitherto has landed us upon a parallel blade of some (as yet) undecided breadth. When one of our ordinary hand cross-cutting saws is examined, it is observed to be taper and not parallel, the tapering being at the edge or back, where the teeth are not. This has been done to meet our practice of using the saw as an instrument for thrust instead of tension. When the teeth near the end farthest from the handle are to operate, and there is no steadiness obtained from the guidance of the sides of the already separated timber, then the whole of the thrust must be transmitted through the necessarily thin blade. An attempt to compensate for this thinness by increasing the breadth is the only course open. It is one not defensible upon any true principles of constructive mechanism, for it is not in the increased breadth or extension of surface that resistance to bending is wanted, but it is in the thickness, and that is impracticable.

In thrust saws, the hand and the arm of the workman occupy a definite position, and the line of pressure on the saw is thus very much determined by the inclination of the handle (that part grasped in the hand) to the line of teeth prolonged backwards. If the handle be placed at such an angle that a large part of the resolved thrust be perpendicular to the line of teeth, then the "bite" may be greater than the other resolved portion of the power can overcome. At another angle the "bite" may be very little, and although the saw thus constructed would move easily, it would work " sweetly," but slowly. The construction is suitable for saws with fine teeth and for clear cuttings. It will be seen from these considerations that there should be preserved a very carefully considered relationship between the size and angle of the teeth and the position in which the handle is fixed, or rather the varying adaptability of the workman's thrust. Indeed, upon fully developed and accurate principles, the timber to be cut should first be examined, its fibrous texture determined physically, and a saw deduced from these data, having teeth and handle so related as to do the required work with a minimum of power.

This multiplicity of saws is not available; and as in music the multiplicity of notes which only the violin can produce are rejected in other instruments, so here the multiplicity of theoretical saws is rejected, and a kind of rough and ready compromise is effected between the position of the handle and the angle and depths of the teeth. It would, however, well repay those whose works are usually of the same character and of the same class of timber, to consider these points, with a view to the selection of saw-anil position of handle suitably constructed to do the work with the least expenditure of power.