This section is from the book "Manual Training: First Lessons In Wood-Working", by Alfred G. Compton. Also available from Amazon: First Lessons In Wood-Working.
Examine your saw carefully. You find that it consists of a number of triangular teeth, each of which acts as a sort of knife. Count the number of teeth to the inch. You will find this different in saws that are intended for different purposes. The one that you have is a "cross-cut" saw for moderately soft wood. If you now examine one of these teeth, you will find that it is pointed, and the front edge is sharp. It would be a useful exercise, and would help you to understand the mode of action of the saw, if you would cut out with your knife from a piece of thin wood (say 1/8 of an inch thick) a model of half a dozen teeth of each of your various saws as you become acquainted with them. When you push the saw across the grain, each of these teeth makes a cut across the fibers, just such as you can make by holding your knife upright and drawing it across the grain. Next, examining the successive teeth, you find the alternate ones sharpened in different ways. While one has its sharp edge towards the left, the next has its edge towards the right. Thus the two sets of teeth make two different cuts across the grain, and these cuts are at a distance apart equal to the thickness of the saw, or a little more, inasmuch as the teeth are spread apart, or "set." All this you will easily make out if you study attentively the saw itself, and not merely this description.
Now, try to make with your knife just such a cut across the grain as one of these teeth makes. You have a piece of waste wood which you will keep by you for this and similar experiments. Hold your knife upright on the piece and draw it along, across the grain. You find, as you have found before, that you cannot cut very deep, because the wood at the side of the knife is not removed, and thus the cut is not wide enough to let the knife enter; but with the saw it is different. When one knife or tooth has made its cut, the next knife not only makes another cut very near and parallel to the first, but it also tears off the little piece of wood between the cuts. The third tooth, therefore, is able to cut a little deeper, and the fourth tooth tears off a little more, and so on. Thus the saw makes a clean cut with parallel sides, and wastes only a small amount of wood.
We can now go on to the use of the crosscut saw. On your bench is a pierce of pine board about 4 feet 6 inches long, 6 inches wide, and | of an inch thick. (Hereafter we will indicate dimensions like this in the following way: 6" x 3/4" - 4' 6", which will be read, "Six inches by three-quarters of an inch, by four feet six inches)." The board is what is called "mill-dressed," that is, the roughness that is always found on boards that have been sawn from the log has been planed off by a planing-machine, leaving a tolerably smooth surface. The piece on your bench has been cut from the end of the board, and you will very likely observe that in the first place it is not square on the end, and in the next place that it is cracked or "checked" at the end. The first is owing to the fact that the log was cut with the ax. as already explained. In many cases the logs are cross-cut with a saw, and then the ends of the boards are square. The cracks or "checks" we will explain in our next lesson.
Now lay the board on the bench, with the checked end to the right, and we will proceed to first mark it square, and then cut it square. For the first purpose we will use the try-square. Place the edge of the wooden part of the square against the edge of the board, letting the steel blade lie flat on the board and square across it. Then, using the edge of the blade as a ruler, draw a pencil-mark; this will run square across the board. You must be careful in drawing this line not to vary the inclination of your pencil, or you will make a line which is not parallel to the edge of the square, and therefore not perpendicular to the edge of the board. Draw such a line just far enough from the imperfect end to leave out all the worst checks. We will then cut off with the saw the imperfect piece thus marked.
There are several ways in which the board may be held while we are making this cut. For this exercise you may hold it in the bench-vise. Observe how the vise works. Open it to the width of your board, lay the board in it, with the imperfect end to the left and the marked face up, and screw the vise up so as to hold the board firmly, the marked piece projecting beyond the end of the bench.
Take the saw in your right hand. (If you are left-handed you will do well, nevertheless, to learn to work with the right hand, or, better still, to work equally well with both hands. It is sometimes a great advantage to be able to use either hand; and there are some things which can only be done with the right.) Set the saw to the left of the mark, just so far that when you cut you will cut exactly up to the mark, but not beyond it. Rest the fingers of the left hand on the wood outside of the mark, holding the thumb up for a guide to steady the saw. Draw the saw backward, letting it rest very lightly on the wood, till you have made sure that the cut will be in the right place; then push it forward, still bearing lightly on the wood. Having started the cut thus with a few gentle strokes, continue it with long strokes, the full length of the saw. Avoid short, jerky strokes. Draw the saw back at each stroke till the hand nearly touches the shoulder, and push it forward till the handle nearly reaches the board. A long, steady stroke cuts smoother as well as faster, is a more agreeable movement, and affords a pleasant exercise.
Be careful not to bear too hard on the saw; if you do, you will bend the saw, and it will make a crooked cut. While working, watch the saw, to see that you keep it perpendicular to the surface of the board. When the cut is nearly finished bear still more lightly, and work with gentler strokes, at the same time holding up with the left hand the piece that you are cutting off, to prevent splintering when the saw comes through.
Having cut off one piece under the supervision of your instructor, you may mark and cut off two or three more, each exactly an inch wide, till you find you can make a smooth and square cut. If you need more practice you must use a piece of waste wood for the purpose, not reducing the length of your board to less than 45". The squareness of the cut should be tested by applying the try-square, with the wooden part first against the edge of the board, and then against the face. The former test will show whether you have cut square across the board, and the latter whether you have cut square through.
 
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