Mathematical Instruments
Book VIII.

# A short Description of the principal Tools used in making of Mathematical Instruments.

The chief and most necessary Tool is a large Vice, serving to hold Work while it is filing, &c. It is necessary that this Tool be well filed, that the Chops meet each other exactly, that they be cut like a File, be in good temperature, that the Screw be adjusted as it should be in it’s Box; and that the whole Tool be well fixed to a Bench. There are also Hand-Vices of different bignesses, according to the Work to be filed.

The Anvil, which serves for hammering Work upon, ought to be very smooth and of tempered Steel, and placed upon a great wooden Billot, so that it may not give way when it is working upon.

There are also Bench-Anvils for strengthening and rivetting small Work; some of these, which are called Bec’s, and serve to make Ferrils upon, &c. have one side conical, and the other in figure of a square Pyramid.

Hand-Saws are made so as to have Branches drawing the Blades (which are of different bignesses) straight by means of Screws and Nuts.

It is necessary to have good Files. The rough ones made in Germany are the best; and the smooth and bastard Files of England are very good. There are also small rough and smooth Files, for filing Work Triangular, Square, Circular, Semi-Circular, &c. Rasps for fashioning of Wood; several sorts of Hammers for straightening, smoothing, rivetting, &c. of Work; Tapes and Plates for making Screws.

Pincers and Knippers of several kinds. Scissars of several Sizes for cutting of Metals. Burnishing-Sticks for polishing Work. Steel-Drills of divers bignesses for making of Holes thro’ Work, having one end filed like a Cat’s Tongue, and the other sharp. These Drills are used different ways; for some of them are placed in a drilling Leath, which is composed of a small square Iron-Bar, and two little Poupets or Heads carrying a Pulley, wherein is placed the Drill in a square Hole going thro’ it, which is turned by means of a little Cat-gut Row. Note, This Tool is placed in a Vice when it is using. Brass or Wood may be drilled also by putting it first into the Vice, and the Drill in a Pulley. Then if the end of the Drill be put into a shallow Cavity made in a Piece of Brass or Iron, placed against your Bread, and the Point thereof be put to the thing you would make a Hole thro’; by turning the Drill swiftly about by means of the Bow, and at the same time pressing it with your Bread: against the thing to be drilled, you will soon make a Hole thro’ it.

The Leath is also of great use; the most simple of them is made of two Brass or Tron Poupets or Heads sliding along a square Iron-Bar, and a Support which also slides along the said Bar, upon which the Tools are laid when they are using. At the Top of the Poupets are two Screws of tempered Steel going thro’ them, which are fixed by means of Nuts. When this Leath is to be used, it must, be placed in a Vice, and the thing to be turned, between the two Points of the Screws; and if you have a mind to turn with your Hand, you must use a Cat-gut Bow.

Great Leaths for turning with one’s Foot are composed of two wooden Poupets, and two wooden side Beams, of a Length and Breadth proportional to the bigness of the Leath, which are sustained by two Pieces of Wood called the Feet of the Leath. These side Beams are placed level, about two or three Inches distant from each other, according to the bigness of the Poupets put between them, and the ends of them are adjusted upon the Feet, which are about four Foot high, and they are likewise joined underneath by two or three cross pieces of Wood, for rendering the Machine more stable and solid.

The Poupets, which are two pieces of Wood of equal Length and Thickness, have one part of each cut so as to go in between the side Beams; and the other part, being the Head, is cut square, and solidly posited upon the side Beams; and that they may be very firm, there are Clefts of Wood drove with a Mallet into Mortice-Holes at the Bottom of the Poupets underneath the side Beams.

In the Head of each Poupet is a tempered steel Point strongly inclosed in the Wood; so that when these two Points are brought to each other, they may exactly touch. There is likewise a wooden Bar going all along, which is sustained by the Arms of the Poupets, which may be lengthened and shortened at pleasure; and this serves as a Rest for the Tools, when they are using.

Against the Ceiling, over the Leath, is fixed an Elastick wooden Rod, having at the End thereof a Cord fastened, which comes down to the Ground, and is fixed to the End of a piece of Wood, called the Treader.

Now when you have a mind to work, the Cord must be put about the Piece to be turned, or about a Mandril adjusted to it; and pressing your Foot upon the Treader, you will turn the Work by means of the Rod which springs; then with proper Tools laid upon the Support, and against the Piece which is turning, you must first fashion it with coarse Tools, and finish it with fine ones.

Because all Work cannot be turned between two Points, one of the Poupets must be taken away, and instead thereof must be placed a Piece of Wood furnished with Iron, adjusted between the side Beams as the Poupets are, and instead of having a Steel Point has a very-round Hole therein, in which goes the Colet of an Iron-Arbor, whose other End is sustained by the Steel Point of the other Poupet.

The said Arbor is fifteen or eighteen Inches long, and is composed thus: at the End, which is supported against the aforesaid Piece of Wood, is a Screw of a very large Thread made round the Arbor, upon which are screwed on divers Brass Boxes, in which are held fad the Pieces of Wood, which serve to place the several Works to be turned. And at the other End of the said Arbor are made several Threads of Screws of different bignesses, that so Screws may be turned.

Near the middle of the said Arbor, is placed a Mandril or wooden Pulley, about which goes a Cord. There may be several other Pieces adjusted on this Arbor, for turning irregular Figures, as Ovals, Hearts, Roses, wreathed Pillars, &c. All these Pieces are filed into the Figures that one would have them make, and have square Holes in the middle of them, which are adjusted to a Square near the End of the Arbor.

When the Pieces are disposed on the Arbor, the pointed End thereof is placed in a little Hole in the Steel Point of the Poupet, and the other End in the abovesaid wooden Piece (placed instead of a second Poupet), which is made so, that there are two Pieces which spring, and push the Figure backwards and forwards, and by this means move the Arbor backwards and forwards, more or less. according to the Figure; and this is the Cause that the Tool gives the proper Figure to the Work, which moves to it, or recedes from it, according to the Motion of the Arbor; for the Tool must always be held fast upon the Support. But since these kinds of Figures are seldom used for Mathematical Instruments, I shall say no more as to this way of turning.

The principal Use of the said Arbor, serves for turning of Rings, making of Grooves in Compasses, and other the like things. And this may be done, in placing the Pieces to be turned upon the Wood belonging to the Boxes (of which we have already spoken), which are adjusted on the Leath for receiving the said Pieces. Note, The Rests or Supports of the Tools are likewise placed according as the Work requires; some before, and some sideways.

Male and Female Screws are formed, by putting the proper Thread on the Arbor into a piece of Wood hollowed into a Screw of the same Thread, which is placed at the Poupet carrying the End of the Arbor. And the other End of the Arbor, where is a Colet of the same Thickness, is put exactly into the Hole of the abovementioned piece of Wood; then if the Treader be put in motion by your Foot, the Work will move backwards and forwards, so as that you may form a Screw or a Nut, with toothed Tools made on purpose, according to the Threads marked upon the Arbor. Note, For turning of Wood, Googes, Chissels, &c. are used. But for Brass and other Metals, smaller Tools of tempered Steel must be used, as Graving-Tools, &c.

Thus have I here, and in the Body of this Work, given a short Account of the Tools commonly used in making of Mathematical Instruments. The others may be easily supplied according to Necessity. But since they are usually made by those that use them, I shall here shew how to chuse the best Metal for their Construction.

The best Steel comes from Germany. This ought to be without Flaws, Black, Veins, or Iron-Furrows. You may know this by breaking of it, and seeing whether the Grain be very fine and equal.

In forging of Tools, or any thing else of Steel, you must take care of over-heating them, and perform it as soon as possible; for the longer they are hot, the more will they be spoiled.

When the Tools are forged and filed, and you have a mind to temper them, you must heat them led-hot ’till their Colour be something redder than a Cherry, and then they must be tempered in Spring or Well-Water: the colder the Water is, the better. And when they are cold, they must be taken out of the Water, and laid presently upon a Piece of hot Iron, so long, ’till the Colour they have contracted by tempering is lost, and they become yellowish; and then they must be thrown again into the Water, without staying ’till they become blue, because they will lose their Force.

To temper Bundles of Files, or other Pisces of Iron, you must take Chimney-Soot, the oldest and grossest being the best, and having finely powdered it, temper it with Piss and Vinegar, putting a little melted Salt therein, until the whole be as a liquid Paste. The Soot being tempered, the Tools must be covered over with it, and this covered with Earth, and the whole Bundle thrown into a strong Charcoal-fire; and when it is become something redder than a Cherry, it must be taken out and thrown into a Vessel full of very cold Water, and then the Files will be sufficiently hard.

We have already shewed the manner of soldering Brass or Silver to each other; and We would have it here observed, that Iron may be soldered to Iron, by putting thin Brass upon the Piece to be soldered, and the Powder of Borax, and then covering it all round with Charcoal, and heating it until we perceive the Brass melts and runs.

Note, Brass cannot be hammered when it is hot, for it will break; but Copper is hammered cold or hot: but this is seldom used in making of Mathematical Instruments, because Brass is finer and more convenient. Brass is made with red Copper and Calamin, which is a Stone giving a yellow Tincture to the Metal, and is found in the Country of Liege, and in France.

Gold and Silver may be hammered cold or hot, and may be melted also nearly as Brass is; and Mathematical Instruments are made with Gold and Silver in the same manner as with Brass.