Mathematical Instruments
Book V. Ch. I.

# Of the Construction and Uses of different Levels.

The first of these Instruments is a Water-Level, composed of a round Tube of Brass, or other solid Matter, about 3 Feet long, and 12 or 15 Lines Diameter, whose Ends are turned up at Right Angles, for receiving two Glass Tubes, 3 or 4 Inches long, fastened on them with Wax or Mastick. At the Middle and underneath this Tube, is fixed a Ferrel, for placing it upon it’s Foot.

There is as much common or coloured Water poured into one End of it, as that it may appear in the Glass Tubes. This Level, altho’ very simple, is very commodious for levelling small Distances. It is founded upon this, that Water always naturally places itself level; and therefore the Height of the Water in the two Glass Tubes will be always the same, in respect to the Center of the Earth.

The Air-Level B, is a very straight Glass Tube, every where of the same Thickness, of an indetermined Length, and Thickness in proportion; being filled to a drop with Spirit of Wine, or other Liquor, not subject to freeze. The Ends of the Tube are hermetically sealed, that is, the End through which the Spirit of Wine is poured must afterwards be closed, by heating it with the Flame of a Lamp, blown thro’ a little Brass Tube, to make the heat the greater; and then when the Glass is become soft, the End must be closed up.

When this Instrument is perfectly level, the Bubble of Air will fix itself just in the Middle, and when it is not level, the Bubble of Air will rise to the top.

## Construction of an Air-Level.

This Instrument is composed of an Air-Level 1, about 8 Inches long, and 7 or 8 Lines in Diameter, set in a Brass Tube 2; which is left open in the Middle for seeing the Bubble of Air at the Top.

It is carried upon a very strong straight Rule, about a Foot long, at the Ends of which are placed two Sights exactly of the same Height, and like that of Number 3, which has a square Hole therein, having two Fillets of Brass very finely filed, eroding one another at Right Angles, in the Middle of which Fillets is drilled a little Hole. There is fastened a little thin Piece of Brass to this Sight, with a small Headed-Rivet, to stop the said Square opening, when there is occasion, and having a little Hole drilled thro’ it, answering to that which is in the Middle of the Fillets. The Brass Tube is fastened upon the Rule, by means of two Screws, one of which marked 4, serves to raise or depress the Tube at pleasure, for placing it level, and making it agree with the Sights.

The Top of the Ball and Socket is riveted to a little Rule, that springs, one of whose Ends is fastened with two Screws to the great Rule, and at the other End there is a Screw 5, serving to raise or depress the whole Instrument when it is nearly level.

The Manner of adjusting this Level is easy, for you need but place it upon it’s Foot, so that the Bubble of Air may be exactly in the Middle of the Tube; then shutting the Sight next to the Eye, and opening the other, the Point of the Object which is cut by the horizontal Fillet is level with the Eye; and to know whether the Air-Level agrees well with the Sights, you must turn the Instrument quite about, and shut the Sight which before was opened, and open the other. Then looking through the little Hole, if the same Point of the Object before observed be cut by the horizontal Fillet, it is a sign the Level is just; but if there be found any difference, the Tube must be raised or depressed by means of the Screw 4, ’till the Sights agree with the Level; that is, that looking at an Object, the Bubble of Air being in the Middle, and afterwards turning the Instrument about, the same Object may be seen.

The Level D is a little Glass Tube inclosed within a Brass Tube, fastened upon a Rule perfectly equal in Thickness, and serves to know whether a Plane be level, or not.

## Construction of a Telescope Air-Level.

This Level is like the Level C, but instead of Sights, it carries a Telescope to discover Objects at a good Distance. This Telescope is in a little Brass Tube, about 15 Inches long, fastened upon the same Rule as the Level, which ought to be of a good Thickness, and very straight.

At the End of the Tube of the Telescope, marked 1, enters the little Tube 1, carrying the Eye-Glass, and a human Hair horizontally placed in the Focus of the Object-Glass 2. This little Tube may be drawn out or pushed into the great one, for adjusting the Telescope to different Sights.

At the other End of the Telescope is placed the Object-Glass, whose Construction is the same as that before-mentioned, belonging to the Semi-Circle.

The whole Body of the Telescope is fastened to the Rule, as well as the Level, with Screws, upon two little square Plates, soldered towards the Ends of each Tube, which ought to be perfectly equal in Thickness.

The Screw 3, is for raising or lowering, the little Fork carrying the human Hair, and making it agree with the Bubble of Air, when the Instrument is level; and the Screw 4, is for making the Bubble of Air agree with the Telescope.

Underneath the Rule there is a Brass Plate with Springs, having a Ball and Socket fastened thereto.

The Level F, is in form of a Square, having it’s two Branches of equal length; at the Junction of which there is made a little Hole, from which hangs a Thread and Plummet, playing upon a Perpendicular Line, in the Middle of the Quadrant, often divided into 90 Degrees. It’s Use is very easy, for the Ends of the Branches being placed upon a Plane, we may know that the Plane is level when the Thread plays upon the Perpendicular in the Middle of the Quadrant.

This Instrument is composed of two Branches, joined together at Right Angles; whereof that carrying the Thread and Plummet, is about a Foot and a half, or two Foot long.

This Thread is hung towards the Top of the Branch, at the Point 2. The Middle of the Branch, where the Thread passes, is hollow, that so it may not touch in any Place but towards the Bottom, at the Place 3, where there is a little Blade of Silver, on which is drawn a Line perpendicular to the Telescope.

The said Cavity is covered by two Pieces of Brass, making as it were a kind of Case, left the Wind should agitate the Thread; for which reason there is also a Glass covering the Silver Blade, to the End that we may see when the Thread and Plummet play upon the Perpendicular. The Telescope 1, is fastened to the other Branch, which is about two Feet long, and is made like the other Telescopes of which we have already spoken. All the Exactness of this Instrument consists in having the Telescope at Right Angles with the Perpendicular.

This Instrument has a Ball and Socket fastened behind the aforesaid Branch, for placing it upon it’s Foot.

There are some of these sort of Levels made of Brass or iron, whose Telescope and the Cavity, in which is included the Thread carrying the Plummet, is about 4 or 5 Feet long, in order to level great Distances at once.

The Telescope is about 1 Inch and a half Diameter, and the Case in which the Thread, carrying the Plummet, is inclosed, is about 2 Inches wide, and half an Inch thick. This Case is fastened with Screws in the Middle, to the Telescope; so that they may be at Right Angles with one another: And at the two Ends of the Telescope are adjusted two broad Circles, in which the Telescope exactly turns; which Circles, being flat underneath, are fastened to a strong Iron Rule.

This Level is supported by two Feet almost like that of Figure E, Plate 12, fastened with Screws to the Extremities of the Iron Rule. Also there are two Openings, covered with Glasses, inclosed in little Brass Frames, which open, that so the Thread and Plummet may be hung to the Top of the Case, and play upon two little Silver Blades, in a Line drawn on them perpendicular to the Telescope. These Blades are placed against the Openings of the Cafe, and the Telescope is like that before spoken of, on the Semi-Circle.

All the Exactness of this Instrument consists in having the Telescope at Right Angles to the Perpendiculars drawn upon the Silver Blades.

To prove this Level, you must place it upon it’s Foot, in such manner that the Thread may exactly play upon the Perpendicular, and note some Object cut by the Hair in the Focus of the Telescope. Then taking off the Thread and Plummet, turn the Instrument upside down, and hanging the Thread and Plummet to the Hook at the Bottom of the Case, which will now be uppermost, look thro’ the Telescope at the aforesaid Object, and if the Thread exactly plays upon the Perpendicular, it is a sign the Instrument is exact; but if it does not, you must remove the little Hook to the Right-hand or Left, ’till you make the Thread fall upon the Perpendicular, both before you have turned the Instrument upside down, and afterwards. You may likewise raise or lower the Telescope, by means of a Screw. Note, Ingenious Workmen may easily supply what I have omitted in this brief Description.

The Instrument H is a little simple Level, founded on the same Principle as the three precedent ones; the Figure thereof is sufficient to shew it’s Construction and Use.

The Level I. places itself, and is composed of a pretty thick Brass Rule, about one Foot long, and an Inch broad, having two Sights of the same Height placed at the Ends of the Rule, and in the Middle there is a kind of Beam (almost like those of common Scales) for freely suspending the Level.

At the Bottom of the said Rule is screwed on a Piece of Brass, likewise carrying a pretty heavy Ball of Brass. All the Exactness of this Instrument consists in a perfect Equilibrium; to know which, it is easy: for holding the Instrument suspended by it’s Ring, and having espied some Object thro’ the Sights, you need but turn the Instrument about, and observe whether the aforesaid Object appears of the same Height thro’ the Sights; and if it does, the Instrument is perfectly in equilibrio: but if the Object appears a little higher or lower, you may remedy it by removing the Piece of Brass carrying the Ball ’till it be exactly in the Middle of the Point of Suspension, and then it must be fixed with a Screw, because, by Experience, the Instrument was found to be level.

## Construction of a Level of Mr Huygens’s.

The principal Part of this Instrument, is a Telescope a, 15 or 18 Inches long, being in Form of a Cylinder, and going thro’ a Ferrel, in which it is fastened by the Middle. This Ferrel has two flat Branches bb, one above, and the other below, each about a fourth Part of the Telescope in length. At the Ends of each of these two Branches are fastened little moving Pieces, which carry two Rings, by one of which the Telescope is suspended to a Hook, at the End of the Screw 3, and by the other a pretty heavy Weight is suspended, in order to keep the Telescope in equilibrio. This Weight hangs in the Box 5, which is almost filled with Linseed Oil, Oil of Wallnuts, or any thing else that will not coagulate, for more aptly settling the Ballances of the Weight and Telescope.

This Instrument carries sometimes two Telescopes close, and very parallel to each other, the Eye-Glass of one being on one side, and the Eye-Glass of the other on the opposite side, that so one may see on both sides, without turning the Level. If the Tube of the Telescope being suspended, be not found level, as it will often happen, put a Ferrel or Ring 4 upon it, which may be slid along the Tube, for placing it level, and keeping it so. And this must be, it there be two Telescopes.

There is a human Hair horizontally strained and fastened to a little Fork in the Focus of the Object Glass of each Telescope, which may be raised or lowered, by means of a little Screw, as has been already mentioned.

For proving this Level, having suspended it by one of the Branches, observe some distant Object through the Telescope, with the Weight not hung on, and very exactly mark the Point of the Object cut by the Hair of the Telescope: Now hanging the Weight on, if the horizontal Hair answers to the same Point of the said Object, it is a sign the Center of Gravity of the Telescope and Weight, is precisely in a Right Line joining the two Points of Suspension, which continued would pass thro’ the Center of the Earth.

But if it otherwise happens, you must remedy it, by sliding the little Ring backwards or forwards. Having thus adjusted the Telescope, that the same Point of an Object be seen, as well before the Weight is hung on, as afterwards, you must turn it upside down, by suspending it to the Branch that was lowermost, and hanging the Weight upon the other. Then if the Hair in the Telescope cuts the aforesaid Point of the Object, it is manifest, that that Point of the Object is in the horizontal Plane, with the Center of the Tube of the Telescope: but if the Hair does not cut that Point of the Object, it must be raised or lowered by means of the Screw ’till it does. Note, You must every now and then prove this Instrument, for fear least some Alteration has happened thereto.

The Hook on which this Instrument is hung, is fixed to a flat wooden Cross, at the Ends of each Arm of which, there is a Hook serving to keep the Telescope from too much Agitation, when the Instrument is using, and for keeping it steady when it is carrying, in lowering the Telescope by means of the Screw 3, which carries it.

There is applied to the said flat Cross, another hollowed Cross fastened with Hooks, Which serves as a Case for the Instrument. But note, The two Ends of the Cross are left open, that so the Telescope being covered from Wind and Rain, may be always in a Condition to use.

The Foot supporting the Instrument, is a round Brass Plate something concave, to which is fastened three Brass Ferrels, moveable by means of Joints, wherein are Staves of a convenient Length put. The Box at the Bottom of the Level is placed upon this Plate, and may be any ways turned; so that the Weight, which ought to be Brass, may have a free Motion in the Box, which must be shut by means of a Screw, that so the Oil may be preserved in Journeys.

## Construction of another Level.

This Instrument is a Level almost like that whose Description we have last given, but it is easier to carry from place to place.

• Number 1. Is the Case in which the Telescope is enclosed.
• 2. Is a kind of Stirrup, where the Screw, serving for the Point of Suspension, passes; at the End of which is a Hook, upon which the Ring, at the End of the Plate carrying the Telescope, is hung.
• 3. Are the Screws above and below for fixing the Telescope, when the Instrument is carrying.
• 4. Are the Hooks for keeping the Case shut.
• 5. Is one End of the Telescope.
• 6. Is the End of the Plate whereon a great Brass Ball 7 is hung, serving to keep the Telescope level.
• There are three Ferrels 8, well fixed to the Bottom of the Stirrup, serving as a Foot to support the whole Instrument. Note, There are sometimes put two Telescopes on this Level, as well as in that other of which we have last spoken.