on the semicircular mirror, exactly over the image of the righthand object seen on the Annex. The reading of the angle will be twice the number indicated by the half-arrow at the extremity of the Line of Sight against the number on the inner ring of the instrument, or double the reading + 100.

If the angle be smaller than 40°, it will be read off by another set of graduations marked on the brass ring, or, it is 100 double the reading.

It is to be understood that this is not a Double Sextant in the sense of the Repeating Circle, or other sextants which take two observations and realize a great angle by accumulating these two observations upon a kind of Double Instrument: such has been done in some cases by sextants with Four Mirrors, and, in other cases, with Three. The present instrument differs from those in this important respect, viz. that it takes any angle, whatever the span may be, without the aid of an intermediate object, and can, if desired, take an angle up to twice 120o, which is double the range of the sextant.

V. 1. THE SPIRIT-LEVEL.

The SPIRIT-LEVEL is constructed of a Tube of Glass externally of an exact cylindrical form; a portion of such glass tubing, the length of the intended level, is cut off and subjected to the process of internally boring on a bent steel rod; this boring being done equally and gradually all round, produces in a very slight degree a curved interior of barrel form; the result of which is, that when the ends of the tube are hermetically sealed and a quantity of Spirit of Wine is enclosed, all but enough to fill it, an Air-Bubble, as it is called, is found shut up with the liquid; and as liquids always find their own level, when this tube, cylindrical outside but barrel-formed inside, is laid on its

side, and that side is resting on a true horizontal line or plane, then the air-bubble ascending, goes to the highest part of the vessel in which it is enclosed, and is necessarily seen in the middle of this internal glass-barrel; the difference between the middle of the bore of the tube and the bore at the ends of it, so slight as to be almost ideal, is sufficient on the least declination of the cylinder from the horizontal position to dislodge the air-bubble and to cause it to move in the direction of elevation. The observer, therefore, is quite sure that, when it lies midway between the two ends of the instrument, it is then the index of the true horizontality of the tube itself; and therefore, of necessity, of the whole instrument in which this tube is properly enclosed.

When the object is merely to level a plane, as for a billiardtable, or a line, as for a wall of masonry, &c., the Polymeter can be used by either of its faces; but if the Angle of Deviation of the plane or line from horizontality be required, then must the instrument be used as a Clinometer: i. e. an instrument combining the Spirit-Level, with a graduated Limb and a Hinge-joint.

2. THE CLINOMETER.

The principal use of the Clinometer to a soldier who is sketching or reconnoitring a country, is to ascertain, with sufficient nearness to truth, the inclination of the principal slopes in his survey. It is laid down in military books that the inclination of such slopes as exceed

60° are inaccessible for infantry,

Hence it is obviously an object of great importance in the delineation of ground, whatever technical system of shading or tinting is adopted, that the surveyor should be able to note down on his plan the elevation or inclination of the chief slopes in the survey; and especially in making a reconnoissance of the incline of the roads. In order to this, the draughtsman must lay his Polymeter, standing on its edge on the ground, on some spot of average slope, the round end of the instrument facing the crest of the hill. The Spirit-Level being in the leg lying uppermost, he must raise that leg by opening the angle of the Sector until the air-bubble be in the middle of its range. When the air-bubble remains there stationary, the level is realized. The angle of inclination, the value of which is to be read on the disc, is to be noted either in his book or on the plan.

It will very much tend to the exact performance of this operation, if the draughtsman be always accompanied by a good smooth-faced walking-stick, with a crook or crutched head, which, failing a 5-feet rod, will enable him to do good work. When the ground is broken or heathery, a stick or rod will be absolutely necessary for this operation. The Clinometer, as in taking the incline of roads, may be used, roughly indeed, without one, but certainly much more efficiently with one. No man ought ever to go out surveying without a stick. It is sure to be in many ways a convenient and useful companion, and if it be also a Tripod with Ball and Socket, it will be a great assurer of accurate work; an aid also as well in taking angles and bearings as in noting the inclination of slopes. See Plate.

A Card-Clinometer with a very small plumb-bob is a very convenient little instrument, cheap and light. In wet weather, however, it would soon become spoiled, and in windy it is good

for nothing. Whatever work it does is realized by the Polymeter, by means of its Spirit-Level. It is not a separate instrument to carry or to lose, and light as the Card-Clinometer is, this Clinometer is lighter still, for it is only another use of what already exists.

3. SLOPE-GAUGE.

A Slope-Gauge differs from a Clinometer in this, viz. that whereas a Clinometer will measure an inclination, it will neither calculate a slope for you, having the base and perpendicular given, nor determine the base and perpendicular of any given slope, whose inclination it ascertains. This is effected by the use of the Metal Square with the Clinometer; a combination that enables you to find, and read off, all the parts of a rightangled triangle, when you have the HYPOTENUSE as well as the ANGLE at which that is inclined to the horizon.

A very important use of this instrument will be found in its application as a slope-gauge, in the erection of field-works, especially where rods and lines are not to be had. The engineer having determined the profile of his intended work, and what the slopes are to be, the sector must be opened to shew the supplement of their angles of inclination from the ground. With this bevel he will be able to gauge a small portion of the slope at either end of the length of the face to be constructed, and having ascertained by the trigonometer the length of the hypotenuse of the profile which will be the breadth of the slope, he will be able to trim the work to the found dimension as it proceeds. The out and inside slopes having been dressed, the other inclines will be regulated by opening the sector to shew the angles of depression or elevation of each incline; the

breadth of each slope, dependent on the base and perpendicular of the triangle of the profile, to which it will be the hypotenuse as before, having been ascertained by the instrument; so that with the Slope-Gauge alone, any field-works may for all practical purposes be as well constructed, as if there had been available the ordinary appliances of pickets and tapes or lines, and more quickly.

VI. THE GUNNER'S QUADRANT.

This is an Instrument by which the elevation of a Gun or Mortar, or Rocket Range, is regulated. This instrument may be applied either within the bore of the gun, or externally, to produce the required elevation of the gun or level of the Mortar-Bed; and in the case of a Rocket Battery, it can be applied to the rod of the Rocket, setting the angle of the Sector to the required angle of elevation, and then altering the inclination of the rods until the air-bubble be seen stationary in its proper place.

For the tables of ranges of guns of every character, of Rockets, &c. the reader is referred to the Hand-Book for Field Service, or Field Pocket-Book*; which, besides containing every thing connected with Artillery that an Artilleryman need know, has exhausted the range of practical science on Military subjects in a form so portable that any man may indeed make it a Field Pocket-Book without inconvenience.

* Parker and Son, 443, West Strand, London.