considered another instrument, although the form, bulk and weight remain unchanged.

The same may be said of the Sun-Dial and the Curve which shews the Equation of Time. Those who prefer the instrument in its former condition, without those graduations and notations necessary to shew the Time and to correct it, may have it, but as neither bulk nor weight are increased by these marks, others may prefer to have them. The instrument was however complete before these additions; they are a convenient addition, just as the repeating works of a Repeater are to the complete works of an ordinary watch.

As might be expected, the improved instrument is dearer than the original one. The Annex makes it £2 dearer, the Telescope £1, the Tripos £1. 10s. dearer.

Those who expect a cheap instrument because the Polymeter is a multum in parvo will be disappointed. It is unreasonable to expect that two, three, or more complete instruments can be furnished at the cost of one. The cost of an instrument depends less on the cost of the materials, than on the difficulty and nicety of the work. Indeed the expense of making the compound instrument is more than the sum of the expenses in making its component parts, owing to the necessary expense in insuring their proper adjustments.

It may be well to specify here all the instruments which the Polymeter in its complete form combines, though its weight is but 14lbs., its dimensions only 7in. of length, 3 of breadth and in. of thickness. These are as follows: 1. Sextant. 2. Double Sextant. 3. Surveying Magnetic Compass. 4. Level. 5. Arti

ficial Horizon. 6. Dial. 7. Scales. 8. Protractor. 9. Thermometer. 10. Gunner's Quadrant, and 11. Callipers, brought into the size and shape of a thin memorandum-book, which its cover forms, besides being, 12. Trigonometer, an instrument nowhere else to be found, and which is perhaps the most useful instrument of all to the man who has occasion to exercise himself much in Heights and Distances, and to avail himself therefore of a mode of doing "Trigonometry without Logarithms."

If a man wants only one or two of the above, but not all, he can please himself. A pocket Compass and a Sextant will however weigh more, and be of greater bulk. He will also lose the value of their combined use, the two together forming an Universal Dial. Neither will these two instruments supply him with a Protractor, Double Sextant, Scales, and the " Trigonometry without Logarithms."

In conclusion, the author would only express his firm conviction that no one who may purchase the Instrument and learn to use it, will find that he has cause to regret the money expended on it.

PART I.

THE USES OF THE POLYMETER.

I. OF THE SECTOR.

WITH the instrument known by the name of the Sector, this Polymeter Sector has very little in common but its form: viz. two rulers combined with a hinge-joint, constituting, when folded, a six-inch rule; and, when opened out from each other to their fullest expansion, a twelve-inch or foot rule.

The ordinary Sector, besides various Trigonometrical Lines graduated on its two legs, has a graduation commonly called the Line of Lines; which are radial lines drawn from the pivot of the hinge-joint, along the faces of the legs of the Sector on one of its sides. And whereas these lines are found, in the common Sector, on the face of the legs, remote from their edges, in order to apply conveniently the points of a pair of compasses, without which auxiliary, the Sector itself is almost useless,—in the Polymeter Sector, on the contrary, these lines, or this Line of Lines, will be found drawn on the inner edges of the faces of one side of the legs of the Sector: the compasses being rarely used, as never being necessary for the purposes for which this instrument is intended. The Line of

Lines is simply two similar scales of equal parts. In the Polymeter, they are 6 inches, divided into half-inches and numbered from 1 to 12; the inch being graduated into 20ths of an inch, and the Half Inch therefore into 10 ths.

The nature of the graduations which are peculiar to the Polymeter Sector, and which occupy the space hitherto devoted to the Trigonometrical Lines, will be described when their use is shewn in sections XII. XIII. XIV. and XV.

It is no peculiarity of this instrument that it should be 12 inches English in length. That length has been assumed as being most convenient. Made for German use, it might be

a German foot in length; for French use, an old French foot or some convenient fraction of the French metre: for some purposes, e. g. for the artillerist's use, of 9 inches length, as giving him a metre of 27 inches for his various occasions: but as six inches is a more handy length than nine, and is sufficient for ordinary use, that length has been maintained for the Englishman's METRE of METRES.

In order to carry on the description of the Polymeter in the classification which takes the Sector and its uses in the simple form, before its application to its contemplated uses in combination with the MIRROR LEVEL and NEEDLE is gone into, the Gunner's Calibres next must be described.

II. THE GUNNER'S CALLipers.

This is an instrument by means of which the diameter of shot and shell can be measured. It is a pair of bow-legged compasses. The new character of ordnance, e. g. shell of 18-inch diameter, has necessitated the introduction of Callipers of the

awkward length of 15 inches. The work is more effectively done by the Polymeter, which not only calibres the largest ordnance but every other circular substance, round timber, casks, &c., while it will, with great exactness, measure the smallest substances as well, e. g. round wire in its various sizes, and also rope, cable, &c.; so that, with a table of relative strength of such commodities, the soldier will be able to tell to what extent, or strain, any such material as he may have at hand may be trusted, whether in heaving, dragging, drawing, binding, or lifting weights.

This use of the Polymeter Calibrers is thus effected:

1. Open the legs of the Sector so that, with the edge of the disc, the object to be calibred within them may be touched or tangented by it. 2. Close the legs until the ball or cylinder be, in like manner, tangented also by the legs: the operation is then done. 3. The result, in length of the diameter, in inches, or in weight of the shot in pounds, will be read off on that part of the disc which is graduated with unequal divisions. If diameter be wanted, the dimension will be observed on the numbers which read from inch to 18 inches; if weight in

pounds, on those from 3 to 68.

Should any one desire to use the instrument for very small dimensions as a wire-gauge, or for very large circumferences, as for instance, a brewer's reservoir, the Heidelberg tun, &c., he may make his own scale, by observation, in the application of the Vernier Scale. As for example, if he finds that the cask of 8 or 18 feet diameter expands the legs of the sector to (say) 73°. 56', he must make a note of that contact in his pocket-book for use at a future time; if a wire of (say) of an inch thick is gauged by 1°. 45', he must make his own scale of such contacts. The Polymeter Calibre is only graduated to suit the ordinary ⚫ uses of the Artillery Man or Officer of the Line. For small