ADVERTISEMENT.

THE following remarks have been written and printed under various difficulties, and amongst many engagements. The Author's residence abroad while these pages were brought out in England is but one of these difficulties. The engagements are of a private nature, and are only alluded to as serving for an apology for the long delay that has occurred in the publishing of the following short Grammar of the Polymeter, as well as for its incompleteness at last. It had been intended to make it fuller, so as to enable the officer, or any other owner of the instrument to work with it sufficiently for practical purposes, without the help of any other book of Geometry or Trigonometry, and independently of a number of Tables which are necessary with other instruments. This design it is hoped will be more nearly attained with the additional help of a Second Part, with which the Author is proceeding, while the present published part will be enough to guide those who have already some slight knowledge of Trigonometry and Surveying in using this instrument with satisfaction to themselves, and with efficiency.

One or two features or applications of the instrument must be noted here, as they can hardly be said to come under any of the heads into which the following pamphlet is divided.

The reader will observe two screws, one in the lower part of each of the mirrors. Their object will be easily perceived, viz. to correct the mirrors' positions if they are not perfectly perpendicular. In the case of the large mirror it will be the more easily done, because the eye can judge with great accuracy of the perpendicularity by looking at the reflection of the disc in it. If this seem to carry on the outline of the disc itself without a break, so that the image on the mirror completes the circle of the hinge, the mirror will be perpendicular. This, of course, assumes that by the construction of the instrument, the diameter of the ring of the hinge is truly in the face of the mirror. Great care is taken in the manufacture that this shall be the case. The perpendicularity of the mirror of the Annex will be ascertained by comparing the images of distant objects in the two when the instrument is in the position to observe the angle 0. There will also be seen a screw running obliquely through one of the sheaves of the hinge; by turning this, the mirror will receive a slight motion round its own centre, in order to correct any accidental deviation from the proper position with respect to the zero point, i. e. to correct mechanically index error. If the mirror be properly adjusted in this respect as well as in perpendicularity, when the instrument is close and the mirror erected, the lines of the image on the mirror will carry on exactly the outlines of the instrument, as seen at the side of the mirror.

There is an application of the instrument when furnished with the Annex in addition to the hinge-mirror, which will prove useful to yachtsmen and sailors.

Supposing a man to be sailing upon a point, and that he desires to anchor his ship in a straight line between some other two points. He will expand the instrument as the double Sextant, so that it commands the angle 180°, and keeping the right-hand object in view in the annex, sail forward until the left-hand object come into view on the other mirror, then letting fall the anchor, the ship will be exactly in a straight line between the objects.

Other uses will present themselves immediately to the navigator whereby much labour in computation and inconvenient reference to books and Tables will be dispensed with. Some of these it is hoped will be illustrated by examples in the Second Part of this little Work.

The use of the Annex will be rendered easier if the observer will mark with a pen or the point of a knife the place on the vernier of the instrument which is opposite the point 90°, when the instrument is set so as to observe the angle 0. For various reasons it has been thought better to leave the slighter trouble to the observers than to have such a mark fixed by the maker. The reading of the disk at the point so marked will readily give the complement of the angle, to degrees, in any observation, and the subdivision of the degree must be obtained by computation from the vernier, i.e. adding the reading that the vernier presents when the instrument is set for the angle 0.

It was stated above that this work had suffered much delay from the many engagements of the writer, but a further cause of delay has arisen from the fact of various improvements having suggested themselves while these pages were going through the press, one of these, and a very important one, is due to the Rev. John Glover, M. A. Trinity College, Cambridge.

These improvements were such, that in the consciousness of the augmented capabilities of the instrument so modified, it became impossible for the inventor conscientiously to present it to the public for sale, or to officers for use, without apprising them of the fact, and giving to all the opportunity of availing themselves of them.

These improvements have necessitated new improvements and new lines of graduation in the instrument, which has been an additional source of delay.

It may, perhaps, be suggested, that it would have been better not to have offered the Polymeter to public attention until it had been complete. To this the inventor would reply, that it was complete as a Sextant, it took a larger angle than any other pocket Sextant, and took it more exactly. Had the

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annex never been thought of, it would still have been a good Sextant. To its having been thought of however, and with much trouble elaborated, is due the fact of the instrument being advanced to the character of a Double Sextant.

Those who wish for the Single Sextant may still have it. The Quintant in fact with the Annex is another instrument, it is in effect a double, not an improved Sextant; it may be