It has already been said, that Bird's construction of Mayer's circle is, in till:, respect, preferable to Borda's; the latter is indeed very inconvenient, because with it an observer has to read the divisions of the two sliders, by which the height of the telescope, from the plane of the circle, is regulated ; for should he, while observing, at tempt any alteration, by using the two screws to suit the objects as their brightness varies, and happens to turn one of them more than the other, he would derange the parallel position of the telescope, and thereby render his observations of no value. The circle of Borda is, in many respects, mechanically defective ; that highly im portant part, the centering of the indices, is very much so, for they move round the circle upon bearings no lon ger than their own thickness; and, consequently, want that steadiness which is derived froin an axis.
The author of the reflecting rircle now under conside ration, had many reasons for furnis' its nl • index n s o swith three verniers. In the first place, he was ch_sirous that as the repeating principle had been abandoned, some contrivance should be substituted for tu.: purpose of re ducing the errors of ever: good dividing. Three read ings which, upon the principle of taking means, in a cross ed observation, (a term we need no longer employ), pro bably reduce the error of dividing to one sixth part of its simple value ; while, at the same time, they perfectly cor rect the error arising from any eccentric motion or the index. This kind of error, a very important one, is never entirely corrected in Borda's circle, except in the case of beginning and leaving off at the same point ; for, should the repetitions be continued to more than a complete round, the error which at that point must have vanished, would be again generated. Moreover, the three read ings, when the angle measueed is the sextantal one (120°) in a backward and forward observation, (answering to right and left in the other constructions,) will just occupy the 720 degrees of this circle.
It might have been sooner noticed, that the degrees of this circle are subdi aided into three parts of 20' each, and that each branch or the index subdivides to 20", the verniers having 60 divisions, whose lenzth is equal in ex tent to 59 of those upon the limb.
The dark glasses, in sets of three, are fixed to the instrument in such a manner, that any or all of them may be used at the same time, as circumstances may re quire. This gives the circle before us a decided supe riority over all the others. Nor is it a matter of small importance, with respect to convenience, that a handle is found both above and below : By one or other of these, in every possible position of the instrument that obser vations can require, it may be held right or left, as is found most convenient to the observer. It must, how
ever, be acknowledged, that the reflecting circle is, un der the best circumstances, held two or three inches far ther from the observer than the sextant is, and, of course, bears proportionally heavier upon his arm. Mr Trough ton is of opinion, that this inconvenience is the princi pal if not the sole cause, that the circle has not yet come into general use ; but we would hope, that an in convenience so trifling, cannot deter a good officer from exercising the best meaty of obtaining the truth ; espe cially, when we consider how much is entrusted to his care, and that the safety of the whole depends, in a great degree, upon in a long voyage, a few points of longitude and latitude, upon which, with confi dence, he can rely.
We arc given to understand, that our present astrono mer royal is a warm friend to the circle ; and that, in the preface to the next publication of Nautical Alma nacks, he intends to recommend this instrument. From the regard we have for the improvement of nautical sci ence, we sincerely wish that Mr Pond's endeavours to ex tend the use of the reflecting circle may be as successful as he can desire.
The following instructions for adjusting and observing with Troughton's reflecting circle, may be acceptable to many of our readers. They are copied from a printed paper, which is usually given with the instrument.
Directions for Observing with Troughton's Reflecting Circle.
" Prepare the instrument for observation by screwing the telescope into its place, adjusting the drawer to fo cus, and the wires parallel to the plane, exactly as you do with a sextant : also set the index forwards to the rough distance of the sun and moon, or moon and star ; and, holding the circle by the short handle, direct the telescope to the fainter object, and make the contact in the usual way. Now read off the degree, minute, and second, by that branch of the index to which the tangent SCITW is attached; also, the minute and second shown by the other two branches ; these give the distance taken on three different sextants; but as yet, it is only to be considered as half an observation: what remains to be done, is to complete the whole circle, by measuring that angle on the other three sextants. 'Therefore set the in dex backwards nearly to the same distance, and reverse the plane of the instrument, by holding it by the oppo site handle, and make the contact as above, and read off as before that is shown on the three several branches of the index. The mean of all six is the true apparent dis tance, corresponding to the mean of the two times at which the observations were made.