\Ve shall close our observations on the reflecting circle with some account of the laudable endeavours of the gentleman, whose name has just been mentioned, to im prove it, and to render it a companion worthy of his other nautical labours.
In a paper published in the Phil. Trans. for 1800, Captain Mendoza has described, at considerable length, one construction, and briefly mentioned others, all of which, however, lead only to extend the repeating prin ciple. \Ve shall confine our account to that which, to ourselves, appears to be the best, and we refer to thc pa per itself for farther information. It is offered as an apology for not having given a figure of this circle, that it is easy to describe its peculiarities in words, but ex tremely difficult to make than appear in a drawing.
The general fabric of this circle is, respecting the frame, position of the glasses, and handles, exactly as in Troughton's construction, to which the repeating pro perty has been restored in a very ingenious manner, and so as to produce double the effect that is done in Borda's, by collecting the sum of backward and forward motion of the index into one reading. For this purpose, there have been added two very light circles, one of which he calls a flying circle, and the other a flying nonius. They are both centred upon the upper end or the socket, which receives the axis of the proper index, and of the great mirror. 'l'hc motions of these two circles are free and independent of each other : they arc situated one above the other close to the limb of' the fixed frame, having no connection whatever with it, except at the centre. It will be remembered, that, in the former construction, the in dex with three branches had backward and forward mo tion ; it is precisely so in this, only this index has but one branch, namely, that with the screws for quick and slow motion. This index carries no vernier, nor are there any divisions upon the limb of the fixed frame to which it applies. The graduation is made upon the flying cir cles, the lower of which is divided into degrees, and every 2ki; the upper one carries opposite verniers, sub dividing the low er (i015 i 1 to 20". There is a clamp at
tached to the index, which lays hold of the flying nonius, and in an observation forwards carries it along of er the face of the flying circle ; and there is a similar clamp, which. laying hold of the flying circle. in an observation backwards, carries it hack under the flying Hollins. The flying circle is, in the ft.irmer case, clamped to the limb of the fixed frame, and in the latter, the nonius is secured in the same manner.
Now, as in the observation forwards, the nonius ad vances upon the circle, and in the one backwards, the circle recedes upon the nonius, it is evident, that the sum of the two motions will be given at one reading off. Instead. however, of reading here, forward and back ward observations are to be repeated, until a sufficient set has been procured, and then the whole space that the circle and nonius have been moved respecting each other may be read off, and on being divided by twice the num ber of forward and backward motions together, will give the required angle. There are two sextants of coarse divisions made' upon the fixed limb, whose zeros are dis tant from each other by the breadth of the index of the index glass ; contiguous to these divisions slide two pie ces, wnicle being set right and left to the angle about to be measured, will stop that index in the requisite posi tions for finding the objects ncariy together in the field of the telescope. This useful contrivance enables an ob server to take a set of sights of any number without look ing at the divisions, the first and last excepted.
Mr Troughton first applied this neat contrivance to the circle of Borda, which, without it, is extremely in convenient to use. It ought to have been mentioned in the account of that instrument, that a previous rough observation must be made for computing at what points upon the limb the two indices must be set, in order that the objects may be found together in the field of view ; and it requires the observer, at e% cry successive sight, to set the indices alternately to the computed angle ; but, with this apparatus, a set may be taken in the dark.