After the above paper was published, several gentle men were of opinion, that the celebrity of Troughton's graduation was owing more to the hand and eye of the artist, than to the method by which it was effected. Troughton, it will be remembered, in one part at least of the paper, expresses himself of a contrary opinion ; and, to shew that he was not mistaken, we insert the following letter, which was addressed to him by a rising artist, who is not too conceited to profit by the skill and experience of a veteran in the art: Dear Sir, " Charing-Cross, 15th July, 181S.
Having now performed the graduation of a circle by your method, I take the liberty of addressing to you the following lines upon the subject. The method which was used at Mr Ramsden's was, before youi's ap peared, considered as the best. I learned it in the course of instruction, and practised it with patience and perseve rance, for it requires much of both. I may, therefore, be allowed to consider myself a competent judge of the two methods ; and, without presuming more than becomes me, give an opinion concerning them. From various motives, I feel great pleasure in saying, that dividing by the eye is greatly preferable to the other method ; the saving in time is very great, and accuracy in the result certain. With these properties, which it possesses in the first degree, were I debarred from using it in future, I should return to the old method with the greatest reluctance. I do not hesitate to say, that I feel myself equal to the dividing of a circle with a degree of accuracy equal to any one except yourself, (nor do I think I should be very far behind you); and I shall solicit that practice, which alone can make me quite your equal in the art. With many thanks for your liberal communications upon this as well as other sub jects, I am, Dear Sir, your most sincere and obliged To Mr Edward Troughton. THOS. JONES.
A paper by the late Henry Cavendish, Esq. called An improvement in the manner of dividing Astronomi cal Instruments," was published in the second part of the Phil. Trans. for 1809. Mr Cavendish introduces his im provement in the following words : " The great inconvenience and difficulty in the com mon method of dividing, arises from the danger of bruis ing of the divisions, by putting the point of the compass into them, and from the difficulty of placing that point mid-way between two scratches very near together, with out its slipping towards one of them ; and it is this im perfection in the common process, which appears to have deterred Mr Troughton from using it, and thereby gave rise to the ingenious method of dividing described in the preceding part of this volume. This induced me to con
sider, whether the above-mentioned inconvenience could not be removed, by using a beam compass with only one point, and a microscope instead of the other ; and I find that in the following manner of proceeding, we have no need of ever setting the point of the compass into a divi sion, and consequently that the great objection to the old method of dividing is entirely clone away." To this end, Mr Cavendish to have * frame for supporting his beam compass, that shall rest upon the circle to ho divided, and which, by bearing against the edge of the latter, may be turned round without altering its distance from the centre. The figure of this frame is triangular, and nearly as large as the circle itself. One of the angles is placed outwards, and the opposite side forms a chord of about 150° to the circle. One end of the beam compass is attached to the outer angle of the frame by a vertical joint, round which it may be turned from ene side to the other at pleasure ; and the joint must be moveable in the direction of the radius, in order that the beam may be adjusted so as to form the chords of different arcs. At the opposite end of the beam is a fixed point, wherewith faint arcs are to be cut across the line of division, and with which the divisions themselves are finally to be made. There should be a groove or slit cut out all along the beam, in which a double microscope with cross wires is to slide, and which may he fixed at any required distance from the point. Two props, one to the right and the other to the left, are to support the end of the beam opposite to the joint in the two positions.
With this apparatus, Mr Cavendish chews how to per form the different operations required in graduating an instrument, namely, to bisect, trisect, and quinquisect ; but does not follow the subdivision through their repeated courses.