Sir George Shuckburgh's 5 feet standard .000165 General Roy's scale of 42 inches .000240 Sir George's equatorial, 2 feet radius .000273 The Greenwich quadrant, 3 feet radius .000455 Mr Aubert's standard, 5 feet long .000700 *The Royal Society's standard, 92 inches long .000795 For the justness of the above statement, I consider my name is pledged ; requesting the permission to say, that if, on the result of each respective examination, as here pre sented, there could have been more than one opinion, it would not have appeared here. I am farther prompted to add, that the above comparative view presents one circum stance to our notice, which cannot do less than gratify eve ry individual, who is at all conversant in these matters ; I mean, the high rank which General Roy's scale takes in the list ; that scale having been made the agent in measur ing the base line of our national trigonometrical survey.
To return, finally, to the dividing of circles ; I must state, as matter of precaution, that great care should be taken during the turning of the outer edge, to have the circle of the same temperature ; for one part may be ex panded by heat, or contracted by cold, so much more than another, as to cause the numbers in the tables of errors to be inconveniently large. A night is not more than sufficient for allowing the whole to take the same temperature, after having been handled by the workmen ; and the finishing touch should be given within a short space of time. But, if the effects of temperature are to be regarded in turning a circle, it is of tenfold more importance to attend to this circumstance, while the examination of the larger arcs of the instrument is carried on ; for it is absolutely necessary, that, during this time, the whole circle should be of the same heat exactly. Few workmen are sufficiently aware of this. They generally suppose the expansion of metals to be a trifle, which need not be regarded in practice ; and wonder how the parts of a circle can be differently heated, without taking pains to make it so. One degree of Faren heit's thermometer indicates so small a portion of heat, that, in such places as workmen are usually obliged to do their business in, it is not very easy to have three thermo meters attached to different parts of a large instrument, showing an equality of temperature within that quantity : Yet so necessary is correctness in this respect, that if a cir cle has the vertex one degree warmer than its opposite, and if this difference of temperature be regularly distri buted from top to bottom, the upper semicircle will actual. ly exceed the lower by 2": And, if such should happen to be the case while the examination of the first dot of the third quadrant is made, the regularity of the whole opera tion would thereby be destroyed.
It may not be improper to remark, that dividing by the eye does not require a more expensive apparatus than the operation of dividing by hand ; and, indeed, less so when the scale of inches is deemed necessary. The method by adjustment is still more expensive, requiring whatever tools Bird's method requires, and, in addition to these, a frame and microscopes, somewhat similar to those for di viding by the eye.
It is somewhat more difficult to give a comparative esti mate of the time, which the different methods of dividing require. I know, that thirteen days of eight hours each are well employed in dividing such a circle by my method; about 52 days would be consumed in doing the same thing by Bird's method ; and I think I cannot err much, when I state the method by adjustment, supposing every dot to be tried, and that two thirds of them want adjusting, to re quire about 150 of such days.
The economy of time, (setting aside the decided means of accuracy,) which the above estimate of its application offers to view, will, I think, be considered of no little mo ment. By the rising artist, who may aspire to excellence, it will at least, and 1 should hope with gratitude, be felt iu the abbreviation of his labours. To me, indeed, the means of effecting this became indispensible ; and it has not been without a sufficient sense of its necessity, that I have been urged to the progressive improvement and completion of these means, as now described. It is but little that a man can perform with his own hands alone ; nor is it on all oc casions, even in frames of firmer texture than my own, that he can decisively command their adequate, unerring use. And I must confess, that I never could reconcile it to what I hold as due to myself, as well as to a solicitous regard for the most accurate cultivation of the science of astro nomy, to commit to others an operation requiring such various and delicate attentions, as the division of my instru-, m ents.
That my attentions on this head have not failed to procure for me the notice and patronage of men, whose approba tion makes, with me, no inconsiderable part of my reward, I have to reflect on with gratitude and pleasure : and as I look with confidence to the continuance of that patronage, so long as the powers of execkition shall give me the in clination to solicit it, I cannot entertain a motive, which might go to extinguish the more liberal wish of pointing out to future ingenuity a shorter road to eminence ; suf ficiently gratified by the idea of having, in the present com munication, contribud to facilitate the operations, and to aid the progress of art, (as far as the limited powers of vi sion will admit,) toward the point of perfection." It can hardly have escaped notice, on perusing the above account, how strictly Troughton has adhered to the MaXiln of Graham. Beginning with bisecting the circle, he has, by his mode of examination, without a change, followed the principle through eight successive courses. The ac tion of the roller is stepping, notwithstanding that it con sists of the exactest species of contact, and closes with out a remainder ; and so fully is he aware of this, that 256 checks are employed. As far as the examination and com putation is carried, Troughton's method, for aught we know, may be as tedious as any other; but, by the con trivance of combining his subdividing-sector with the roll er, he throws the quinquisections and trisections altogether into a species of engine dividing, and thereby reduces the remaining part of the work to a labour little surpassing that of cutting the divisions.