" Mr Mayer made his observations with his six-foot mu ral arch, from the year 1756 to the time of his decease : with it he settled the mean obliquity of the ecliptic, to the beginning of the year 1756, at 23° 28' 16" ; which Dr Bradley settled by his observations, made in the year 1750 and 1751, at 23° 28' 18". The difference is agreeable to what ought to arise from the gradual diminution of the obliquity of the ecliptic at the rate of about 3 a second in a year," Sce. That two different observers, with instruments of different radii, and in different parts of Europe, should so nearly agree, is matter of no small astonishment, and sufficiently proves, that a mean of several observations, made by good observers, with accurate instruments, pro perly adjusted, will always lead us either to the truth itself, or extremely near to it.
Excepting the means of rendering the common subdivi sion of the circle bisectional, and his care in avoiding er rors from expansion, Bird's method of cutting the strokes was its most important deviation from the practice of Gra ham. The latter made his dots in the tangential line, which supported the resting point of the compass, while the other point, at a considerable distance, traced the divi sions. Bird, by making his dots extremely near to the outer ends of the strokes, and resting the point in an undivided tangential line, avoided any error that might arise from an alteration of the length of the beam duting the operation, which was a serious objection to Graham's way of proceed ing. We should, however, have been afraid that the rest ing point, on being simply dropped into the line, and having apparently nothing to hold it there, might have been in danger of slipping, did not we know that artists themselves, provided the metal be sound, are apprehensive of little or no erior on this account.
Soon after the publication of Bird's method, that of the Duke de Chaulnes made its appearance, which has in the preceding Section been noticed as applicable to a dividing engine. He was the first who employed double microscopes in the graduation of the circle ; a practice which, in the hands of others, the Duke's work, known or unknown to them, has essentially improved the art. There are also two more peculiarities in De Chaulnes' method, that de serve to be noticed. One is its being purely visual. The whole is done by the eye, except cutting the real divisions; and even this, to prevent the errors of the hand, is perform ed by machinery. The other is, that, to avoid superfluous marks upon the limb, he had provided, ready for his pur pose, a competent number of thin pieces of brass, about one third of an inch long, and one-sixth broad, with a fine line upon the surface of each, drawn perpendicular to its length.
To make these pieces adhere to the surface that was to re ceive the divisions, their under planes were thinly coated with wax, and thereby made capable of being easily adjust ed to their places, and of retaining that position until the divisions represented by them were inserted.
The circle to be divided moves round horizontally upon a vertical axis, within a strong frame of wood, to which the microscopes are fixed, and applicable to any part of it.
The first step is, to bisect the circle. To this end one of the brass pieces is to be made fast with screws, at the place which is intended to be zero, the line upon its sur face being directed towards the centre. A microscope is affixed to the frame, with its radial wire coincident with the line, and its cross one a tangent to the circle. Another mi croscope is secured on the frame, by estimation or any better way, diametrically opposite to the first, and one of the waxed pieces placed under it, so that the line and wires may have to each other, and to the circle, the same rela tion as above. Let the circle be turned half round within the frame, so as to bring the zero line coincident with the radial wire of the other microscope. if now the line of the waxed piece be found exactly tinder the wire of the first microscope, it is evident that the circle is bisected ; but as this can hardly happen in the first instance, the apparent error must be corrected one half, by sliding the waxed piece towards the wire, and the other half by moving the microscope to it. The circle must again be turned half round, to verify the correction, or, if necessary, to afford means for a second correction, and the operation repeated until the lines exactly coincide with the wires in both posi tions of the circle. This being done, the microscope which has under it the zero piece should be regarded as fixed, and let its name be A ; the other, which we will call B, is to be taken off, and reserved for future use. In the room of B there is to be fixed the tracer or cutting point, so that if the piece were taken off, which it must not be, the tracer would cut a line exactly in its place, or diametrically oppo site to the zero line. By this contrivance, it becomes ne cessary only to divide hall the circle ; for if the divisions of one semicircle are brought successively to the wire of A, the tracer will cut their opposites in the other.