Mr Smeaton, in a paper to be more particularly noticed presently, justly remarks the want of a unity of principle in Mr Bird's method ; for he proceeds partly on the ground of the protracted radius, and partly upon that of the com puted chord ; which, as Smeaton observes, may or may not agree. Bird, without doubt, used the radius and its parts, in order to secure an exact quadrant ; but Smeaton, treating exactness in the total arc as of little value to tronomy, would, in order to secure the more essential pro perty of equality of division, reject the radius altogether, and proceed entirely upon the simple principle of the com puted chord. The means pursued by my brother, to reach the point which terminates the great bisectional arc, is the only part in which it differs from Bird's method ; and I BMA it is without prejudice that I give it the preference. It is obvious, that it is as well calculated to procure equali ty of division as the means suggested by Smeaton, at the same time that it is equal to Bird's in securing the precise measure of the total arc. It proceeds entirely upon the principle of the protracted chord of 60° and its subdivi sion ; and the uncertainty which is introduced into the work, by the sparing use which is made of subdivision by S and 5, is, in try opinion, likely to be much exceeded by the errors of a divided scale,* and those of the hand and eye in taking off the computed chords, and applying them to the arc of the instrument to be divided.
Ramsden's well known method of dividing by the engine unites so much accuracy and facility, that a better can hard ly be wished for ; and I may veilture to say, that it will never be superseded in the divisions of instruments of mo derate radii. It was well suited to the time in which it ap peared ; a time, when the improvements made in nau tical astronomy, and the gi owing commerce of our coun try, called for a number of reflecting instruments, which never could have been supplied, had it been necessary to have divided them by hand ; however, as it only applies to small instruments, it hardly conies within the subject of this paper.
The method of Hindley, as described by Smeaton, t I will venture to predict, will never be put in practice for dividing astronomical instruments, however applicable it might formerly have been for obtaining numbers for cut ting clockwork, for which purpose it was originally intend ed. It consists of a train of violent operations with blunt tools, any one of which is sufficient to stretch the mate rials beyond, or press them within their natural state of rest ; and, although the whole is done by contact, the na ture of this contact is such, as I think ought rather to have been contrasted with, than represented as being similar to, the nature of the contact used in Smeaton's Pyrometer, which latter is performed by the most delicate touch : and is represented, I believe justly, to be sensible to the part of an inch. Smeaton has, however, acquitted himself well, in describing and improving the method of his friend ; and the world is particularly obliged to him for the histo rical part of his paper, as it contains valuable information, which perhaps no one else could have written.
The only method of dividing large instruments now practised in London, that I know of beside my own, has not yet, I believe, been made public. It consists in dividing by hand with beam compasses and spring dividers, in the usual way ; with the addition of examining the work by microscopes, and correcting it, as it proceeds, by pressing forwards or backwards by hand, with a fine conical point, those dots which appear erroneous ; and thus adjusting them to their proper places. The method admits of con siderable accuracy, provided the operator has a steady hand and good eye ; but his work will ever be irregular and inelegant. He must have a circular line passing through the middle of his dots, to enable him to make and keep them at an equal distance from the centre. The bisectional arcs also, which cut them across, deform them much ; and what is worse, the dots which require correction (about two thirds perhaps of the whole) will become larger than the rest, and unequally so in propor tion to the number of attempts which have been found necessary to adjust them. In the course of which opera tion, some of them grow insufferably too large, and it be comes necessary`to reduce them to an equality with their neighbours. This is done with the burnisher, and causes a hollow in the surface, which has a very disagreeable ap pearance. Moreover, dots which have been burnished up are always ill defined, and of a bad figure. Sir George Shuckburg Evelyn, in his paper on the Equatorial,' de nominates these 4 doubtful or bad points ;' and (considering the few places he examines) they bear no inconsider able proportion to the whole. In my opinion, it would be a great improvement of this method, to divide the whole by hand at once, and afterwards to correct the whole ; for a dot forced to its place as above, will seldom allow the compass-point to rest in the centre of its apparent area ; therefore other dots made from these will scarcely ever be found in their true places. This improvement also pre vents the corrected dots from being injured or moved by the future application of the compasses, no such applica tion being necessary.
I will now dismiss this method of dividing, with observ ing, that it is tedious in the extreme ; and did I not know the contrary beyond a doubt, I should have supposed it to have surpassed the utmost limit of human patience.§ When I made my first essay at subdividing with the roller, I used this method, according to the improvement suggest ed above, of correcting a few primitive points; but even this was too slow for one who had too much to do. Per haps, however, had my instruments been divided for me by an assistant, I might not have grudged to have paid him for the labour of going through the whole work by the method of adjustment ; nor have felt the necessity of contriving a better way.