We will follow Professor Lax no farther in his ingeni ous and laborious examination ; suffice it to say, that, by pursuing the same principle of comparing short arcs with their multiples, he obtains the errors of every individual division of his circle, down to the ten-minute spaces into which it is graduated.
Mr Lax says, that with his microscopes and his circle of one foot radius, he cannot commit an error greater than three quarters of a second in reading off, and with this datum, and that of the number of times that some divisions have been dependent upon previous examinations, he rec kons upon a possibility of error in extreme cases amount ing to 9".63. This is a very large quantity: the truth how ever is, that the examiner not only underrates the ability and integrity of artists, but also the powers of his own method. To make out the above quantity, Mr Lax is obliged to suppose, that at every step he commits the greatest possible error, and that, in every course, the error lies in that direction which produces the greatest accumu lation. After the examinations have been completed, and the calculations made, the Professor says: The time and labour required for this examination are no doubt very considerable ; but it ought to be recollected, that it will render any great degree of precision, in divi ding the instrument, totally unnecessary. Whoever, in deed, employs this method of examination, will be virtu ally the divider of his own instrument ; and all he will ask of the artist, is to make him a point about the end of every five or ten minutes, whose distance from zero he will de termine for himself, and enter in his book, to be referred to when wanted. We may likewise observe, that, by this ex amination, we shall not only be secured against the errors of division, but against those that arise from had centring, and from the imperfect figure of the circle, and which in general, are of too great a magnitude to be neglected." Now, the greatest part of all this is certainly very true ; yet we doubt if astronomers in general will not save them selves the expellee of the apparatus, and the trouble of performing the work : and we think that they will con tinue, as heretofore, to demand of the artist the utmost ex ertion of his talents.
Professor Lax has shewn the analogy between his me thod of examination and that of observing by repetition, as much practised abroad, which is but another way of re ducing the errors of dividing. As, however, things do not easily get out of their usual course, we are of opinion, that the paper under consideration will have no tendency to re lax the efforts of the artists of this island to approach the point of truth, any more than the improvement of the art of graduation will, upon the continent, supersede the use of the repeating circle.
We are not satisfied with the inclining microscope. In or der that this should occasion no error, the plane which bears the graduation should be almost a miracle of truth. Were the microscope so fixed as to be capable of being inclined as much the contrary way, the effect of parallax would be contrary too; and if a succession of the same angle were repeated in both positions of tl:e microscope, an identity of results would prove our doubts to be groundless, or a dis agreement between them strew the thing we are afraid of.
In the second part of the Phil. Trans. for the year 1814, we meet with a paper by Captain Hater: it is called, " An Improved Method of dividing A.tronomical Circles, and other Instruments." To give a general idea of this method, which is itself ideal, is all that we think necessary ; and with it, and a ge neral remark or two, we shall close our article.
This method is extremely like that of the Due de Chaulnes: the chief difference between them is, that, in stead of the waxed pieces, Captain Kater proposes to per form the work by means of two pieces which arc to be clamped upon the elide to be graduated, and adjusted to their places each by two appropriate screws. lie would use three double microscopes, one plain with cross wires, the other two with micrometers: they are to be applied to an exterior arc exactly like that which Professor Lax used in the examination or his circle. Captain Kater leaves the manner of fixing the arc to the frame of the instrument to the ingenuity of the artist, who may practise the method ; a task by no means easy, considering the stability that would be required. The cutting-frame of Ilindley is to be used, which being property placed at one extremity of the exterior arc For tracing the divisions, the plain microscope should be fixed over the tracer, and adjusted to a line drawn with it exterior to the circles which are to bound the length of the divisions: this is called the line of verification. The fixed microscope not only regards this line and a clot upon the cutting apparatus, but also assists the cyc in tracing the divisions. This is altogether a good contrivance ; for by it the stability of the several parts may be examined at pleasure, and, if necessary, rectified. The two microme ter microscopes are also applied to the exterior arc, and have a range upon it from contact to a distance of one-fifth part of the circle. After being clamped, they have each a screw-adjustment in the line of the radius, and the ad justment for the correct angular opening is found in the micrometer wire.