In describing the apparatus, Mr. Cavendish has not entered further
than was necessary to explain the principle, and has left the com-
pletion of it to the skill of any artist who may choose to adopt
it.
Since the utmost precision in making astronomical observations, and in reading OK the indication given by any instrument, will be of no avail if the instrument itself be not divided with proportional ac- curacy, the author felt the importance of estimating the probable amount of errors that might occur in Bird’s method of dividing by continual bisection, and has also contrived a method of examining the divisions of any circle, and of measuring, within certain limits, the actual errors in every part of it.
The apparatus by which this examination is efi'ccted, is first mi- nutely deScribed, and consists of a brass arc, rather more than 90° in length, placed concentric with the circle to be examined, and firmly attached to the frame which supports the microscopes. On this are an upright pillar is made to slide, carrying a micrometer microscope, which may thus be fixed at any distance not exceeding 90° from one of the microscopes belonging to the circular instrument; and as the position of the micrOScope is inclined, it may be made to point to the same division upon the circle that is under the micrometer itself.
In the process of examination which follows, the position of the point of 180° having been first ascertained by means of the opposite micrometers belonging to the instrument, the arcs of 90° on each side are next examined by the moveable microscope, and the errors noted accordingly + or —. The microscope is then placed at the distance of 60° from the micrometer, and the first sextant is thus compared with every succeeding arc of 60° in the circle; and in the same manner, the first octant is compared with every succeeding arc of 45°, and the first are of 30° with so many of the succeeding arcs of 30° as are necessary for determining each 15° of the whole circle.
The next intervals employed by Mr. Lax are those of 5° and 3", from which, and from their multiples, the value of 1°. 2°, and 4°, are derived; and, in a similar manner, all the succeeding intervals down to the smallest interval to which the circle happens to be divided.
However, since the method of examination itself is liable to some error, the author computes the extent to which this may possibly amount; and upon a circle of one foot radius, he finds the greatest aggregate error to which he could be liable, in points most remotely deduced, might be 9"‘63: but in a circle of three feet radius, the error would be reduced to 3"'21 ; and with glasses of higher magni- fying power, and by frequent repetition of the reading off. the true
