335 



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. 



On a Method of examining the Divisions of astronomical Instruments. 

 By the Rev. William Lax, A.M. F.R.S. Lowndes's Professor of 

 Astronomy in the University of Cambridge. In a Letter to the Rev. 

 Dr. Maskelyne, F.R.S. Astronomer Royal. Read June 1, 1809. 

 [Phil. Trans. 1809, p. 232.] 



Since the utmost precision in making astronomical observations, 

 and in reading off 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 effected, 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 arc 

 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 arc 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 



