404 Determination of the Errors of Division [Aug. 



employing a large number of divisions, and by occasionally shifting 

 the zero point of the instrument to another set of divisions ; 

 the employment of several divisions at each observation is objec- 

 tionable only as far as regards fatigue, and loss of time to the ob- 

 server ; but to the shifting of the zero point there are objections to 

 be urged of a much more serious nature ; it is true, in the determi- 

 nation of fixed angles, such as the altitude, or north polar distance of 

 the fixed stars, the plan of shifting the zero point of an instrument is 

 applied with some advantage, but in the determination of the 

 ever-changing places of the sun, moon, and planets, the shifting of the 

 zero point is of no avail whatever; and in the determination of parallax, 

 of the coefficients of aberration, nutation, &c. to which a good set of 

 observations are applicable, the plan cannot be employed at all. With 

 this view of the subject, since the erection of the Madras Mural Circle, 

 in January 1831, I have employed the circle without shifting the zero 

 point : and this circumstance, added to the fact of the division of this 

 instrument having been effected upon an entirely new plan, rendered it 

 very desirable that some knowledge of the amount of error of division 

 should be obtained ; accordingly I set to work as follows. 



It is well understood that parallel rays of light after passing through 

 an object glass, converge and meet eventually at a point which is called 

 the principal focus : the converse of this is, that rays of light which 

 diverge from the focal point after passing through the object glass 

 will pursue a parallel course, and hence will appear distinct when 

 viewed through an astronomical telescope adjusted to the solar 

 focus. To be better understood in what follows, I must here refer to the 

 description of the Madras Mural Circle given in volume I. of the Re- 

 sults of the Madras Observations for 1831 : it is there stated, that " the 

 telescope is furnished with an axis of its own, which works into the 

 axis of the circle ;" hence it will appear plain that the telescope being 

 undamped at the two ends from the circle, it moves on its own axis 

 independently of the circle, or on being clamped to the circle, it moves 

 with it at pleasure. Thus much being premised, I clamped the circle, so 

 that corresponded with the zero of the reading microscope A, and 

 read off B, the opposite microscope ; I then directed the telescope to 

 the object glass of a Dollond's five feet achromatic, in the focus of 

 which I had previously fixed a pair of lines crossing one another at an 

 angle of about 30° ; these lines which were distinctly seen, were bisect- 

 ed by the movable wire of the telescope, the telescope being first 

 firmly clamped to the circle ; the circle was now loosed, and moved 

 with the attached telescope to the object glass of another telescope, (a 12 

 inch theodolite telescope for want of a better,) the cross wires of which 



