INTRODUCTION. XXIX 



brought to bisection in a similar manner. Two other readings of the azimuth circle were made 

 \vith i In- microscopes to the north; and the mean of the four readings showed the division to 

 which the vernier of that circle should be set, in order that the plane of the vertical circle should 

 be at right-angles to the magnetic meridian. 



Moving the vertical circle 90 in azimuth, it coincided with the plane of the magnetic me- 

 ridian, and the needle directed itself approximately to the inclination. Let us suppose the 

 needle at rest, with its marked side next the microscopes, and to the east. By means of the 

 tangent screw, the central lines of the microscopes were then alternately brought to bisect its 

 ends, and three readings of the vertical circle were noted for each pole, the needle being raised 

 and gently lowered to the agates between the pairs of readings. Then turning the microscopes 

 180, so that the upper became the lower one, three similar pairs of readings were obtained ; 

 and the vertical circle being moved 180 in azimuth, like numbers of readings were made with 

 the same formality. 



Next, the axle of the needle was inverted on its supports, so that the marked face was away 

 from the microscopes. Six other readings being made, the face of the instrument was again 

 turned to the east, and the first series closed by an equal number of readings in reversed posi- 

 tions of the microscopes. 



By means of the bar-magnets the poles of the needle were now reversed. One of the former 

 was held in each hand in a nearly vertical position, and drawn from the axle to the extremities 

 of the needle, usually about ten times, when the latter was turned over in the wooden frame 

 holding it, so that the other flat side became uppermost; and in this position the bar-magneto 

 were drawn over it a like number of times. Care was taken to draw the north pole of the bar- 

 magnet from the axle to the extremity of the north pole of the needle, and the south pole of the 

 other bar-magnet in the opposite direction from the axle. 



Twenty-four readings, made, as were those of the first series, in inverted positions of the mi- 

 croscopes and needle on the agates and reversed face of the vertical circle, completed the experi- 

 ments. By readings under so many changes we eliminate, errors which might arise from 

 deviation of the line joining the zero points of the circle from the horizontal and excentricity of 

 the microscopes, inclination of the magnetic axis to the axis of form, and non-coincidence ot the 

 centre of gravity with the centre of motion. 



Very shortly after commencing the experiments, it became evident that the axle of one of 

 the magnets had been injured. There was not leisure at the time to investigate with the requi- 

 site care which was the defective one; but the observations were continued throughout with 

 both magnets, and all are inserted, however discordant. On returning home, it was found that 

 the axle of magnet A 1 was bent ; and from a mean of several experiments, the observed 

 was ascertained to be 23'. 1 less than the true inclination. This was determined by observing 

 the inclination in several known magnetic azimuths with both magnets, and computing the 

 true inclination from the formula 



tan 6 =. tan y cosec a, 



in which 6 the true inclination, 



351 = the inclination observed, 

 =r the azimuth of the vertical circle. 



If the inclination thus inferred is the same as the inclination given by the inagtoet when in 

 the magnetic meridian, there is neither defect in the axle nor polarity in the other portions of 

 the instrument. 



Another mode of ascertaining the same defects is from observations of the inclination in any 

 two vertical planes perpendicular to each other. Then, if the inclinations in these two planes 

 be represented by y and y ', 



Cot 3 = cot 2 7 + cot 1 ? '. 



