INCLINATION. 593 



the zero of the vernier when the plane which passes through the 

 axis of the mirror is vertical. This determination will be useful 

 in making the needle vertical in certain cases ; nevertheless, in 

 ordinary observations it is sufficient to turn the mounting through 

 1 80, when the difference of the readings give twice the angle of 

 the needle with the vertical. 



2nd. The defect of centring is eliminated by the mean of the 

 readings for the two ends of the needle. 



3rd. After having observed the needle in one position, it is 

 inverted; the mean of the readings eliminates the defect of paral- 

 lelism of the magnetic axis with the line of the points. 



4th. The weight of the needle increases or diminishes the ap- 

 parent inclination when the centre of gravity is eccentric and situate 

 above or below the axis of rotation. The inverse effect is observed 

 by reversing the magnetism of the needle, and the mean of the 

 results is again taken. 



5th. If the plane of the agates, although parallel to the vertical 

 axis of the circle, is not itself horizontal, the needle has a tendency 

 to roll in one direction or the other, and the error changes its sign 

 when the apparatus is turned through 180. This error is again 

 eliminated by the mean of the readings. We are further certain 

 that the difference does not exist if half the difference of the read- 

 ings corresponds to the vertical given by the plumb-line. 



1165. Nevertheless, as several sources of error act simul- 

 taneously, it is necessary to demonstrate that the compensation 

 due to these reversals is exact, especially as regards the position 

 of the centre of gravity. 



Let us suppose that the needle moves in a plane which makes 

 the angle a with the magnetic meridian. The apparent inclination I a 

 (305) satisfies the equation 



cotl a = cotl cos a. 

 Let: 



I' be the inclination given by the line of the points OA of the 

 needle (Fig. 243); 



G, the centre of gravity of the needle, situate at the distance d 

 from the axis on the right line which makes the angle 7 with the 

 line of the points ; 



/?, the angle of the line of the points with the magnetic axis OB ; 



F, the component of the terrestrial field in the plane of the 

 needle, in C.G.S. units; 



/, the weight of the needle in the same units ; 



Mj, its magnetic moment. 



VOL. II. Q Q 



