86 Prof. E. Bouty's Studies on Magnetism. 



The optic axis of the telescope will be normal to the mirror 

 when the image of the objective occupies the centre of the field. 

 The other conditions, relative to the scale, may be fulfilled ap- 

 proximately; and we shall see by-and-by how this is accom- 

 plished. 



It is to be remarked that, when a needle is introduced into the 

 axis of the tube T, the centre of gravity of the suspended system 

 is in general displaced slightly ; but it is easy to see that this 

 displacement has no influence on the readings. In fact we can 

 produce the corresponding displacement of the suspended system 

 by the combination of two rotations : — one about an axis per- 

 pendicular to the mirror, without influence on the phenomenon 

 of reflection ; the second about a horizontal axis parallel to the 

 mirror, the effect of which is to raise or lower the normal to the 

 mirror in a vertical plane — that is, to raise or depress the image 

 of the scale. This perturbing effect is, besides, reduced to its 

 minimum by disposing the mirror parallel to the axis of the tube 

 in which the needles are placed. The rotation about the axis of 

 suspension, produced by the introduction of a magnetized needle, 

 is due solely to the earth's action, as we have above supposed. 



Corrections and Mode of Observation. — The axis of the tubeT 

 is never quite horizontal ; but when we confine ourselves to rela- 

 tive measurements (we shall see how absolute measures are 

 reduced to relative ones), it is enough if the axis has always the 

 same inclination. For this the weight of the needles introduced 

 into the tube must be very little in proportion to the total weight 

 of the apparatus. 



We have supposed that the vertical planes which contain the 

 axis of the tube and the axis of the directing needle form a right 



7T 



angle. In general they make with each other an angle -^ — /S : 



the precise formula which would replace formula (1) on this hy- 

 pothesis would be 



,, sin a ,_ x 



z=M , (In) 



cos (a + p) v ' 



in which, to quantities of the second order relative to /3, 



x = M tan a(l+/3 tana) (3) 



If the needle be turned in the tube end for end, the angle of the 



two planes becomes £-+& and we have, a' denoting the new 



deviation, 



a? = Mtan*'(l— /3tana'); .... (4) 



from which, adding (3) and (4) term to term, and observing 



