VARIATION APPARATUS. 613 



and let a be the angle of this bar with the perpendicular to the 

 magnetic meridian ; the condition of equilibrium is 



HM cos a = C sin 0, 

 and the simultaneous variations of the elements give 



dC 



- + T- - tan a da = + cot d6. 

 MM C 



If c is the coefficient of variation with the temperature of the 

 bifilar couple, observing that a is very small, we may write 



- = co\.0 



This arrangement has the advantage that the variations of de- 

 clination do not interfere to any sensible extent. The coefficient 

 (a + c) is determined as a whole by the observations themselves, 

 and the value of cot 6 is given directly in the installation of the 

 bifilar. 



1186. To obtain variations of the vertical component, the 

 changes of direction of a magnetised bar are observed which rests 

 by a knife-edge on an agate support, like the beam of a balance, 

 and which is adjusted so as to keep in equilibrium when nearly 

 vertical. The axis of rotation may be perpendicular or parallel to 

 the magnetic meridian. 



Let us consider the general case. Let Z and H' be the vertical 

 and horizontal components of the projection of the terrestrial field 

 on a plane perpendicular to the axis of rotation, I' the apparent 

 inclination in this plane, 6 the angle which the magnetic axis of 

 the bar makes with the horizon, /3 the angle of the plane per- 

 pendicular to the axis with the perpendicular d let fall from the 

 centre of gravity on this axis of rotation, Q=/^ the product of 

 the weight of the bar by the distance d. The equation of equi- 

 librium is 



ZM cos B = Q sin ({3 + 0) + H'M sin (9. 



As the angle is very small, the variations give, apart from 

 quantities which may be neglected, 



MdZ + ZJM = Qcosfid6 + sin /3 dQ + H'M dd . 



