228 Inslrnclionsfor the Scientific Expedition 



of the declination are regularly observed. For this purpose it is only 

 necessary to employ the latter telescope as a collimator, the tele- 

 scope being reversed in its Y supports, if necessary. A fixed col- 

 limator may also be conveniently substituted for the distant mark. 

 This mode of observation has the advantage of connecting the ab- 

 solute determination directly with the regular series of observatidns ; 

 and it is manifest that it is sufficient, without any other means, to 

 determine whether any, and what changes may have occurred in the 

 position of the fixed telescope. 



The fixed telescopes, furnished to each observatory, have an aper- 

 ture of 1|^ inches, and focal length of 14 inches. They should be 

 fixed upon a stone pillar, or upon a finii pedestal of wood resting on 

 solid masonry unconnected with the floor. 



In observing the declination changes the fixed telescope (above re- 

 ferred to) is alone employed. The observation consists simply in 

 noting the point of the scale coinciding with the vertical wire, at 

 three successive limits of the arc of vibration. The three readings 

 being denoted by a, b, c, the mean point of the scale corresponding 

 to the time of the middle observation is 



i(a-\- 2b + c). 



This mode of observation is sufficient where the observer is not limited 

 to a precise moment of observation. Otherwise the more exact me- 

 thod pointed out by Gauss is to be preferred*. 



The changes of position of the scale may be converted into an- 

 gular measure, the angle corresponding to one division being known. 

 In general, however, this reduction will only be required in the 

 monthly mean results. 



Before the true changes of the declination can be deduced from 

 the observed readings, it is necessary to apply a correction depending 

 upon the force of torsion of the suspension thread. For supposing 

 that the plane of detorsion has been brought (by the adjustments 

 above described) to coincide with the magnetic meridian, it is ma- 

 nifest that on every deviation of the magnet from that its mean po- 

 sition, the torsion force will be brought into play ; and as this force 

 tends to bring back the magnet to the mean position, the appa- 

 rent deviations must be less than the true. The ratio of the torsion 

 force to the magnetic directive force is experimentally determined 

 by turning the moveable arm of the torsion circle through any given 

 large angle (for example 90°), and observing the corresponding 

 angle through which the magnet is deflected. Let u denote the 

 latter angle, and v the former ; then the ratio in question is 



G _ u . 

 F v — u 



in which G is the coefficient of the torsion force, and F the moment 

 arising from the action of the earth's magnetic force upon the free 

 magnetism of the bar, the direction of the action being supposed to 

 be perpendicular to its magnetic axis. The ratio of the two forces 



* See Taylor's Scientific Memoirs, vol. ii. part v. p. 44. ei scq. 



