Elastic Solids to Metrology. 613 



for I. In this way we find 



a/Z=0*5765, or a = 30'125 cm. 



The interval between the two supports is approximately 

 only *03 cm. less in the second instance than in the first. 



Application to Deflexion- Bars of Magnetometers. 



§ 36. In A, B, B', and C it is the length of the bar itself 

 that has to be considered. D and E are representatives of a 

 different class. They serve to support a carriage holding a 

 magnet. The carriage may have a groove fitting on the bar, or 

 a projecting pin fitting in one of a series of holes in the upper 

 surface. In either case, supposing the adjustment perfect 

 and the bar strictly horizontal, the centre of the magnet — 

 which is the fundamental point — will be vertically over a 

 certain graduation on the bar, and at a constant height h 

 above the neutral plane. In actual use, however, the bar 

 bends under its own weight and that of the magnet and 

 carriage combined. This is illustrated diagrammatically in 

 fig. 7, supposed to be a vertical section containing the 



Fig. 7. 



Fl-. 



magnetic axis NS and the line of centres OAC of the bar. 

 The arrangements are such that INS is parallel to the tangent 

 at C, while the normal at C passes through C the centre of 

 the magnet. F in fig. 7 represents the centre of a second 

 magnet whose suspension is ivertically over 0, and whose 

 height is altered until F appears central, as seen through 

 a sighting-tube, temporarily substituted for NS. The mag- 

 netic reductions suppose NS horizontal, in the same horizontal 

 plane with F, and at a distance from it equal to OAC, 

 or c. In reality NS is inclined to the horizon at an angle 

 tan" 1 {dyjdx) x=c ; and if we suppose — which is not strictly 

 true — that the sighting-tube is as heavy as the magnet, the 

 true distance of C' from F is not c but 



c{ 1 + i (dyldx)\= c \ + h(dyldx) x = c . 

 Phil Mag. S. 6. Vol. 2. No. 12. Dec. 1901. 2 S 



