614 



Lr. C. Chree : Applications of 



The bar D rests throughout its central 29 cms. on a hori- 

 zontal plate, to which it is bolted at two points each 14 cm. 

 from the centre. Thus the half on one side of the centre is 

 practically a rod of 61 — 14, or 47, cms. length, clamped at 

 •one end so that y and dy/dx vanish with x. The bending 

 and stretching are thus the same as in the half of a bar 

 94 cms. long supported at its centre. 



The bar E rests on horizontal pins which pass through two 

 holes drilled through the bar at the level of its neutral line. 

 It may thus be regarded as supported, the distance of the 

 supports from the centre being half the distance (b* cm.) 

 between the pins. Consequently for E we have Z = 45, a = 3. 

 The magnet with its carriage weighs approximately 122 

 grammes in the case of D, and 390 grammes in the case of E. 



Commonly the magnet is used at two fixed distances, its 

 centre being either 30 or 40 cms. from the centre of the bar. 

 What we want to know in the present case is the slope at the 

 particular point where the additional weight acts. As already 

 explained, this is the precise point where the Bernoulli-Euler 

 results are likely to be least exact ; still, the uncertainty is 

 hardly likely to be serious. Employing the values given for 

 co, &c. in Table I., I find the following data for the slope 

 and for the quantities on which the distance C'F in fig. 7 

 depends : — 



Table VIII. 



Magnet at 



BarD. 



Bar E. 



30 cm. 



40 cm. 



30 cm. 



40 cm. 



Angle of slope of magnet = 



hdy/dx ^cms.) = 



\c (dy/dx) 2 (cms.) = 



78" 

 •00189 

 2xHT 6 



113" 

 •00273 

 6xl0~ 6 



115" 



00379 



5xl0~ g 



163" 



•00537 



13xl0~ 6 



§ 37. So far as concerns the effect on the magnetic obser- 

 vations, the departure of the magnetic axis from horizontality 

 is negligible, and the value of (cj '2) (dyjdx) 2 is wholly insig- 

 nificant. It is otherwise, however, with hdy/dx, especially in 

 the case of bar E, where the error introduced is almost 

 exactly twice as great as with D. In both bars the value of 

 hdy/dx varies pretty closely as the distance c. This is so far 

 fortunate, as it minimises the indirect effect on a certain 

 correction supplied by magnetic theory, whose accuracy is 



