278 DR. L. N. G. FILON ON THE 



levels correspond to parts of the spectrum also at different levels, we see that the 

 band is no longer straight and vertical, but curved, the convexity being towards the 

 red. This convexity is, however, so small that it would not in any case be observable. 

 If the condition (6) of 2 is not exactly satisfied the band will still be straight, 

 to a first approximation, but no longer vertical. Thus when the bending moment 

 varies from cross-section to cross-section for light passing to the right of the 

 mid-section the band is tilted one way, for light passing to the left it is tilted the 

 reverse way. The integral effect will be that the thickness of the band will no 

 longer be uniform, but the band is still symmetrical with regard to a vertical line, 

 corresponding to light going through the mid-section. The settings which are made 

 on the middle of the baud are therefore unaffected. 



11. Imperfect Vertical Adjustment of the Knife-edges. 



It will also happen that the knife-edges will not all be at exactly the same height, 

 so that the axes of the two slabs are not exactly horizontal and parallel. The effect 

 will be that for rays passing through in a plane distant x from the central section 



Zi z 2 +a-(z l h) = A + Bx 



instead of being exactly constant, B being a small coefficient. 



This will broaden the band and render it more diffuse, but will not shift its centre. 

 Observation shows that this effect must be very small, as, in general, the band is very 

 well defined. 



12. Error due to Weight of Beams themselves. 



In computing the stresses no heed has, so far, been paid to the fact that the 

 weights of the glasses themselves will introduce certain stresses in the slabs. The 

 weight of each slab is on the average 120 grammes. This, although very small 

 compared with the total load in most cases, may introduce a small error in the case 

 of the band of the first order, which corresponds to a smaller load. 



For the beam N the weight of the glass was found to introduce practically no 

 bending moment in the centre, as the supports were very nearly at the quarter and 

 three-quarter span points. 



For the beam F the moment introduced is the same as if the weight on this slab 

 were increased by exactly its own weight. 



It is quite easy in practice to eliminate this by adding a small counterpoise to the 

 weight on N. 



13. Error due to Imperfect Annealing. 



We now come to the only error with the exception of that due to rise and fall 

 which is sufficiently important to be allowed for in the reduction of the observations. 



