392 Lord Blythswood and Dr. Marchant on 



If be the angle of tilt, the effective width of a step 

 ■=s cos 0~t sin 0, where s = 'b mm. and t=7'5 mm. q. p. 

 A tilt of one degree, therefore, will reduce the effective width 

 of a step to *75 of its original value. 



In position 2 (fig. 4) the width of the steps is only reduced 

 to s cos 0, where is the angle of tilt, and cos 0=1, when. 6 

 is small. 



The amount of light passing through the instrument is 

 clearly not much affected. A tilt of one degree in this 

 direction will only diminish the effective width of the steps 

 by one part in 5000. As is shown later, a tilt of one degree 

 is approximately that required to obtain the double-order 

 condition from the single-order condition, or vice verm with 

 yellow light. 



It has generally been found best to work with the order 

 next to that obtained in the direct position, or even the second 

 order from that position, When working in the equal-order 

 condition, it is best to work with the first and second orders 

 away from the direct position. If the direct-position order 

 was used, it was found that the dispersion of the order, say, 

 to the left of the direct-position order (the direct-position 

 order being supposed to be the left-hand one) was not equal 

 to that of the order to the right of the other equal order. In 

 fig. 5 the distance AB was not equal to the distance DC. 

 This would introduce uncertainties in the measurements. 



Fig. 5. 



^ — DIRECT POSITION 

 f ORDER. 



A BCD 



It should be noticed that the direct position is not neces- 

 sarily that in which only a single order is showing brightly ; it 

 may be a position when two equal orders are showing, or two 

 orders one brighter than the other, this depending entirely 

 on the retardation produced by the plates of the echelon for 

 the particular light under examination. The effect of not 

 working with the direct-position order, but with, say, the 

 third order away from it, will not affect the constant by 

 more than '06 per cent., since the value of m in the equation (2) 

 is of the order 5000 for yellow light. Or, considering the 

 change in the amount of retardation produced by tilting the 



