486 Mr Filon, On the variation with the wave-length 
In onr case a is always less than this value, being in fact of 
the order 7t/180 and therefore small. But J 1 (a)< ol\ 2 and tends 
to a/ 2 if a be small. So that the intensity never actually vanishes, 
but it falls to a very small minimum whenever 
2 ttC . , 
_ ) =2n7r 
, \n 
or pyo-qy=-Q- 
This therefore corresponds to a black band in the field of view. 
If now y 0 {n) , y 0 (n+1) be the y 0 ’s of two consecutive black bands 
Cp(y 0 (nH) -y 0 {n) ) = \. 
This equation is of precisely the same form as in the ideal case 
previously discussed, except that the coefficient p is slightly 
different. 
Hence, in so far as relative values of 0 for different Vs are 
concerned, y 0 {n+1) — y 0 (n) being the quantity observed, no error what- 
ever will be introduced by the obliquity, or by the finite solid 
angle of the pencils. 
As a matter of fact p is known, as all the quantities which 
enter into its calculation can be easily measured : so the absolute 
values can be deduced when required. 
5. It was now necessary to find the exact wave-length of the 
light corresponding to any vertical line on the scale. 
To do this the arc lamp, which was used to give a continuous 
spectrum, was removed and the spark-holder with the poles made 
of the alloy mentioned above was placed behind the slit. 
The spark spectrum of the alloy then appeared on the scale. 
The positions of 25 of the most prominent lines of this spec- 
trum, ranging from X4000 to \6800, were then carefully read off 
on the horizontal millimetre scale. The lines were identified and 
their accurate wave-lengths obtained. 
The wave-lengths were then plotted on squared paper to the 
scale divisions. A smooth curve was drawn as nearly as possible 
through the 25 or so points obtained and from this the wave- 
length corresponding to any given scale division could be read off 
practically correct to the first three figures. 
Before each experiment the “zero” was determined by reading 
off the position on the scale of a well-defined, easily recognizable, 
line of the comparison spectrum. The wave-lengths for each 
observation could then be deduced by means of the diagram. 
The spectrum was carefully re-mapped and a new diagram 
plotted, at certain intervals, especially whenever the lenses, prism 
or beams had been moved or shaken in any way. 
