1913]
FINE SLITS IN THIN OPAQUE SCREENS
185
From these formulae the following numbers have been calculated for the value of - ir^dty/dcc:
TABLE VI.
M = % kb = l kb=J2 kb = 2
cosa=0 cosa= ±1 T3716 + 0-0732 i - 1-5634 + 0-0710* l-1215+0-2885i -l-6072+0-2546t 0-8824+0-5653i -1-5693+0-44011 0-5499 + l-0860i -1-3952 + 0-65671
They correspond to the value of M/ formulated in (95).
Following the same method as in case (i), we now combine the two
solutions, assuming
M* = A ^(bz~f) + Bb~2(b2~'y2')3/'i, ...:...........(107)
and determining A and .5 so that for cos a = 0 and for cos a = + 1, dtyldtc shall be equal to — ilc. The value of ty at a distance in front is given by (76), in which
7 [\trd -?'^ (A ^ B\ (108}
*J y~ 2 V +4 )...................( )
We may take the modulus of (108) as representing the transmitted vibration, in the same way as the modulus of (67) represented the transmitted vibration in case (i).
Using p, q, r, s, as before, to denote the tabulated complex numbers, we have as the equations to determine A and B,
•• Ar + Bs ~ iJc/7r, ...................(109)
xi so that
2 ps — qr
For the second fraction on the right of (110) and for its modulus we get
in the various cases
Kb** i 1-1470 - 0-1287 i, 11542,
M>= 1, 11824 - 0-6986 i, 1'3733,
fc&"=V2, 0-6362-1-0258 i, 1-2070,
Jcb= 2, 0-1239 - 0-7303 i, 07407.
And thence (on introduction of the value of Job) for the modulus of (110)
representing the vibration on the same scale as in case (i)
TABLE VII.
lib Modulus
1 0-1443
1 0-6866
s/2 1 -2070
2 1-4814