324 
PROF. H. iM. MACDONALD ON THE EFFECT PRODUCED BY 
When the point P is at a distance from the edge of the screen great compared with 
a wave-length these expressiojis are sensibly the same as those of the known accurate 
solution, as Vq is very large unless tlje line OP makes an angle which is very small 
with the line through 0 making an angle tt-I-Si with the plane of the screen, or with 
the line through 0 making an angle tt —with the plane of the screen, and in these 
cases the results are the same. 
When the magnetic force in tlie incident waves is parallel to the edge of the 
conductino- screen 
o 
a= 0, /3 = 0, y = g.*(Vt + xco35.+ysm5,) 
in the incident waves, and the assumed electric current distribution on the positive 
side of the screen is given by 
- ^ = 0, y = 0, 
and on the negative side of the screen by 
a = 0, ^ = 0, y = 0, 
whence the components of the magnetic force due to the assumed surface distribiition 
at a point P {x, y, z) are 
a = 0, = 0, 
0 giK(V(+Jic-osai-)') 
dy r 
dxi, ch^, 
and, by a similar analysis to that in the preceding case, when the point 
negative side of the screen 
where 
y— _^.«(V!+3-eos3i + i/sin5,) 2 -Vi j (lu, 
Uo = 2' - (XR) sin d-j. 
P is on the 
having the same meaning as above, and therefore the resultant magnetic force on 
the negative side of the screen is given by 
giK(Vi + rcos5,+ysma,) 2-’/2 
When the point P is on the positive side of the screen the magnetic force is 
given by 
gi/t(Vi + 3-cos5,+.?/sin3,)_j_ gi/c(Vi + TC0s3i-!/siil5i) 2-'/i f 6~ 
J -«(, 
these results again agreeing with the known accurate solution when the point P is at 
a distance from the edge great compared with a wave-length. Again, when the 
conducting screen is an infinite plane with a slit in it of breadth 2d bounded by 
parallel edges, taking the origin in the middle line of the slit, this line being the axis 
