236 
DR. j. YOUNG AND PROFESSOR G. FORBES ON THE 
dl _ E 
dn~~ 2 N 
but when 
hH 
II 
1 
s 
+ 
whence 
n=(p— l)N, I=E(1 
b=a— N{2(1 — /c)+p 
I= f{ 2 ( 1—K )+-P —1 
n 
N 
dl 
3. In the case of a wheel with any width of teeth, the value of in the middle of 
C171 
an even phase, is the same as in the two previous examples in magnitude, but of 
opposite sign, and the maximum intensity is E(l — k). Suppose that it is the p xlx 
phase which we are considering, p being even ; then 
dl _ E 
dn~ ' AN" 
but when 
whence 
and 
I=l|(«+o) 
n=p'N ) I=E(1 — k) 
c=N{2(1 — K)—p} 
If we have two distant reflectors, A and B, nearly in the same line, but at different 
distances D A and D B , and having consequently different speeds N A and N B , and 
different intrinsic brightnesses E A and E B . Then, if D A be greater than D B , N A is less 
than N b , and we shall have equalities of brightness of A and B at different speeds. 
The first equality is in the first phase of B and the second of A. The second equality 
is in the second phase of B and the third of A, and so on. The r th equality is in the r th 
phase of B and the r+l| th of A, provided that r(N B —N A ) is less than 2N A . We need 
not consider any other case. 
4. Let us consider the case of the A 11 equality when r is even. Here B is increasing, 
A is decreasing. We have then pp=r-\-l, and p%=r, 
I A =I B ; or^{2(l- K )+(,•+!)-!-£} =| B {2(l-K0-r+£} 
* We are taking account of the possibility of k being different for A and B. But in practice this is 
never the case. 
