5 
We may also write (1) in the form 
'E, 
g — wiftsecQy,^ 
The integration of this expression might be troublesome. 
Usually 0 will be a small angle; suppose then that we 
neglect the cube. From (2) and (3) we deduce with this 
supposition 
0 = 
fir 
jih + H — k 
and the integral may be written in the form 
9 n rn 
/ € -wMl +pr*)rdr 
RV 
o 
where p has been written for 
2(fih + H - hy 
we may also write it in the form 
2 a 
w e 
fR 
—mh I e~ 
rtvphr 2 rdr 
The integral taken betv/een the assigned limits is 
1 _ q— mpKR- 
a £ -mh / 
mR?ph\ 
If we expand the term e“ TO ^ R2 and neglect terms containing 
the fourth and higher powers of It, we shall obtain for the 
mean intensity 
ae- 
2 J 
If, as is usual, H be large compared with It, the mean 
intensity would differ very little from the intensity of the 
central ray. An examination of the term ^, Ra - will show 
if a correction is necessary in any case. 
“Correction of the Formula used in Photometry by Ab- 
sorption when the medium is not perfectly transparent/’ by 
James Bottomley, D.Sc., F.C.S. 
