crystallized bodies on homogeneous light. 8 1 
within limits less than the very trifling irregularities of the 
outlines themselves. 
The graphical construction of these curves is rendered 
extremely easy by the elegant and well-known property of 
the lemniscate, in which the rectangle under two lines drawn 
from the foci (or poles) to any point in the periphery, is inva- 
riable throughout the whole extent of the curve. This is 
easily shown from its equation, and the value of this constant 
rectangle in any one curve is expressed by a b. 
We must next enquire how the constant parameter b varies 
in passing from ring to ring. To this end I projected the 
rings, illuminated by red light only, on a screen as before, 
and having outlined the successive loci of the minima of 
illumination, and laid down the poles, found the values of a b 
in the several lemniscates, as in the following table : 
Order of 
the mini- 
mum. 
Observed 
values of a b 
in square 
inches. 
Differences. 
Values of a b 
computed from 
formula a b — 
i'S 9 X n 
Excess of computed 
above observed 
values of a b 
o 
II 
K 
o-oo 
0-00 
000 
I 
162 
1-62 
1-59 
— 003 
2 
3U65 
1-545 
3-i8 
-f 0-02 
3 
4-69 
1525 
4-77 
+ 0-08 
4 
6'2J 
1-58 
6- 36 
+ 0-09 
5 
7-87 
i-6o 
7-95 
4- 0-08 
6 
9-56 
1-69 
9-54 
— 0-02 
7 
1 ro9 
i -53 
11*13 
+ 0-04 
8 
,2 77 
1-68 
12-72 
— 0-05 
9 
H ‘33 
1-56 
i 4 - 3 ‘ 
— 0-02 
IO 
15-93 
r6o 
Mean 1-59 
15-90 
— 0-03 
The nature of the illumination not allowing the delineation 
to be performed with the same freedom and precision as in a 
fuller light, the values of a b in the second column are the 
means of a great number of measures, taken in every pai t 
MDCCCXX. M 
