OF ILLUMINATING LIGHTHOUSES. 
219 
But in a parabolic reflector the area of the circles A d A„ B b' B„ 
C d C„ &c. are to each other as A? 2 , B b'^ 2 , C d V2 , &c., or as D d, 
Db', D d, &c., or as their equals A a, B b, C c. Let D F A, &c. be 
any variable angle = 6, the corresponding absciss x, and make 
D F = p one fourth of the parameter. Then 
(p + x) cos 6 — p — x, 
whence 
l — COS i 
x = 
p. 
1 + cos i 
And as the angle 6 depends upon the angle formed between the 
axis of the reflector, and a line drawn from it to the eye, we are 
enabled to ascertain the ratio in which the illuminating power in- 
creases and diminishes, when the reflector makes a revolution in a 
given time. 
The following Table shows the illuminating power of the re- 
flector and lens at the end of every second of time during the passage of the light. 
The reflectors with Argand lamps being supposed to be placed on three sides, and 
revolving in 8 minutes, that with the lime ball and the lens having eight sides, and 
revolving in 21 minutes 20 seconds, making the time from the appearance to the re- 
appearance of the light in each 160 seconds. The illuminating powers are expressed 
in Argand lamps as placed in reflectors 21 inches diameter. 
Seconds of 
Time. 
3 Sides. 
3 Sides. 
8 Sides. 
8 Sides. I 
Single Reflector 
with Argand 
Lamp. 
Ten Reflectors 
with Argand 
Lamp. 
Single Reflector 
with Lime Ball. 
French Lens. 
1 
•0285 
•285 
7-72 
? 
2 
•0617 
•617 
16-51 
? 
3 
•1019 
1-019 
27-33 
10-4 
4 
•1501 
1-501 
40-66 
10-4 
5 
•2133 
2-133 
57-48 
10-4 
6 
•2937 
2-937 
79-35 
10-4 
7 
•4019 
4-019 
108-98 
10-4 
8 
•5555 
5-555 
151-35 
10-4 
9 
•7905 
7-905 
216-98 
10-4 
10 
1-0000 
10-000 
264-00 
10-4 
11 
1-0000 
10-000 
264-00 
10-4 
12 
1-0000 
10-000 
264-00 
10-4 
13 
1-0000 
10-000 
264-00 
10-4 
14 
1-0000 
10-000 
264-00 
10-4 
15 
1-0000 
10-000 
264-00 
10-4 
16 
1-0000 
10-000 
264-00 
10-4 
17 
•7905 
7-905 
216-98 
10-4 
18 
•5555 
5-555 
151-35 
j 
19 
•4019 
4-019 
108-98 
? 
20 
•2937 
2-937 
79-35 
Dark. 
21 
•2133 
2-133 
57-48 
22 
•1501 
1-501 
40-66 
— 
23 
•1019 
1-019 
27-33 
24 
•0617 
•617 
16-51 
25 
•0285 
•285 
7-72 
— 
26 
Dark. 
Dark. 
Dark. 
2 G 
MDCCCXXXVII. 
