MR. G. T. WALKER OK BOOMERANGS. 
angle, the more difficult is the throwing of the implement, and when 2a = 150° or 
upwards, and the material of which the boomerang is made is light, throwing it 
against a wind requires skill of a high order. 
The values of the constants 4, . . . have been calculated for boomerangs whose 
arms are 36 centims. in length and 5 centims. in width, the mass per unit area being 
five-eighths of a gramme. 
When these constants are substituted in the equations of steady motion, it is found 
that for a boomerang whose arms are at right angles, corresponding to the values 
U = 2000, n = 40, kU = 7, XU^ = 5, 
are the velocities 
Hi - -’^-- + — + 1.9 cos e 
P T 
n. 
jL _ _ 
p 
G80 480000 
P 
6.8 cos 6 )> 
— 1600 cos 0 
( 3 ). 
If we make n = 30, the values of Oo, iv given by the equations are too large; 
this is due to the fact that the theoretical limit of stability (n = 22) is not sufficiently 
exceeded. 
If the value of kU be taken as 5 instead of 7 (these being estimated inferior and 
superior limits of kJJ corresponding to c = 6, _/= 1/6, and c — 7, f = 1/5) there 
appear 
3.2 , 270 , . 
-f- —h cos u 
P ^ 
2.9 2100 . „ . 
= — ~-—0.7 cos 9 k 
P ^ 
630 460000 
iv = —-- 1400 cos 9 
P -r 
(4). 
The velocities corresponding to a larger spin 
U = 2000, 11 = 50, kU = 5, XU~ = 5, 
are 
2.8 , 100 . . 
= — — -|--f- • 4 cos 9 
P 
n, — — 
w — 
1.2 1200 
P r 
240 __ 215000 
P '!■ 
-3.2 cos 9 
— 790 cos 9 
(5). 
