EXPERIMENTS ON THE TIME OF ROLLING. 
629 
these series of experiments, Mr. Rawson verified these mean values by calculating^ 
from them the times of oscillation by the following equivalent formula: — 
f=^: 
+ 
gh 
.Fc|, 
TT 
which I had previously communicated to him, in which Fc^ represents that complete 
elliptic function of the first order whose modulus is c. The results of these experi- 
ments and calculations are given in the following Table : — 
Gross weight 
of model. 
Amplitude of 
oscillation on 
either side 
of vertical. 
Time of 
oscillation by 
experiment. 
Value of by 
formula ( (see 
Appendix). 
Mean value of 
It deduced 
from the pre- 
ceding column. 
Time of oscillation calcu- 
lated from the formula 
with the preceding value 
of k, verifying that value. 
lbs. 
o / 
5 0 
// 
in. 
in. 
// 
•8190 
11*983 
•8348 
197*18 
7 30 
•8905 
12*562 
10*465 
•8352 
10 0 
•7930 
11*554 
•8359 
2 30 
•7280 
11*070 
•7280 
255*43 
5 0 
7 30 
10 0 
•6500 
•7800 
•6760 
10*451 
11-784 
11*706 
9*3294 
*6500 
Table of the times of the oscillation in water of a model vessel as determined, — 1st, by 
the experiments of Messrs. Fincham and Rawson ; and 2ndly, by the formula (22,), 
■nk 
t— 
Constants of formula. 
Angle of 
oscillation ^i. 
Time of oscillation in 
seconds by formula. 
Time of oscillation in 
seconds by experiment. 
Weight of model =197*18 lbs. 
O 
5 
*75637 
*798 
w,=o 
10*465 in. 
10 
•75840 
*798 
A, = 4*9 in. 
15 
*76172 
*840* 
f=*75668|l +*46924 sin^ i 5, j 
20 
•76641 
•784 
Weight of model =255*43 lbs. 
5 
*61094 
*658 
w,=o 
A=9-3294in. 
10 
*61289 
*665 
Aj = 5*97 in. 
15 
*61471 
*616 
f=*6l033ll + *56021 sin^ 1 (3, 1 
20 
*64811 
*602 
t 2 'J 
23. General considerations applicable to the stability of floating bodies. 
An exceedingly small pressure is sufficient to move a floating body from its posi- 
tion of stable equilibrium. As the inclination becomes greater the pressure must 
bi increased until it attains, in a given position, its maximum value. Now if instead 
of this variable and continually increasing pressure we conceive a constant one to 
* This experiment was faulty. 
