640 
EXPERIMENTS OF MESSRS. FINCHAM AND RAWSON. 
Cylindrical Model. 
Model at ultimate deflec- 
Weight of the 
Distance from 
Model at rest, without the 
Model at rest, with the 
tion. with deflecting 
model and deflect- 
centre of model 
deflecting weight. 
deflecting weight. 
weight. 
ing weight. 
to P and Q. 
Deflect- 
Weight 
L. 
hk. 
Ns. 
Po. 
Ly. 
Nr. 
Vp. 
U. 
Nn. 
ing 
of 
P. 
Q. 
weight. 
model. 
lbs. Av. 
Ihs. Av. 
ft. in. 
ft. in. 
8iV 
... 
6 
lOi 
4Ar 
1-957 
197-18 
.3 6y 
5 4| 
1 
8 
H 
... 
6 
lOi 
41 
3 6i 
5 4f 
H 
9i 
... 
3 61- 
4 Of 
6 
... 
4| 
7_3- 
34^ 
3f 
1-957 
255-43 
3 6h 
5 4f 
1 
K3.) 
5^ 
7 
...<•• 
3 61- 
4 Of 
J 
6 
31 
n 
m 
Of 
5-0285 
255-43 
3 H 
5 4f 
1 
,(4.) 
33i 
21 
3 6i 
4 Of 
8i 
34 
5 
11^ 
24,V 
2* 
2-8225 
197-18 
3 61- 
5 4f 
.(5.) 
36i 
lOA 
3 61 
4 Of 
J 
The position of the water-line corresponding to the extreme position into which 
the model rolled being thus determined in every experiment, the corresponding dis- 
placement was also known. In fig. 1, this displacement having a triangular section 
eMf, its centre of gravity h could readily be determined by construction. In fig. 2, 
the displacement having a circular section, its centre of gravity h could be de- 
termined by known rules. Drawing a perpendicular he from h upon BD, this line 
measures the depth of the centre of gravity of the immersion in the extreme position 
into which the vessel rolls, and Her, measures it in the vertical position ; therefore the 
difference of these lines measures its elevation in the act of roiling. In like manner 
the perpendicular G6 measui’es the depth of the centre of gravity of the model when 
the water-line was BD, and Ga was its depth in the vertical position, therefore the 
difference of these lines is its elevation in the act of rolling. 
Thus the elevations of the centre of gravity of the model and of the centre of gra- 
vity of the displaced fluid, in the act of rolling, are found, and its weight being known, 
the work which must have been done upon it to cause it thus to roll may be deter- 
mined according to equation 6. 
But the work actually done upon it by the deflecting weight may, in like manner, 
be determined ; for if a perpendicular Qo be drawn from Q on BD, the length of this 
line will be the height of Q when the water-line was BD, and Qm was its height in 
the vertical position, therefore the difference of these lines is the space through which 
the deflecting weight has descended vertically ; and the j)roduct of this distance of the 
deflecting weight gives the work actually done by it upon the rolling body. This 
amount of work ouglit, by the theory, to be the same with that found as above from 
equation 6; and the coinparison of results thus obtained, by theory and experiment, 
constitutes a verification of the formula, and is given in the Table, p. 615. 
A single example will show the way in which the calculations were made. 
