628 
EXPERIMENTS ON THE TIME OF ROLLING. 
rolled, sweep parallel to the surface of the cylinder. A pencil was fixed at the extre- 
mity of this arm and pressed lightly by a spring upon the surface of the cylinder, 
which was covered by a piece of paper. The frame which carried this cylinder ad- 
vancing in the direction of its axis, and the vessel at the same time rolling so as to 
sweep the arm over its surface perpendicular to that direction, a zigzag line was, by 
the combination of the two motions, described, as represented in the diagram on the 
preceding page, of which each two consecutive loops mark the beginning and end of 
the same oscillation, and the distance AM between them, measured in the direction in 
which the frame moved, shows the space traversed by it in the time occupied by that 
oscillation. This space being known from the experiment, and the rate at which the 
frame travels uniformly being also known, the time occupied in the oscillation may 
be determined*. 
At a certain point the amplitudes of the oscillations will be observed suddenly to 
increase. This is due to the return of the wave created by the vessel in the act of 
rolling and reflected by the sides of the tank-f-. 
Before the times of oscillation could be calculated by the formula (22.) to compare 
them with those determined by experiment, it was necessary that the moment of inertia 
of the floating body should be ascertained. To ascertain it by calculation would 
have been a difficult task, involving in some respects an uncertain result ; it was 
sought therefore by experiment. 
With this view a knife-edge was fixed at each extremity of the cylinder, so as accu- 
rately to coincide with its axis prolonged. The vessel taken out of the water was 
then made to rest by means of these knife-edges on two hard steel plates, accurately 
adjusted to the same level, and in this position it was allowed to oscillate, the times 
of its oscillations being determined as before. It then became possible to determine 
the moment of inertia from the following well-known formula — 
Two series of experiments were made, the model vessel being loaded in the one 
series so as to weigh 197' 18 lbs. gross, and in the other so as to weigh 255*43 lbs. 
Having obtained from the above formula a mean value of k in respect to each of 
* The apparatus, and the method of experimenting with it, are more fully described in the Appendix. It 
will be observed that in the diagram the amplitudes of the successive oscillations are shown to have dimi- 
nished, up to a certain point. This diminution was found in a great number of experiments to take place with 
remarkable uniformity. The uniform diminution of the amplitude of oscillation as the body comes to rest, is 
of course due to the absorption of the vis viva of the rolling body by the water which it puts in motion, to the 
friction of the water which adheres to it on the rest of the water, to the resistance of the air, and to the fric- 
tion and abrasion of the parts of the rolling body itself in the act of rolling. Mr. Rawson has made some 
experiments on this subject, the results of which he communicated to the British Association for the Advance- 
ment of Science. 
t The precision with which the instant of the return of this wave and its progress are indicated, seems to 
show this method of experimenting to be well-suited to determining the velocities of waves. 
