956 



mersions could in every position be readily determined, and this 

 difference therefore ascertained. Thus the verification of the theo- 

 rem became in every experiment practicable, and in all the accord- 

 ance of the experiment with the theorem was remarkable. Did not 

 the demonstration of it rest upon a mathematical basis, these experi- 

 ments would indeed themselves be sufficient to establish it. 



In its general application to the conditions of the stability of a 

 vessel, the author places this theorem under an analytical form suffi- 

 ciently simple to be applied in practice, and involving no other data 

 than such as may be determined by methods familiar to naval archi- 

 tects and generally assumed in their calculations. 



With reference to the conditions of quick and sloiv rolling, the 

 discussion of which is the object of the second part of the paper, it 

 is necessary in the first place to determine geometrically the position 

 of the axis about which the vessel is, at any given period of its incli- 

 nation, rolling. It is shown to be perpendicular to two lines, one of 

 which is a vertical line passing through the centre of gravity of the 

 plane of flotation in that position, and the other a horizontal line 

 passing through the centre of gravity of the vessel and parallel to 

 the plane in which any point of the body is rolling. The position 

 of the axis of rolling being thus known, the determination of the 

 time of rolling is comparatively easy. 



The author gives formulae for the times of rolling and pitching, 

 which, like those for the angles of rolling and pitching, have been 

 subjected to the test of experiments detailed in the paper, and have 

 in like manner been confirmed. 



The apparatus used for determining the times of oscillation of the 

 models was contrived by Mr. Fincham. An arm was fixed in the 

 direction of the length of the floating body so as to project from its 

 extremity, and to the end of this arm a pencil was fixed vertically. 

 The vessel being then prevented from displacing itself laterally whilst 

 in the act of oscillating on an axis passing through its centre of 

 gravity and of which the extremities were received between vertical 

 guides, as the vessel oscillated a line was traced by the pencil upon 

 a piece of paper adjusted upon a board curved of a suitable form, 

 which was carried along by clock work with a uniform motion in 

 the direction of the length of the vessel upon a carriage, that tra- 

 versed a railroad resting upon the edges of the tank. A zigzag 

 line was thus described on the paper, each turn in which corre- 

 sponded to an oscillation, and the distance between two successive 

 turns determined — from the known rate of the motion of the carriage 

 • — the time in which the oscillation was made. 



The formulae given for the amplitudes and the times of oscillation 

 afford the means of determining these, from the lines of ships, before 

 they are constructed-, and the author suggests that a vessel being 

 fixed upon whose properties in respect to rolling are known, it would 

 be expedient to compare with them those of all others which are 

 proposed to be constructed ; it being a possible thing (by the aid 

 of such formulae) to determine whether these will roll under the like 

 circumstances through greater angles^ or quicker than the standard 



