1871J Animal Mechanics. 397 



the forces of gravity and of buoyancy tend to keep the ship upright, and if she 

 has been heeled over, to restore her to the upright position, and that tendency 

 constitutes the statical stability or stiffness of the ship. Amongst waves the 

 same forces, combined with the reactions due to the heaving motions of the 

 water and of the ship, tend to place her in the position called upright to the 

 wave surface; that is, with her originally vertical axis normal to the wave sur- 

 face. If the ship yielded passively to that tendency, like a broad and shallow 

 raft, she would accompany the waves in their rolling ; and thus, a ship having 

 great stiffness may be very deficient in steadiness. Every ship has, like a pen- 

 dulum, a natural period of rolling, depending on her stiffness, or tendency to 

 right herself, and her moment of inertia, being a quantity depending on 

 the distribution of her mass. Stiffness tends to shorten, and inertia to 

 lengthen, the period. It was shown in 1862, by Mr. Froude, that the greatest 

 unsteadiness and the greatest danger of being overturned take place when the 

 periodic times of rolling of the ship and of the waves are equal ; for then each 

 successive wave adds to the extent of roll ; and if the coincidence of the 

 periods were exact, the ship would inevitably be overturned in the end. 



In the course of the present spring it has been pointed out that in 

 well-designed ships a safeguard exists against the occurrence of such dis- 

 asters. It is well known that no pendulum is absolutely isochronous ; but 

 great oscillations occupy a longer time than small oscillations. In like 

 manner, no ship is absolutely isochronous in her natural rolling ; but great 

 angles of roll occupy longer periods than small.* Hence, supposing a ship to 

 encounter waves of a period equal or nearly equal to her own natural period 

 for small angles of roll, her angle of rolling is at first progressively increased ; 

 but at the same time her natural periodic time of rolling is increased, until it 

 is no longer equal or nearly equal to the periodic time of the waves ; and thus 

 she in a manner eludes the danger arising from coincidence of periods. In 

 order, however, that this safeguard may act efficiently, it is essential that the 

 natural period of the ship for the smallest angles of roll should not be 

 less than the period of the waves ; otherwise the first effect of the progressive 

 increase of angle will be, not to destroy, but to produce coincidence of 

 period ; and the result will be great unsteadiness of motion, and possibly great 

 danger.* 



The speaker described the above principles as being the latest additions 

 to our knowledge of the theory of the relations between ships and sea-waves ; 

 and he illustrated them by means of experiments on a machine so constructed 

 as to imitate the dynamical condition of a ship rolling amongst waves. 



Animal Mechanics. — A few weeks ago the Rev. Samuel Haughton, M.D., 

 D.C.L., F.R.S., of Dublin, delivered a series of three Tuesday Afternoon Lec- 

 tures at the Royal Institution, on " The Principle of Least Action in Nature, 

 illustrated by Animal Mechanics." 



Dr. Haughton said that Alphonso Borelli taught Mathematics in the Univer- 

 sity at Naples towards the close of the seventeenth century ; he was also Pro- 

 fessor of Anatomy at the University, and his book shows that his scheme of 

 uniting Anatomy with Geometry had the honour of being approved by the 

 Pope, and pronounced to contain nothing dangerous to faith or morals. This 

 book was published in 1680 under the title of " De Motu Animalium." It is 

 full of mistakes because of the want of knowledge of the author of the com- 

 position of forces discovered by Newton ; but with all its defects it is the only 

 book which can be called a systematic scientific treatise on Animal Mechanics. 

 Two Germans, Edward and Wilhelm Weber, of Gottingen, tried in later times 

 to unite Anatomy and Geometry, and between them produced a very good 



* An exception to this rule exists in the case of that form of ship known as the " Symondite," 

 in which the sides flare out at and near the water-line, so as to make the stiffness increase 

 faster than the angle of heel. In such ships the period of rolling shortens when the angle 

 increases ; and thus the well-known unsteadiness of large vessels of that model is accounted 

 for. In a small boat, whose natural periodic time for the smallest angle of roll is shorter than 

 that of any of the waves she encounters, the Symondite model does not promote unsteadiness ; 

 for the shortening Qf the natural period of rolling removes it farther from coincidence with 

 the period of the waves. 



