148 



NATURE 



\_yune 12, 1879 



fact that animals possess faculties differing from those of man 

 is an insuperable obstacle to a perfect analysis of their intelli- 

 gences. 



Name these faculties as you please, call them "inherited 

 habit," "inherited memory," it is perfectly certain that man 

 does not possess them. H. D. Barclay 



IV/LLIAM FROUDE 



qp HE death of Mr. W. Froude, F.R.S., is a loss to 

 ■*■ science that cannot well be estimated. For many 

 years he laboured with great ability and success in a field 

 of research that was beset with difficulties, and had pre- 

 viously been almost barren of results. He was educated 

 at Westminster, and went from there to Oxford, where 

 he distinguished himself in mathematics. After leaving 

 Oxford he became a ciril engineer, and assisted Mr. 

 Brunei in railway and other engineering work. He re- 

 tired from active professional hfe in 1846, but his love of 

 applied science retained such a hold upon him that he 

 never ceased to occupy himself with important scientific 

 investigations, and the solution of practical problems of 

 peculiar difficulty. His intimacy with Mr. Brunei led to 

 his mind being directed towards the study of those laws 

 of nature which govern the motion of floating bodies. 

 Mr. Brunei had devoted himself, among other things, to 

 the improvement and development of iron steamship 

 construction. In the Great Western and Great Britain 

 he had made great advances in this direction ; while in 

 the Great Eastern he showed that iron and steam power 

 could be employed in the production of ships of practi- 

 cally unlimited dimensions, and that by means of these 

 agencies all the advantages appertaining to increased size 

 might be realised. 



In designing ships of such exceptional character and 

 dimensions, Mr. Brunei found little to guide him in judg- 

 ing of their behaviour at sea. They were so different to 

 any vessels afloat whose behaviour and qualities might 

 have been ascertained, that he was unable to appeal to 

 experience, while the light of science was so feeble and 

 doubtful as to afford him no aid. Nobody at that time 

 knew anything of the laws upon which a ship's motion at 

 sea depends. There was a large mass of traditional ex- 

 perience, but this was often at variance with fact, owing 

 to phenomena which are familiar to seamen being re- 

 garded as absolute, and possessing a reality of existence 

 as well as of appearance ; while, as must be obvious, they 

 are only relative in their character, and cannot be accu- 

 rately defined without making due allowance for the 

 position and motion of a ship, with reference to the sea. 

 The rules and maxims that had been adopted upon such 

 incorrect and distorted data, were either unimportant or 

 misleading; they were of no value. Mr. Froude said, 

 quite correctly, in 1861, that our shipbuilders, while 

 extending their knowledge in other directions, seem to 

 have guided themselves by rhetorical phrases or random 

 speculations in this particular branch of their art, "so 

 that when a new ship is sent to sea, her constructor has 

 to watch her behaviour in a seaway, with as anxious and 

 uncertain an eye as if she were an animal he had bred 

 and was rearing, and hoped would turn out well, not a 

 work which he had himself completed, and whose per- 

 formance he could predict, in virtue of the principles he 

 had acted on in its design." 



Mr. Froude, at the request of Mr. Brunei, commenced 

 in 1856 an investigation into the laws of motion of a ship 

 among waves. This had been previously attempted by 

 D. Bernouilli, Euler, Moselcy, and others, but without 

 success. None of these writers had realised the funda- 

 mental conditions of the action of wave-water upon a 

 ship, viz., that the direction and intensity of the fluid- 

 pressure at any point is continually changing, and that the 

 direction of pressure is normal to the surface of equal 

 pressure passing through that point. They based their 

 -theories upon hypotheses respecting wave-action that 



were all more or less erroneous, and prevented any useful 

 result being realised. Mr. Froude's method of dealing 

 with the subject was, first of all, to determine the manner 

 in which a wave acts upon a ship ; or, in other words, the 

 mode of operation of the agency whose effects he wished 

 to comprehend. In this he was completely successful, 

 and proved in an unexceptionable manner the mechanical 

 possibility of that form of motion known as the trochoidal 

 sea-wave. On the assumption that the motion of each 

 particle on thej surface of a wave describes an exact 

 circle, whose diameter is the height of the wave from 

 hollow to crest — which agrees with the results of observa- 

 tion — and that the motions of all particles lie' in vertical 

 planes which cut the wave-ridges at right angles, he 

 deduced the theory that the form of the wave would be 

 trochoidal, and that the periodic time would be equal to 

 the time occupied by a heavy body in falling through a 

 height equal to the circumference of a circle whose dia- 

 meter is the length of a wave. It also followed that all 

 sub-surfaces of equal pressure would be trochoids of the 

 same length as the surface-wave, but of a height which 

 would diminish with the depth in accordance with the 



equation — = e —d, where e is the base of Napierian 



logarithms, L the length of the wave from hollow to 

 crest, d the depth of the centre of the circle described by 

 any particle below that of the circle described by the 

 surface-particle, ;;i the radius of the circle at the depth d, 

 and ro that of the circle at the surface. Prof. Rankine 

 also independently deduced the same theory. A striking 

 feature of the investigation was the rapid decrease in the 

 motions of the particles as they are traced to lower depths. 

 Prof. Stokes showed that for all waves of ordinary pro- 

 portions, the motion at a depth equal to the length of the 

 whole wave from crest to crest is only -^\y; of that which 

 belongs to a surface particle. The dynamical conditions 

 of wave-water being thoroughly investigated and estab- 

 lished, Mr. Froude next proceeded to base upon it a 

 scientific theory of the roHing of ships among waves. 



The subject was first brought before the public by Mr. 

 Froude in a paper read before the Institution of Naval 

 Architects in 1861. He stated that he felt some diffidence 

 in bringing forward " what assumes to be a tolerably com- 

 plete theoretical elucidation of a difficult and intricate sub- 

 ject, which has hitherto been treated as if unapproachable 

 by the methods of regular investigation." He pointed out 

 that the characteristic feature of the dynamical laws to which 

 it would be necessary to refer the movements of a ship 

 when rolling is the gradual accumulation of angle during 

 several successive rolls, the cumulative action thus growing 

 up into a maximum, and then dying out by very similar 

 gradations until the ship becomes for a moment steady, 

 when a nearly [similar series of excursions commences 

 and is reproduced ; while in reference to the momentary 

 pause, or cessation of motion, it seems clear that it occurs, 

 not because the waves themselves cease, or cease to act, 

 but because the last oscillation has died out at a moment 

 when the ship and the waves have come to occupy, rela- 

 tively, a position of momentary equilibrium. This is 

 so closely analogous to what happens when a pendulum is 

 subjected to a series of impulses, partially synchronous 

 with its own excursions, that it seemed probable that the 

 laws which govern the latter class of phenomena would be 

 found, mutatis mutandis, applicable to the elucidation of 

 the former also. The investigation of the laws of rolling 

 motion, when thus regarded, therefore assumed the form 

 of the inquiry, " What is the cumulative result of the 

 continuous action of a series of consecutive waves 

 operating on a given ship ? " 



In order to determine this it was necessary first to de- 

 termine how each individual wave will act upon a ship at 

 each instant of time; or, in other words, "What is the 

 position of momentary equiKbrium for a body floating on 

 a wave, and what accelerating force towards that position 



