50 



NATURE 



[Nov. 1 8, 1875 



sensible progress beyond his fellows who had continued 

 doing their ordinary more varied work. Though some 

 part of this might be owing to his being outside the 

 regular classes, yet by far the greater part was due to the 

 monotonous work palling upon him and dulling his 

 brain. 



The education of young children should be made like 

 their picture-books. The pictures should be such as will 

 induce the little learner to read and study the letterpress 

 in order to find out more about them, and for that pur- 

 pose they can scarcely be too numerous. A boy when his 

 mind first opens to the world around him is like a man in 

 a large strange house. He must needs go about and 

 learn the arrangement of the building, peer into every 

 room, examine the varied prospect from every window, 

 before he can decide which rooms he will make his own ; 

 but when once he has made his choice, he will probably 

 keep to one or two rooms and seldom enter the others.* 



G. Herbert West 



Ascham House School, Bournemouth 



THE THEORY OF "STREAM LINES" IN RELA- 

 TION TO J HE RESISTANCE OF SHIFSf 



nPHE address of the President of a Section would year by year 

 possess an appropriate interest, if it could always consist of 

 an exposition of the progress made during the past year in the 

 department ot science which the Section embraces. And many 

 of the addresses to this and other sections have conformed to this 

 pattern with marked success. 



But the adequate preparation of an address shaped in this 

 approved mould would require a range of experience and a grasp 

 of thought such as few possess ; and custom has wisely saiKtioned 

 a type of address which, though less appropriate to the occasion, 

 need not be either uninteresting or inapposite. And we, in this 

 Section, have not to search far for instances in which its Presi- 

 dent has charmed and instructed us by a masterful exposition of 

 some single subject in practical science, or by a timely reminder 

 of the improvident manner in which wc deal with some precious 

 store of natural wealth, 



I must express a hope that it will not be regarded as a convei'- 

 sion of liberty into license, if the subject I have chosen obliges 

 me to introduce a further innovation, and to use diagrams and 

 experiments in order to make my meaning clear. 



I propose to treat of certain of the fundamental principles 

 which govern the behaviour of fluid, and this with special refer- 

 ence to the resistance of ships. By the term "resistance" I 

 mean the opposing force which a ship experiences in its progress 

 through the water. 



Considering the immense aggregate amount of power expended 

 in the propulsion of ships, or, in other words, in overcoming the 

 resistance of ships, I trust you will look favourably on an attempt 

 to elucidate the causes of this resistance. It is true that im- 

 proved results in ship-building have been obtained through accu- 

 mulated experience ; but it unfortunately happens that many of 

 the theories by which this experience is commonly interpreted, 

 are interwoven with fundamental fallacies, which, passing for 

 principles, lead to mischievous results when again applied beyond 

 the limits of actual experience. 



The resistance experienced by ships is but a branch of the 

 general question of the forces which act on a body moving 

 through a fluid, and has within a comparatively recent period 

 been placed in an entirely new light by what is commonly called 

 the theory of stream-lines. 



The theory as a whole involves mathematics of the highest 

 order, reaching alike beyond my ken and my purpose ; but I 

 believe that, so far as it concerns the resistance of ships, it can 

 be sufficiently understood without the help of technical mathe- 

 matics ; and I will endeavour to explain the course which I have 

 myself found most conducive to its easy apprehension. 



It is convenient to consider first the case of a completely sub- 

 merged body moving in a straight line with uniform speed 

 through an unlimited ocean of fluid. A fish in deep water, a 

 submarine motive torpedo, a sounding lead while descending 



■■ My experience has been entirely with boys, but I feel sure that ele- 

 mentary science might be taught with at least equal advantage to little girls. 



t Address to the Mechanical Section of the British Association, Bristol, 

 August 25, 1875; by William Froude, C.E , M.A., F.R.S. President of 

 th« S«cUen. k«vis«d nad eKten«i«d by th« nutbor. 



through the water, if moving at uniform speed, are all examples 

 of the case I am dealing with. 



It is a common but erroneous belief that a body thus moving 

 experiences resistance to its onward motion by an increase of 

 pressure on its head end, and a diminution of pressure on its 

 tail end. It is thus supposed that the entire head end of the body 

 has to keep on exerting pressure to drive the fluid out of the 

 way, to force a passage for the body, and that the entire tail end 

 has to keep on exerting a kind of suction on the fluid to induce 

 it to close in again— that there is, in fact, what is termed //»s 

 pressure throughout the head end of the body, and minus pressure 

 or partial vacuum throughout the tail end. 



This is not so ; the resistance to the progress of the body is not 

 due to these causes. The theory of stream-lines discloses to us 

 the startling but true proposition, that a submerged body, if 

 moving at a uniform speed through a perfect fluid, would en- 

 counter no resistance whatever. By a perfect fluid, I mean a 

 fluid which is free from viscosity, or quasi-solidity, and in which 

 no friction is caused by the sliding of the particles of tlie fluid 

 past one another, or past the surface of the body. 



The property which I describe as " quasi-solidity " must not 

 be confused with that which persons have in their minds when 

 they use the term "solid water." When people in this sense 

 speak of water as being "solid," they refer to the sensation of 

 solidity experienced on striking the water-surface with the hand, 

 or to the reaction encountered by an oar-blade or propeller. 

 What I mean by "quasi-solidity" is the scrt of stiffness which 

 is conspicuous in tar or liquid mud ; and this property undoubt- 

 edly exists in water, though in a very small degree. But the 

 sensation of solid reaction which is encountered by the hand or 

 the oar-blade, is not in any way due to this property, but to the 

 inertia of the water : it is in effect this inertia which is errone- 

 ously termed solidity ; and this inertia is possessed by the perfect 

 fluid, with which we are going to deal, as fully as by water. 

 Nevertheless it is true, as I am presently going to show you, that 

 the perfect fluid would offer no resistance to a submerged bodj 

 moving through it at a steady speed. It will be seen that th<j 

 apparent contradiction in terms which I have just advanced is 

 cleared up by the circumstance, that in the one case we are deal^ 

 ing with steady motion, and in the other case with the initiation 

 or growth of motion. 



In the case of a completely submerged body in the midst o^ 

 an ocean of perfect fluid, unlimited in every direction, I need 

 hardly argue that it is immaterial whether we consider the body 

 as moving uniformly through the ocean of fluid, or the ocean of 

 fluid as moving uniformly past the body. 



The proposition that the motion of a body through a perfect 

 fluid is unresisted, or, what is the same thing, that the motion of 

 a perfect fluid past a body has no tendency to push it in the 

 direction in which the fluid is flowing, is a novel one to many 

 per£ui)s ; and to such it must seem extremely startling. It arises 

 from a general principle of fluid motion, which I shall presently 

 put before you in detail — namely, that to cause a perfect fluid to 

 change its condition of flow in any manner whatever, and ulti- 

 mately to return to its original condition of flow, does not 

 require, nay, does not admit of, the expenditure of any power, 

 whether the fluid be caused to flow in a curved path, as it must 

 do in order to get round a stationary body which stands in its 

 way, or to flow with altered speed, as it must do in order to get 

 through the local contraction of channel which the presence of 

 the stationary body practically creates. Power, it may indeed 

 be said, is first expended, and force exerted to communicate 

 certain motions to the fluid ; but that same power will ultimately 

 be given back, and the force counterbalanced, when the fluid 

 yields up the motion which has been communicated to it, and 

 returns to its original condition. 



I shall commence by illustrating the action on a small scale 

 by fluid flowing through variously sh.aped. pipes ; and I must 

 premise that in the greater part of what I shall have to say, I 

 shall not require to take account of absolute hydrostatic pressures. 

 The flow of water through pipes is uninfluenced by the absolute 

 pressure of the water, 



I will begin with a very simple case, which I will treat in 

 some detail, and which will serve to show the nature of the 

 argument I am about to submit to you. 



Suppose a rigid pipe of uniform sectional area, of the form 

 shown in Fig. i, something like the form of the water-line of a 

 vessel. 



The portions AB, BC, CD, DE are supposed to be equal in 

 length, and of the same curvature, the pipe terminating at E in 

 exactly the same straight line in which it commenced at A, so 



