460 
NATURE 
[ Oct. 6, 1870 
whole lifetime, and let us use them by giving living and intelli- 
gent learning, not obsolete and parrot instruction. Those who 
are believers in the teaching of the great secondary schools of 
this country will deem my aspirations for the improvement of 
primary education, low and utilitarian, Frankly I admit the latter. 
Such a style of education will never realise Lord Brougham’s 
hope that the time may come when every working man in 
England will read Bacon ; but it might contribute to the fulfil- 
ment of Cobbett’s desire, that the time might come when every 
man in England could eat bacon. I deny, however, that the 
utilitarian view of primary education is ignoble. The present 
system is truly ignoble, for it sends the working man into the 
world in gross ignorance of everything that he is to do in it. 
The utilitarian system is noble, in so far as it treats him 
as an intelligent being, who ought to understand the nature 
of his occupation, and the principles involved in it. The 
great advantage of directing education towards the pursuits and 
cccupations of the people, instead of wasting it on dismal 
verbalism, is that, while it elevates the individual, it at the 
same time gives security for the future prosperity of the nation. 
In the industrial battles of peoples, we are content to leave our 
working classes armed with the old Brown Bess of warfare, while 
men of other countries are arming themselves with modern 
weapons of precision. In the competition of nations, the two 
factors of industry—raw material and intellect, applied to its 
conversion into utilities—are altering their values. The first is 
rapidly decreasing, the second quickly augmentingin value. We 
anchor our hopes on the sand, which the advancing tide of 
knowledge is washing away, while other nations throw out their 
anchors on firm ground accumulating around, and enabling their 
vessels to ride in safety. There are instances of nations, rich 
in the natural resources of industry, yet poor from want of 
knowledge how to apply them ; and there are opposite examples 
of nations utterly devoid of industrial advantages, but consti- 
tuted of an educated people who use their science as a com- 
pensation for their lack of raw material. Spain is an example 
of the first class, and Holland of the second. Having pointed 
out at some length the contrast between these two countries, in 
consequence of the difference of their culture, Dr. Playfair pro- 
ceeded to show the necessity of good physical training, to argue 
in favour of a compulsory educational system, and of graded 
education, and to define the true position and qualifications of 
teachers in primary schools. 
THE BRITISH ASSOCIATION 
LECTURE ON STREAM LINES IN CONNECTION WITH 
ARCHITECTURE, BY PROF. RANKINE 
THE lecturer stated that his object was to give a brief sum- 
mary of the results of some application of the mathematical 
theory of hydrodynamics to questions regarding the design- 
ing of the forms of ships, and the mutual actions between a 
ship and the water in which she floats. The art of designing 
the figures of ships had been gradually developed by pro- 
cesses resembling those called ‘‘natural selection,” and the 
“‘strugele for existence” in the course of thousands of years, 
and had arrived in skilful hands at a perfection which left 
little more to be desired, when the object was to design a 
ship that should answer purposes and fulfil conditions 
which had previously been accomplished and fulfilled in the 
course of practical experience. But cases now frequently arose 
in which new conditions were to be fulfilled; and purposes 
accomplished beyond the limits of the performance of previous 
vessels, and in such cases the process of gradual development by 
practical trials made without the help of science was too slow 
and too costly, and it became necessary to acquire and to apply 
scientific knowledge of the laws that regulate the actions of the 
vessel on the water and of the water on the vessel. Amongst 
the questions thus arising were the following : What ought to be 
the form of the immersed surface or skin of a ship in order that 
the particles of water may glide smoothly over it? And, the 
form of such a surface being given, how will it affect the motion 
of particles in its neighbourhood, and what mutual forces will be 
exerted between the particle of water and that surface? Practical 
experience, unaided by science, answers the first question by 
saying that the surface ought to belong to a class called ‘‘ fair 
surfaces” (that is, surfaces free from sudden changes of direction 
-and of curvature) of which various forms have in the course of 
-ages been ascertained by trial, and are known to skilful ship- 
NAVAL 
builders. That answer is satisfactory so far as it goes ; but in 
order to solve problems involving the mutual actions of the ship 
and the water, something more is wanted, and it becomes neces- 
sary to be able to construct fair surfaces by geometrical rules 
based on the laws of the motion of fluids, and to express their 
forms by algebraic equations. There were many very early 
attempts to do this, but through not being based on the laws 
of hydrodynamics, they resulted merely in the finding of empirical 
rules for reproducing when required forms which had previously 
been found to answer in practice, and did not lead to any know- 
ledge of the motions of the particles of water or of the forces 
exerted by and upon them ; and they had little or no advantage 
over the old process of modelling by the eye and hand, and of 
“fairing” the lines with the help of an elastic rod called a 
“batten.” As regards this process, indeed, the mathematical 
methods about to be referred to are to be regarded, not asa 
substitute for it in designing the form of a ship, but as a 
means of arriving at a knowledge of the mutual actions 
between her and the water, which the old process is 
incapable of affording. The earliest method of constructing the 
figures of ships by mathematical rules, based on hydrodynamical 
principles, was that proposed by Mr. Scott Russell about 
twenty-five years ago, and since extensively practised. It con- 
sisted in adopting for the longitudinal lines of a ship curves 
imitated from the outlines of waves in water. The motions 
which surfaces formed upon this model impress on the water 
were known to a certain degree of approximations. These 
‘*wave-lines,” however, although they were fair curves in the 
sense already mentioned, were by no means the only fair curves, 
but were enly one class out of innumerable classes of curves 
having the property of gliding smoothly through the water ; 
and it was well known in practice that vessels had proved sue- 
cessful whose lines differed very widely from wave-lines. It was 
therefore desirable that methods should be devised of construct- 
ing by mathematical rules based on the laws of the motions of 
fluids, a greater variety of curves possessing the requisite pro- 
perty of fairness, and not limited to the wave-line shape. Such 
had been the object of a series of researches that had been 
communicated to the Royal Society at different dates since 1862. 
They related to the construction of what it has been proposed to 
call stream-lines. A stream-line is the track or path traced by 
a particle of water in a smoothly and steadily flowing current. 
If, when a ship is gliding ahead through the water with a certain 
speed, we imagine the ship to be stationary, and the water to be 
flowing astern past the ship in a smooth and steady current with 
an equal average speed, the motions of the ship and of the par- 
ticles of water relatively to each other are not altered by that 
supposition; and it becomes evident that if the form of surface 
of the skin of the ship has the property of fairness, all the tracks 
of the particles of water, as they glide over that surface, are 
stream-lines, and the surface itself is one containing an indefinite 
number of stream-lines, or, as it has been called, a stream-line 
surface. It is also to be observed, that when we have deduced 
from the laws of the motion of fluids the relations which exist 
between the form of the stream-lines in different parts of a 
current, and between those forms and the velocities of the par- 
ticles as they glide along different parts of those lines, we know 
the relations between the form and speed of a ship whose surface 
coincides with a certain set of these stream-lines, and the motions 
of the particles of water in various positions in the neighbour- 
hood of that ship. The lecturer then proceeded to explain, and 
to illustrate by diagrams, the methods of constructing stream- 
lines. These methods were based upon the application to 
stream-lines in a current of fluid of a mathematical process 
which had previously been applied by Mr. Clerk Maxwell to 
lines of electric and magnetic force. A current of fluid is repre- 
sented on paper by drawing a set of stream-lines so distributed 
that between each pair of them there lies an elementary stream 
of a given constant volume of flow. Thus, while the direction 
of flow is indicated in any given part of the current by the 
direction of the stream-lines, the velocity of flow is indicated by 
their comparative closeness and wideness apart, being evidently 
greatest where these lines lie closest together, and least where 
they are most widely spread. If, upon the same sheet of paper, 
we draw two different sets of stream-lines, these will represent 
the currents produced in one and the same mass of fluid by two 
different sets of forces. The two sets of lines form a network, 
and, if through the angles of the meshes of that network we draw 
a third set of stream-lines, it can be proved from the principle of 
the composition of motions, that this third set of lines will repre- 
