ny 
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Oct. 6, 1870] 
NATURE 
46 
sent the current produced in the same mass of fluid by the com- 
bination of the forces, which, acting separately, would produce 
the current represented by the first two sets of stream-lines 
respectively. The third set may be called the resultant stream- 
lines. Suppose, now, that a third set of component stream-lines 
are drawn representing the current produced by a third set of 
forces : this will form a network with the previously drawn re- 
sultant stream-lines, and a set of lines drawn through the angles 
of the meshes of this new network will represent the resultant 
current produced by the combination of the three sets of forces ; 
and so on to combinations of any degree of complexity that may 
be required. In order to draw a system of stream-lines suited 
for the longitudinal lines of a ship, three sets at least of com- 
ponent stream-lines must be combined. One of these is a set of 
parallel straight lines, representing a uniform current, running 
astern with a speed equal to the actual speed of the vessel. 
A second set consists of straight lines radiating from a point 
called a focus in the forepart of the vessel, and they represent 
the diverging motion that is produced by the ship displacing 
the water near her bows. The third set of component stream- 
lines consists of straight lines converging towards a second 
focus in the afterpart of the vessel; and they represent the 
motion of the water closing in astern of the ship. The resultant 
stream-lines thus produced present a great variety of forms, all 
resembling those of actual ships having all proportions of length 
to breadth, and all degrees of bluffmess and fineness at the 
ends, ranging from the absolute bluffness of a sort of oval 
to a bow and stern of any degree of sharpness that may be re- 
quired. It has been proposed to call stream-lines of this sort 
Oogenous Neoids ; that is, ship-like lines generated from an 
oval, because any given set of them can be generated by the flow 
of a current of water past an oval solid of suitable dimensions. 
The pre erties of these curves were investigated in 1869. They 
have, however, this defect, that the absolutely bluff ovals are the 
only curves of the kind that are of finite extent ; all the fixed 
curves extend indefinitely in both directions, ahead and astern ; 
and in order to imitate the longitudinal lines of a fine-ended 
vessel, a part only of some indefinitely extended curve must be 
taken. In 1870 an improvement in the construction of such 
curves was introduced, by which that defect was overcome ; it 
consisted in the introduction of one or more additional pairs of 
foci, involving the combination of at least five sets of component 
stream-lines. By this device it is possible to imitate longitudinal 
lines of actual vessels by means of complete closed curves, with- 
out rising portions of indefinitely extended curves ; and thus the 
motion of the particles of water, as shown by the stream-lines 
that lie outside the closed lines representing the form of the 
vessel, becomes more definite and accurate. The lecturer men- 
tioned that the idea of employing four foci and upwards had 
been suggested to him by the experiments of Mr. Froude 
on the resistance of boats modelled so as to resemble the 
form of a swimming bird ; for which purpose stream-lines with 
four foci are specially adapted. It has been proposed to call 
such lines Cycnogenous Neoids—that is, ship-like curves of 
shapes like that of aswan. In such curves the outer foci—that 
is, the foremost and aftermost—are situated in or near the stem 
and sternpost of the vessel, which are represented in plan by 
small horse-shoe curves, as if they were rounded off at the 
corners instead of being squared, as in ordinary practice. The 
inner foci are situated respectively in the fore and after body. 
When the foci of the longitudinal lines of a vessel have been 
determined, the proportion borne by the aggregate energy of 
the motion impressed on the particles of water to that of the 
motion of the vessel herself can be approximately determined. 
The lecturer next proceeded to explain the bearing of some of 
the mechanical properties of waves upon the designing of 
vessels, especially when these properties are taken in combination 
with those of stream-lines. It had long been known that ships, 
in moving through the water, were accompanied by trains of 
waves, whose dimensions and position depended on the speed of 
the vessel ; but the first discovery of precise and definite laws 
respecting such waves was due to Mr. Scott Russell, who pub- 
lished it about twenty-five yearsago. The lecturer now described 
in a general way the motions of the particles of water in a series 
of waves, and illustrated them by means of a machine designed 
for that purpose. He showed how, while the shape of the wave 
advances, each individual particle of water describes an orbit 
of limited extent ina vertical plane. The periodic time of a 
wave, its length, the depth to which a disturbance bearing a 
given ratio to the disturbance at the Surface of the water extends, 
and its speed of advance, are all related to each other by laws 
which the lecturer explained. He then stated that Mr. Scott 
Russell had shown that when the vessel moved no faster than the 
natural speed of advance of the waves that she raised, these waves 
were of moderate height, and added little or nothing to her re- 
sistance ; but when that limit of speed was exceeded, the waves 
and the resistance caused by them increased rapidly in magnitude 
with increase of speed. His own (Professor Rankine’s) opinion 
regarding these phenomena was, that when the speed of the 
vessel was less than or equal to the natural speed of the waves 
raised by her, the resistance of the vessel consisted wholly, or 
almost wholly, of that arising from the friction of the water 
gliding over her skin ; and he considered that this opinion was 
confirmed by the results of practical experience of the performance 
of vessels. The wave motion, being impressed once for all on 
the water during the starting of the vessel, was propagated 
onward like the swell of the ocean, from one mass of water to 
another, requiring little or no sensible expenditure of power to 
keep it up. But when the ship was driven at a speed exceeding 
the natural speed of the waves that she raised, these waves, in 
order to accompany the ship, were compelled to spread outwards 
instead of travelling directly ahead ; and it became necessary 
for the vessel, at the expense of her motive power, to keep 
continually originating wave-motion afresh in previously 
undisturbed masses of water ; and hence the waste of power 
found by experience to occur when a ship was driven at a 
speed beyond the limit suited to her length. This di- 
vergence or spreading sideways of the train of waves had a 
modifying effect on the stream-lines representing the motions of 
the particles of water. It caused them, in the first place, to 
assume a sinuous or serpentine form ; and then, instead of closing 
in behind the ship to the same distances from her course at 
which they had been situated when ahead of her, they remained 
permanently spread outwards. In other words, the particles of 
water did not return to their original distances from the longi- 
tudinal midship plane of the vessel, but tzre shifted laterally 
and left there, much as the sods of earth are permanently shifted 
sideways by the plough. The place of the water which thus 
fails to close in completely astern of the vessels is supplied by 
water which rises up from below and forms a mass of eddies 
rolling in the wake of the ship. This was illustrated by a dia- 
gram. Lastly, the lecturer explained the principles according to 
which the steadiness of a ship at sea is affected by storm-waves, 
and the difference between the properties of steadiness and stiff- 
ness. The mathematical theory of the stability of ships had been 
known and applied with useful results for nearly a century ; 
but in the course of the last ten years it had received some im- 
portant additions, due especially to the researches of Mr. Froude 
on the manner in which the motions of the waves affect the 
rolling of the vessel. A stiff ship is one that tends strongly to 
keep and to recover her position of uprightness to the surface of 
the water. A steady ship is one that tends to keep a position 
of absolute uprightness. In smooth water these properties are 
the same ; and astiff ship is also a steady ship. Amongst waves, 
on the other hand, the properties of stiffmess and steadiness 
are often opposed to each other, A stiff ship tends as 
she rolls, to follow the motions of the waves as they roll. 
She is a dry ship; but she may be what is called uneasy, 
through excessive rolling along with the waves. The property 
of stiffness is possessed in the highest degree by a raft, and by a 
ship which, like a raft, is broad and shallow, and whose natural 
period of rolling in smooth water is very short compared with the 
periodic time of the waves. In order that a ship may be steady 
among waves, her natural period of rolling should be consider- 
ably longer than that of the waves; and in order that this 
property may be obtained without making the vessel crank, the 
masses on board of her should be spread out sideways as far as 
practicable from her centre of gravity ; this is called ‘‘ winging 
out the weights.” A vessel whose natural period of rolling in 
smooth water is only a little shorter or a little longer than that 
of the waves, has neither the advantages of stiffness nor those 
of steadiness, for she rolls to an angle greater than that of the 
slope of the waves ; and her condition is specially unsafe if her 
natural period of rolling is a little greater than that of the waves, 
for then she tends to heel over towards the nearest wave-crest, to 
the danger of its breaking over her deck. This is called ‘ roll- 
ing against the waves.” The most dangerous condition is that 
of a vessel whose period of rolling in smooth water is equal to 
that of the waves that she encounters, for then every successive 
wave makes her roll through a greater angle ; and under these 
