508 
NATURE 
[ Sept. 23, 1886 
that at a distance of two or three wave-lengths from the last 
of the ircegularities if the breadth of the canal is small in com- 
parison with the wave-length, or at a distance of nine or ten 
breadths of the canal if the breadth is large in comparison 
with the wave-length, the condition of uniform corrugations 
with straight ridges perpendicular to the sides of the canal, 
would be fairly well approximated to, even though the irregu- 
larity were a single projection or hollow in the middle of the 
stream. But the subject of the present communication is 
simpler, as it is limited to two-dimensional motion ; and our 
inequalities are bars, or ridges, or hollows, perpendicular to the 
sides of the canal. Thus, in our present case, we see that the 
condition of ultimate uniformity of the standing waves in the 
wake of the irregularities is closely approximated to at a 
distance of two or three wave-lengths from the last of the 
inequalities. 
A mathematical treatment of the problem thus presented, 
which will appear in the October number of the Paz/osophical 
Magazine, gives, among other results, the following conclu- 
sions :— 
Generally, in every case when V< s/oD the upper surface of 
the water rises when the bottom falls, and the water falls when 
the bottom rises. 
On the other hand, when V> vp, the water surface rises 
conyex over every projection of the bottom, and falls concave 
over hollows of the bottom ; and the rise and fall of the water 
are each greater in amount than the rise and fall of the bottom ; 
so that the water is deeper over elevations of the bottom, and is 
shallower over depressions of the bottom. 
Returning now to the subject of standing waves (or corruga- 
tions of the surface) of frictionless water flowing over a hori- 
zontal bottom of a canal with vertical sides, I shall not at pre- 
sent enter on the mathematical analysis by which the effect of a 
given set of inequalities within a limited space, AB, of the 
canal’s length, in producing such corrngation in the water after 
passing such inequalities, can be calculated, provided the slopes 
of the inequalities and of the surface corrugations are everywhere 
very small fractions of a radian. I hope before long to com- 
municate a paper to the Philosophical Magazine on this subject 
for publication. I shall only just now make the following 
remarks :— 
(1) Any set of inequalities large or small must in general give 
rise to stationary corrugations large or small, but perfectly sta- 
tionary, however large, short of the limit that would produce 
infinite convex curvature (according to Stokes’s theory an obtuse 
angle of 120°) at any transverse line of the water surface. 
(2) But in particular cases the water flowing away from the 
inequalities miy be perfectly smooth and horizontal. This is 
obvious because of the following reasons : 
(i.) If water is flowing over plane bottom with infinitesimal 
corrugations, an inequality which could produce such corruga- 
tions may be placed on the bottom so as either to double those 
previously existing corrugations of the surface or to annul them. 
(ii.) The wave-length (that is to say, the length from crest to 
crest) is a determinate function of the mean depth of the water 
and of the height of the corrugations above it, and of the volume 
of water flowing per unit of time. This function is determined 
graphically in Stokes’s theory of finite waves. It is independent 
of the height, and is given by the well-known formula when 
the height is infinitesimal. 
(iii ) From No. ii. it follows that, as it is always possible to 
diminish the height of the corrugations by properly adjusted 
obstacles in the bottom, it is always possible to annul them. 
(3) The fundamental principle in this mode of considering the 
subject is that, whatever disturbance there may be in a perpetu- 
ally sustained stream, the motion becomes ultimately steady, all 
agitations being carried away down stream, because the velocity 
of propagation, relatively to the water, of waves of less than 
the critical length, is less than the velocity of flow of the water 
relatively to the canal. 
In Part II., to be published in the November number of the 
Philosophical Magazine, the integral horizontal component of 
fluid pressure on any number of inequalities in the bottom, or 
bars, will be found from consideration of the work done in 
generating stationary waves, and the obvious application to the 
work done by wave-making in towing a boat through a canal 
will be considered. The definitive investigation of the wave- 
making effect when the inequalities in the bottom are geometric- 
ally defined, to which I have just now referred, will follow ; and 
I hope to include in Part II., or at all events in Part ILI. to be 
published in December, a complete investigation, illustrated by 
drawings, of the beautiful pattern of waves produced by a ship 
propelled uniformly through calm deep water. 
On a New Form of Current-Weigher for the Absolute Deter- 
mination of the Strength of an Electric Current, by Prof. 
James Blyth.—The object of this paper is to describe a method 
of absolutely determining the strength of an electric current by 
measuring in grammes’ weight the electro-magnetic force be- 
tween two parallel circular circuits, each carrying the same 
current. For convenience of calculation the circles have the 
same radius, and are placed with their planes horizontal. The 
construction of the instrument is as follows :—A delicate chemi- 
cal balance is provided, and the scale-pans replaced by two 
suspended coils of wire. Each of these is made of a single turn 
of insulated copper wire (No. 16 about) fixed in a groove rouna 
the edge of an annular disk of glass or brass of suitable diame- 
ter. The disk is made as thin and light as possible consistently 
with perfect rigidity. By means of two vertical pillars of brass 
this annulus is attached to a rigid cross-bar of dry wood or vul- 
canite, in the middle of which is placed a hook for suspending 
the whole from one end of the balance-beam. On each side of 
the hook, and equally distant from it, two slender rods of brass 
are screwed in in the wooden bar, which support two small plati- 
num cups for holding mercury or dilute acid. The position of 
these cups is so adjusted that, when the whole hangs freely, the 
cups are in line with the terminal knife-edge of the balance- 
beam, and have their edges just slightly above its level. The 
free ends of the insulated wire surrounding the disk, after being 
firmly tied together for a considerable length and suitably bent, 
are soldered to the brass supports of the platinum cups, which 
thus serve as electrodes by means of which a current may be 
sent through the suspended coil. A precisely similar coil is 
suspended from the other end of the balance-beam. We now 
come to the arrangement by means of which a current is led 
through the suspended coils, so as to interfere as little as 
possible with the sensibility of the balance. This constitutes 
the essential peculiarity of the instrument, and is effected in the 
following way :—An insulated copper wire, having its ends 
tipped with short lengths of platinum, is run along the lower 
edge of the beam, and is firmly lashed to it by well-rosined silk 
thread. The ends of this wire, bent twice at right angles, are 
so placed that their platinum tips dip vertically into one of each 
pair of the platinum cups which are attached to the vertical rods 
of the suspended coils. From the other cup of each pair proceed 
two similarly tipped copper wires, which run along the upper 
edge of the beam, and are also firmly tied to it. | These wires, 
however, only proceed as far as the middle of the beam, where 
they are bent, first outwards, one on each side of the beam, at 
right angles to it, and then downwards, so that the platinum 
tips are vertical. The latter dip into two platinum cups attached 
to two vertical rods, which spring from the base-board of the 
balance. These rods are placed at equal distances on each side 
of the beam, and are of such length that the platinum cups are 
in line with the central knife-edge of the beam and have their 
edges just a little above its level. There are thus in all six cups 
and six dipping wires. Three of these are in line on one side 
of the beam, and three on the other. Also the line joining the 
points of each pair of dipping wires is made to coincide with 
the corresponding knife-edge ; and, further, the edges of the 
cups are all in the same plane when the balance is in equilibrium. 
From this it will be obvious that any motion of the beam in the 
act of weighing causes only a very slight motion of the platinum 
wires, which dip into the fluid contained in the cups. The 
resistance, due to the viscosity of the fluid, is thus very small, 
even in the case of mercury, and much smaller still when dilute 
acid is used. In point of fact, the diminution of sensibility due 
to this cause is less than in the case of determining the specific 
gravity of solids by weighing in water in the ordinary way. With 
clean mercury it is quite easy to weigh accurately to a milligramme. 
The fixed coils, constituting two pairs, have the same diameter as 
the suspended coils, and, like them, are made of single turns of in- 
sulated wire wound round the edges of circular disks of glass or brass. 
The disks of each pair are fixed at the requisite distance apart 
toa cylindrical block of wood, so as to have their planes exactly 
parallel and their centres in the same straight line. 
this they are turned up and finished on the same cylindrical 
block on which they are finally to rest. When in position they 
are so placed that, when the balance is in equilibrium, each 
suspended coil hangs perfectly free to move with its plane hori- 
zontal and exactly midway between a pair of fixed coils, For 
To insure | 
