188 T. A. Hirst on Ripples, - 
upper half of the sht, whilst the light of the other spark passes 
through the lower half of the slit, so that the two spectra are 
seen one directly above the other. If both pair of electrodes are 
pure, both the spectra are alike; if a metallic salt is brought on 
to one of the electrodes, the lines peculiar to that metal appear 
in the one spectrum in addition to those present before. These 
are recognized at the first moment, because they are absent in the 
other spectrum. The lines which are common to the two spectra 
may serve, when they are once for all drawn, as the simplest 
mode by which to represent the position of the lines of the other 
metals employed. 
“1 have proved that in this way the metals of the rare earths, 
yttrium, erbium, terbium, &c., may be detected in the most cer- 
tain and expeditious manner. Hence we may expect that, by 
help of Ruhmkorff’s coil, the spectrum-analytical method may 
be extended to the detection of the presence of all the metals. 
I trust that this expectation may be borne out in the continuation 
of the research which Bunsen and J are jointly carrying on with 
the object of rendering this method practically applicable.” 
XXIX. On Ripples, and their relation to the Velocities of Currents. 
By T. Arcuer Hirst, Mathematical Master at University 
College School, London. 
[Concluded from p. 20.] 
[With a Plate. ] 
al. 4 he art. 20 it was shown that when a jet or partially im- 
mersed solid cylinder is made to describe a circle of 
radius a in still water, the ripple it produces has a cusp C (fig. 7, 
Plate I.), which describes another circle whose radius r has to 
a the same ratio that the velocity X, with which the waves causing 
the ripple are propagated, has to the velocity u of the jet; and 
further, that the angle @ between the radii to the jet and to the 
cusp varies with 7, in accordance with the relation 
tan ($,—6)=¢,= eel oils os ela 
Hence if the axis of polar coordinates pass through, and rotate 
with the jet, this is the equation of a curve upon which the cusp 
of the ripple must le, no matter with what velocity the jet may 
be rotating. The curve itself, as may be easily shown (Plate LV. 
fig. 2), lies entirely within the cir cle (a); it commences at the jet A, 
r=a, 6=0, where it touches the axis O A, and proceeds inwards, 
turning its ‘convexity towards the centre 0, until on arriving at 
