346 
are so analogous, that if the distance of the contacts, the 
duration of the change at the seat of excitation (mono- 
phasic variation), and the rate of propagation are known, 
at is easy to forecast the curve of the diphasic variation. 
By a similar method to that employed in the study of 
NATURE 
[AucusT 10, 1899 
and this change spreads from the excited spot to parts 
at a distance at a rate which varies with temperature. 
The interval of time between the culmination of the 
electrical response and that of the change of form is 
much more obvious in the leaf than in the heart, because 
muscle, the effect at the distal contact can be partially or | the mechanism by which the latter manifests itself works 
Fic. 7.—Response of veratrinised muscle to instantaneous stimulation. 
‘entirely cancelled. All that is necessary is to destroy by 
heat the surface under the distal electrode. The result 
of this operation is that, as in muscle, the devitalised 
area becomes, while unexcited, negative to all uninjured 
parts, and that if the surface is excited in the neighbour- | 
hood of the uninjured contact, the photographic curve 
assumes characters which correspond with those of the 
monophasic curve of muscle, with this noteworthy 
difference that its duration is that of the ventricular beat. 
This can be best understood from the photographic | 
curves reproduced in Fig. 8, with reference to which it is | 
to be noted that the rate of movement of the plate on | 
which the movement of the mercury column is projected | 
is fen times as slow as the slowest 
rate of movement used in observations 
of muscle. Had the excursion been 
projected on a plate moving at the 
same rate, the first half of the curve 
would have had a contour similar to 
the veratrine curve. It expresses a 
sudden coming into existence of a 
difference of potential between the 
two contacts which may be main- 
tained (in the heart) for more than 
two seconds. 
In the second curve of Fig. 8 the 
curve begins as in the first, but the 
effect on the electrometer of the 
change which is taking place at the 
proximal electrode is immediately 
afterwards counteracted and balanced 
by the similar change at the distal 
contact, and is followed by a period 
of indifference, the end of which is 
marked by a descent of the column. 
This (as was explained by the lecturer 
many years ago) means that the effect 
at the distal electrode over-lasts that 
very slowly, as compared even with 
cardiac muscular fibres. This con- 
trast, however, affords no ground for 
doubting that the two processes are, 
as regards their intimate nature, 
analogous. 
MATHEMATICS OF THE 
SPINNING-TOP. 
Il. 
T is instructive at this stage to go 
behind the various relations given 
by Darboux and Routh, connecting 
A, B, C, D, and 6, and the accented 
letters, and to examine their inner 
geometrical significance ; various in- 
teresting theorems of Geometrical 
Conic Sections will be required, which will show the 
practical utility of the study of this elegant subject, as 
presented in Taylor's “ Geometry of Conics.” 
In the first place we can connect up the notation of 
Darboux and Routh by taking 
a, b, c,h HV, HT, HP, ae D D = 
i OD A’ B @ JOD: 
Darboux’s a, 4, c, # being of the same dimensions as 7, 
an angular velocity estimated in radians/second. 
From the fundamental property of the herpolhode as 
the trace of the points of contact of a quadric surface, 
rolling about its centre O on a fixed plane GH, namely, 
(28) 
which occurs at the proximal. 
The lecture concluded with a com- 
parison of the electromotive proper- 
ties of the leaf of the fly-trap with 
those of muscle. If the same method of exploration is | 
applied to the surface of the leaf as to the ventricle of the 
heart of the frog, it is easy to show that the phenomena 
srved after excitation in the two structures are es- | 
sentially analogous. In both an electrical change is the 
immediate result of a localised instantaneous excitation, | 
NO. 1554, VOL. 60] 
F'Uve_ SCCORAS. 
Fic. 8.—Monophasic and diphasic photographic curves of the ventricle of the heart of the frog. 
that the radius vector GH and the tangent HK are con- 
jugate on the rolling surface, combined with the 
properties of conjugate diameters, we can deduce the 
1‘ Ueber die Theorie des Kreisels.” F. Klein und A. Sommerfeld. 
Heft i, ii. Pp. 196 and 197 to 512. .(Leipzig: Teubner, 1897-8.) (Con- 
tinued from p. 322.) 
ee 
