NATURE 
| Feb. 1, 1883 
Nevertheless on the whole, and in the long course of 
time, the forces of the grand old volcano may be dying 
out. For in an earlier work than any other that I had 
ever met with before about Teneriffe, I have lately read a 
very different account of the average state of the summit 
crater, to what it has been in, ever since the days of modern 
travelling and visitation began. 
The book [ allude to, in the possession or the Earl of 
Crawford and Balcarres, is an exquisitely illuminated MS. 
volume in vellum, by the Chevalier Edmund Skory, of the 
date of about 1582, and dedicated to that name so dear to 
all the students of Natural Science, viz. : 
“ Sir Frances Bacon, 
“the knower and lover of all good Arts.” 
The very first dipping into its old MS. pages brought 
out a quaint proof of its antiquity, by its involuntary allu- 
sions to Garachico, as a city that was necessarily the 
island's chief delight and glory ; the seat of its Govern- 
ment, the abode of its commerce, the place of all its ship- 
ping, and of course, because it was so prosperous, destined 
to live a queen for ever, and to be the joy of all peoples. 
Yet it is now, and has beea for nearly two centuries as 
deserted as another Tyre ; hardly fit to be the habitation 
of foxes, a mere howling wilderness of black rocks, for a 
few fishermen to spread their nets upon. 
This happily preserved author then in the Earl’s valuable 
library, who had abundant experience of Teneriffe more 
than a century previous to Garachico’s Herculaneum fate, 
speaks of — 
« Great stones being, with noyse, fyre and smoke, many 
‘times cast forthe’’ out of the craterlet on the top of the 
peak. 
Also that, ‘On the sommer time the fyers doe ofte 
breake forth from out the hole in the topp of this hill ; into 
which, if you throw a great stone, it soundeth as if a great 
weight had fallen upon infinite store of hollow Brasse.” 
C. P1azzi SMYTH 
FOHANN BENEDICT LISTING 
NE of the few remaining links that still continued to 
connect our time with that in which Gauss had 
made Gottingen one of the chief intellectual centres of 
the civilised world has just been broken by the death of 
Listing 
If a man’s services to science were to be judged by the 
mere number of his published papers, Listing would not 
stand very high. He published little, and (it would seem) 
was even indebted to another for the publication of the 
discovery by which he is most widely known. This is 
what is called, in Physiological Optics, Listing’s Law. 
Stripped of mere technicalities, the law asserts that if a 
person whose head remains fixed turns his eyes from an 
object situated directly in front of the face to another, the 
final position of each eye-ball is such as would have been 
produced by rotation round an axis perpendicular alike to 
the ray by which the first object was seen and to that by 
which the second is seen. “Let us call that line in the | 
retina, upon which the visible horizon is portrayed when 
we look, with upright head, straight at the visible horizon, 
the horizon of the retina. Now any ordinary person 
would naturally suppose that if we, keeping our head in 
an upright position, turn our eyes so as to look, say, up 
and to the right, the horizon of the retina would remain 
parallel to the real horizon. This is, however, not so. If 
we turn our eyes straight up or straight down, straight to 
the right or straight to the left, it is so, but not if we look 
up or down, and also to the right or to the left. In ¢hese 
eases there is a certain amount of what Helmholtz calls 
“ wheel-turning ” (Aad-drehung) of the eye, by which the | 
horizon of the retina is tilted so as to make an angle with | 
the real horizon, The relation of this “ wheel-turning ”’ 
to the above-described motion of the optic axis is expressed 
by Listing’s law, in a perfectly simple way, a way so 
simple that it is only by going back to what we might 
have thought nature should have done, and from that 
point of view, looking at what the eye really does, and 
considering the complexity of the problem, that we see 
the ingenuity of Listing’s law, which is simple in the 
extreme, and seems to agree with fact quite exactly, 
except in the case of very short-sighted eyes.” The 
physiologists of the time, unable to make out these things 
for themselves, welcomed the assistance of the mathema-_ 
tician. And so it has always been in Germany. Few 
are entirely ignorant of the immense accessions which 
physical science owes to Helmholtz. Yet few are aware 
that he decame a mathematician in order that he might 
be able to carry out properly his physiological researches. 
What a pregnant comment on the conduct of those 
“ British geologists” who, not many years ago, treated 
with outspoken contempt Thomson’s thermodynamic 
investigations into the admissible lengths of geological 
periods ! 
Passing over about a dozen short notes on various sub- 
jects (published chiefly in the Gottingen “‘ Vachrichten”), 
we come to the two masterpieces, on which (unless, as 
we hope may prove to be the case, he have left much 
unpublished matter) Listing’s fame must chiefly rest. 
They seem scarcely to have been noticed in this country, 
until attention was called to their contents by Clerk- 
| Maxwell. 
The first of these appeared in 1847, with the title 
Vorstudien zur Topologie. \t formed part of a series, 
which unfortunately extended to only two volumes, called 
Géttinger Studien. The term Topology was introduced 
by Listing to distinguish what may be called qualitative 
| geometry from the ordinary geometry in which quantita- 
tive relations chiefly are treated. The subject of knots 
| furnishes a typical example of these merely qualitative 
relations. For, once a knot is made on a cord, and the 
free ends tied together, its nature remains unchangeable, 
so long as the continuity of the string is maintained, and 
| is therefore totally independent of the actual or relative 
dimensions and form of any of its parts. Similarly when 
two endless cords are linked together. It seems not un- 
likely, though we can find no proof of it, that Listing 
was led to such researches by the advice or example of 
Gauss himself; for Gauss, so long ago as 1833, pointed 
out their connection with his favourite electromagnetic 
inquiries. 
After a short introductory historical notice, which shows 
that next to nothing had then been done in his subject, 
Listing takes up the very interesting questions of Inversion 
(Umkehrung) and Perversion (Verkehrung) of a geome- 
trical figure, with specially valuable applications to images 
as formed by various optical instruments. We cannot 
enter into details, but we paraphrase one of his examples, 
which is particularly instructive :— 
“© A man on the opposite bank of a quiet lake appears in the 
watery mirror perverted, while in an astronomical telescope he 
appears inverted. Although both images show the head down 
and the feet up, it is the dioptric one only w hich :—if we could 
examine it :—would, like the original, show the heart on the left 
side ; for the catoptric image would show it on the right side. 
In type there is a difference between inverted letters and per- 
verted ones. Thus the Roman V becomes, by inversion, the 
Greek A; the Koman R perverted becomes the Russian $]; the 
Roman L, perverted and inverted, becomes the Greek Tr. Com- 
positors read perverted type ithout difficulty :—many newspaper 
readers in England can read inverted type. * ** The numerals 
on the scale of Gauss’ Magnetometer mus’, in order to appear to 
the observer in their natural position, be both perverted and 
inverted, in consequence of the perversion by reflection and the 
inversion by the telescope.” 
Listing next takes up helices of various kinds, and dis- 
cusses the question as to which kind of screws should be 
~~ SS 3? oe | 
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