Fune 30, 1870} 
NATURE 
The introduction of a new word or phrase has often 
marked an epoch in the history of a science ; many of 
the theories systematised by Darwin are to be found in 
the writings of others before the happy phrase “ natural 
selection” gave them a simple and enduring shape. Of 
like importance is Mr. Grove’s expression, “ correlation of 
forces,” and we find in these proceedings several words, 
the introduction of which appears likely to play an im- 
portant part in the development of the science. 
The word “ quantic” for a “rational and integral func- 
tion” has been for many years in use, but “ deficiency ” 
for the number by which the double points of a curve 
(including cusps) fall short of the maximum +} (7-1) (7-2), 
and “unicursal curves” for those curves in which the 
deficiency = 0, or, in other words, curves in which the 
co-ordinates (x, y, 2)can be expressed as rational and 
integral functions of a parameter @, were first used by Prof. 
Cayley before this society. 
The history of mathematics is enriched by an interesting 
paper by Mr. Merrifield, showing that the Arabs were 
acquainted with the property of the radical axis. 
Prof. Sylvester’s proof of Newton’s celebrated rule for 
the discovery of imaginary roots, hitherto undemonstrated, 
and Prof. DeMorgan’s simple proof that every function 
has a root (which we should be glad to see in a fuller 
form) are the principal gains in the mere demonstration of 
known truths. We could wish to see in print the other com- 
munications made to the society by Professors Sylvester 
and DeMorgan, especially those by the former relating 
to unicursal derivation of successive points on cubic 
curves, and to residuals. : 
We heartily congratulate the society on the vitality and 
enthusiasm evident in every page of its proceedings, and 
join with them in their hope that they may shortly obtain 
a tenement of their own worthy of the great, albeit un- 
ostentatious, work in which they are engaged. 
AGING 
Jahrbuch der K.-K. Geologischen Reichsanstalt. Band 
XIX. Nos. 3 and4. 1869. 
OF this admirable repertory of memoirs on the geology of 
the Austrian Dominions, the last two numbers for 1869 
have lately reached us. This publication contains the cream 
of the communications made by members of the Imperial 
Geological Institution, to which tiie carrying out of the 
survey of that great and varied tract of country subject to 
the Austrian sovereign is entrusted; it always includes 
many papers of great importance to the student of 
general geology, and the portions now before us present 
no falling off in this respect. Of strictly geological papers 
Prof. D. Stur is the principal contributor. He describes 
the occurrence of brown coal in the district of Budafa, in 
Hungary ; reports at considerable length on the results of 
the geological survey of the environs of Schméllnitz and 
Géllnitz, also in Hungary; and contributes two other 
papers of more strictly local interest ; but the most im- 
portant of all the geological memoirs is F. von Hauer’s 
notice of the geology of the Western Carpathians, a most 
interesting district in every respect. Dr. M. Neumayr’s 
contributions to the knowledge of indigenous fossil faunze 
contain descriptions of the univalve shells of the fresh- 
water marls of Dalmatia, and of the Congerian strata of 
Croatia and Western Sclavonia; the species, many of 
which are new, are well represented on four pilates. Five 
plates are also devoted to the illustration of another 
paleontological paper, which will probably possess the 
most interest of all for extra-Austrian geologists —namely, 
Dr. E. von Mojsisovics’s memoir on the Cephalopod- 
fauna of the Alpine Muschelkalk, some of the species 
included in which are remarkable for their wide geogra- 
phical distribution, especially the characteristic species of 
the zone (Arcestes or Ammonztes Studeri), which ranges 
to the Himalayas in one direction, and to Spitzbergen in 
another. 
LETTERS TO THE EDITOR 
[The Editor does not hold himself responsible for opinions expressed 
by his Correspondents, No notice is taken of anonymous 
communications. | 
Parhelia 
(1.) Seen near Llandudno on 23rd of Fune, by JOSEPH PAGET 
THIs evening the phenomenon of which a sketch is enclosed 
was seen here, viz. :— 
A BC, a portion of a circle of 45° diameter, resting at B and 
C on mock suns from which a sheaf of light proceeded outwards. 
D, a portion of another circle of go° diameter, at the apex 
of which was an inyerted portion of another circle E of 45° 
diameter. 
(2.) Seen at Highfield House, near Nottingham, on 23rd of Fune 
At 75 36™ p.M., there was an extraordinary appearance in the 
heavens. Immediately above the true sun,at a distance of 23°, 
was an oval-shaped mock sun 6, colourless and not bright ; at 
the distance of go” from the true sun, and on its horizontal level 
were two double mock suns, a B, strongly prismatic and very 
brilliant. They were oval, and from each a flame-like ray ex- 
tended in the opposite direction to the true sun, portions of 
a circle of go” in diameter passed through these mock suns and 
3 he 
Sun } 
also through an unusually large mock sun y, situated 45° immedi- 
ately above the true sun, and which was prismatic and almost 
too brilliant to look at; from this mock sun there was also a 
portion of a circle of 45° in diameter. 
The phenomenon faded away at 74 53™ p.m. The weather 
had been hot from the 13th inst., reaching 86°8° in the shade 
on the 21st, end 86°6° on the 22nd ; whilst on the 23rd (the day 
of this occurrence) it was only 72°, and on the morning of the 
24th, the minimum temperature had fallen to 42-9’ at four feet, 
and to 38°2° on the grass, or a fall of 43°8° in temperature in 
