24 
NATURE 
[Marcu 5, 1914 
sented in Mr. Cave’s book. When we find irregular 
fluctuations in the wind velocity we must look for 
corresponding irregularities in temperature and pres- 
sure differences at the several levels. These irregu- 
larities are obvious characteristics of the observations 
of wind velocity, pressure difference, and temperature 
difference.—G. M. Dobson: Pilot balloon ascents at the 
Central Flying School, Upavon, during the year 1913. 
These balloon ascents are made with the object of 
obtaining information which will be of use for pilots 
in flying. The results given in this paper are based 
upon ninety-seven ascents. It is found that the direc- 
tion of the wind veers from, and its velocity increases 
with, increasing height above the ground, until the 
gradient direction and velocity are reached. The 
gradient velocity is usually reached at a height of 300 
metres, though the gradient direction is not found 
until a height of about 800 metres. At higher altitudes 
the velocity tends to increase, and the direction con- 
tinues to veer, slightly beyond the gradient velocity 
and direction. 
CAMBRIDGE. 
Philosophical Society, February 9.—Prof. Seward, 
vice-president, in the chair.—A. S$. Marsh: The history 
of the occurrence of Azolla in the British Isles and in 
Europe generally. Azolla filiculoides has recently been 
found in Jesus Ditch, Cambridge. This species, which 
is now common in the Norfolk Broads, has been 
several times wrongly described as A. caroliniana, an 
earlier introduction, from which it is distinguished by 
its larger size, different habit, and the microscopic 
characters of the reproductive organs.—R. C. McLean: 
Amitosis in the parenchyma of water plants. The 
author described the occurrence of the direct. or 
amitotic form of nuclear division in the cortical paren- 
chyma of certain water plants. The nuclei show pecu- 
liar sigmoid forms and remain associated in pairs in 
the cells. The phenomenon is most frequent in 
actively growing regions, so cannot be due to senility. 
—Agnes Arber : Root development in Stratiotes aloides, 
L., with special reference to the occurrence of amitosis 
in an embryonic tissue. An account is given of certain 
features of the general development and the cytology 
of the adventitious roots of Stratiotes aloides. The 
various points dealt with include the nature of the 
root-cap, the origin of the lacunz of the middle cortex, 
&c. The greater part of the paper, however, is con- 
cerned with an account of amitosis in the root-cap, 
cortex, and stele of the immature root. 
DUBLIN. 
Royal Irish Academy, February 23.—Rev. Dr. 
Mahaffy, president, in the chair.—M. W. Iho eiAy 
Extension of number by the introduction of the 
symbols +, —, and 7. Recognising that quantities 
of the same kind are divisible into two groups, usually 
styled positive and negative quantities, to distinguish 
the author called a unit to measure quantities of one 
group a, and a unit to measure quantities of the other 
group 8. Two quantities, such as 12a and 98 combine 
to give 3a, and so on. Denoting ordinary numbers 
by a, b, c, he defined +a written in front of any 
quantity ba or bB, to mean that the quantity is to be 
multiplied by a and the unit not altered, and by —b 
that the quantity is to be multiplied by b and the unit 
altered to the other unit, so that +baa=baa, 
—baa=baB, —baB=bac, +baB=baB. The rule of 
signs in this generalised multiplication is then obvious, 
and as bB=~—ba, the symbol B may be dispensed with, 
and any quantity may be expressed in the form xa, 
where x is an ordinary number with the sign + or — 
prefixed to it, and forms a generalised number, or real 
number. From these definitions he developed the 
algebra of real numbers, which is incomplete in the 
NO} 23TAbeV.On. 62 | 
well-known ways. To generalise number further so 
that all operations may be performed, he began with 
a group of four fundamental units a, a’, B, 6’, arranged 
in cyclical order instead of two. Of these four ‘an’ 
opposite pair, a, 8, are a pair of units considered 
before, and the other pair are any other similarly related 
pair whatsoever. Defining ia written in front of any 
quantity ba or ba’, or bB or bf’ to mean that the quan- 
tity is to be multiplied by a and the unit altered to the 
next in cyclical order, it follows that 2?=—1, 2?=—2, 
| 2*=1, and that any quantity aa+bB+ca'+d’ can be 
written in the form (x+7y)o. Thus the further 
generalised quantity is (x+iy)a, and further generalised 
number x+iy. From these definitions he developed 
the algebra of complex numbers. 
Paris. 
Academy of Sciences, February 23.—M. P. Appell in- 
the chair.—E. Guyou;: The homogeneity of equations 
and the simplification of problems when certain quan- 
tities become small.—Paul Sabatier and M. Murat: 
Contributions to the study of benzhydrol: the prepara- 
tion of benzhydrol and _ tetraphenylethane. In the 
preparation of benzhydrol by the Grignard synthesis 
from benzaldehyde or ethyl formate and_ phenyl- 
magnesium bromide the yield of benzhydrol is poor, 
symmetrical tetraphenylethane appearing as the main 
product of the reaction. This has now been traced to 
the conditions of hydrolysis of the organo-magnesium 
compound. During the fractional distillation of the 
ether solution of the reaction products decomposition 
of the benzhydrol takes place, and this has been shown 
to be due to the catalytic action of small proportions of 
impurities in the liquid, since a similar change does 
not occur when pure solutions of benzhydrol are dis- 
tilled. The conditions for obtaining a good yield of 
the benzhydrol are given.—A. Véronnet: The cooling 
of the earth : its evolution and duration. The formula 
established is similar to that of Fourier, but the proof 
is simpler. The time is 2-46 times that given by the 
Fourier hypothesis, but it remains of the order of 
millions of years.—M. Fessenkoff: The capture of 
comets by Jupiter.—J. Guillaume ; Observations of the 
sun made at the Observatory of Lyons during the 
fourth quarter of 1913. Tables are given showing the 
number of spots, their distribution in latitude, and the 
distribution of the faculae in latitude.—_J. Darmois : The 
method of Laplace.—G. Pick: The evaluation of dis- 
tances in functional space. Ph. Franck ; The approxi- 
mate evaluation of the smallest characteristic value of 
some integral equations.—G. Kowalewski: Intrinsic 
geometry and the first fundamental proposition of 
Sophus Lie.—Alfred Rosenblatt : Certain integrals of a 
system of two ordinary differential equations of the — 
first order satisfying initial singular conditions.—Louis 
, Benoist and Hippolyte Copaux : Some new proofs of the 
laws of transparency of matter for the X-rays in the 
special case of complex mineral salts. The substances 
examined included potassium ferrocyanide, cobaltic 
chloropentammine and potassium  silocomolybdate. 
There was a good agreement between the found values 
and those calculated on the assumption that the trans- 
parency to the X-rays is an atomic property.—B. 
Szilard : The measurements of electrical potentials at 
a distance without wires. A disc coated with o-1 milli- 
gram of radium bromide is insulated and: connected 
with a static electrometer. When the disc is placed 
facing a charged conductor it acquires a_ potential 
varying with the distance, and this potential as read 
off on the electrometer can be used to measure the 
potential of the charged conductor. For the instru- 
ment described, the disc being at a distance of one 
metre from the charged plate, the voltage shown by 
the electrometer was about one-twentieth of that of the 
plate. Various practical applications of the method 
