May 20, 1915| 
NATURE 
335 

whole series of curves with other frequencies; (2) 
that the distinctness of the combination-tones would 
on this theory vary greatly with phase-relationship of 
the primaries; (3) that the tones would disappear when 
the energies of the primaries are not very unequal. 
Voigt applies a similar method to the case. where the 
upper tone is weak compared to the lower to account 
for Koenig’s second beat-tone. The first of the above 
objections again applies. Everett supposed that the 
distortion of the vibration-curve in passing through 
the ear would bring in the note the frequency of which 
is the highest common factor of the primary fre- 
quencies. The effect of a special kind of distortion 
has been tested, consisting in a proportional reduction 
of ordinates in one direction. The result does not 
confirm Eyerett’s contention, but shows the appearance 
of the summation and difference tones.—Miss Maud 
Saltmarsh ; Experiments on condensation nuclei pro- 
duced in gases by ultra-violet light. (1) Nuclei pro- 
duced in air by ultra-violet light which has traversed 
a few centimetres of air are not affected by an electric 
field of 50 volts per centimetre. (2) The nuclei are 
equally effective in producing condensation of water, 
toluol, and turpentine vapours, and they are formed 
even by light which has traversed 50 cm. of air. 
(3) Alcohol vapour condenses without expansion on 
much smaller nuclei than does water vapour. (4) No 
nuclei were formed by the light unless oxygen or CO, 
was present in the gas. (5) No trace of H,O, could 
be detected in the clouds formed on the nuclei. (6) 
Oxygen containing ozone also contains nuclei for 
condensation, and these nuclei have similar properties 
to those formed by ultra-violet light. (7) The nuclei 
can be destroyed by heating the air containing them. 
It seems probable that the nuclei formed by ultra- 
violet light do not cause condensation by virtue of any 
particular chemical composition, but that they are 
particles large enough to act like dust particles as 
centres round which condensation can begin.—S. 
Butterworth ; The self-induction of solenoids of appre- 
ciable winding depth. The existing formule for coils 
of this type—viz., those of Rosa and Cohen—are 
shown to be inaccurate, the error amounting to one- 
fifth of 1 per cent. for the best formula when the 
winding depth is one-tenth the diameter of the coil. 
For greater winding depths .the error is larger. The 
inaccuracy in Rosa’s formula is due to the neglect 
of curvature in correcting for thickness, while in 
Cohen’s formula the error is due to the approximate 
method of development. New formule are developed 
by methods which are free from such approximations, 
and which apply to any coil for which the length is 
greater than twice the diameter, and the winding 
depth is less than one-tenth the diameter. _ These 
formule are capable of giving eight-figure accuracy. 
Simplified formula are also given which are suitable 
when only four-figure accuracy is required. 
Mathematical Society, May 13.—Sir Joseph Larmor, 
president, in the chair.—Dr. Bromwich ; The diffraction 
of waves (i) by a wedge, (ii) by a circular disc.— 
W. E. H. Berwick : An invariant modular equation of 
the fifth order.—G. B. Mathews: A direct method in 
the multiplication theory of the lemniscate function. 
MANCHESTER. 
Literary and Philosophical Society, April 27.—Mr. F. 
Nicholson, president, in the chair.—Prof. W. H. Lang : 
Studies in the morphology of Isoétes :—Part iii., The 
structure and growth of the rhizophoric region of 
I. lacustris, and the development and arrangement of 
the roots. Part iv., The progressive growth of the 
young plant of J. lacustris, and the nature of the 
cortical extension of the stock. In part iii. the struc- 
ture of the rhizophoric lower region of the 
stock of J. lacustris; the nature of its meri- 
NOM227.7, VOLII95|| 

stematic growth; the way in which the segmenta- 
tion of the growing line leads to the growth of a root- 
bearing surtace, exposed by the progressive splitting, 
and to the carriage outwards of the roots initiated close 
to the meristem are described in detail. The organisa- 
tion of the central vascular axis of the rhizophore 
behind the meristematic line is shown to correspond 
remarkably to that of the stem-stele as described in 
part ii. The arrangement of the roots, their exogenous 
insertion, and the course of the root-traces are com- 
pared with the corresponding features of Stigmaria. 
In part iv., the progressive growth and organisation 
of the young plants of I. lacustris are traced from the 
stage of an advanced embryo to that at which a smal 
plant exhibits adult characters as regards root- and 
leaf-arrangement. The symmetry of the plant is only 
evident when the second leaf and second root are 
developed. Further roots arise from a meristem estab- 
lished at the base of the vascular axis of the shoot long 
before any cambial activity has begun. The rhizo- 
phore continues from this meristem as a region of pro- 
gressive growth, bearing roots acropetally. It may 
correspond strictly to the root-bearing region in Lepi- 
dodendreze. The primary root in Isoétes is lateral to 
the axis of the rhizophore; the construction of the 
plant thus appears fundamentally distinct from the 
Gymnosperms and Angiosperms, where the first root 
continues the axis of the plant and behaves as a tap- 
root. The progressive cortical growth of the young 
plants of Isoétes appears to continue uninterruptedly 
into that of the adult stock. 
May i1.—Prof. S. J. Hickson, president, in the 
chair.—Dr. Arthur Harden, Prof. W. W. Haldane Gee, 
and Dr. H. F. Coward: A report on the Dalton 
diagrams. <A report on a collection of about 150 
original pen-and-ink diagrams used by John Dalton. 
They describe the elementary principles of mechanics, 
heat, optics, and astronomy; the laws of expansion 
by heat; the special scale of temperature used by 
Dalton; meteorological subjects; and chemistry and the 
atomic theory. The diagrams dealing with the atomic 
theory show that Dalton used graphic formule for 
“compound atoms’? much more frequently than would 
be suspected from a study of his printed books or note- 
books. Many sheets illustrate the atomic composition 
of inorganic and organic substances. The latter are 
almost completely ignored in Dalton’s published works, 
and in consequence his representation of them would 
be unknown at the present time were it not for the 
information disclosed by these diagrams. The formulz 
are, however, very different from those now accepted. 
One of the diagrams is a list of atomic weights and 
symbols made in 1807, and is, so far as is known, the 
second list presented in public by him. 
PARIS. 
Academy of Sciences, May 10.—M. Ed. Perrier in the 
chair.—E. Bompiani: The equations of Laplace with 
equal invariants.—G. H. Hardy: The problem of 
divisors of Dirichlet.—Et. Delassus: The holonomial 
movements with multiple forms of Bagrange.—G. 
Chesneau : Contribution to the study of coloured glass 
of the Middle Ages. Analyses of violet, blue, green, 
and red glass, dating from the end of the thirteenth 
century, from Rheims Cathedral. The oxides of copper, 
nickel, cobalt, manganese, and iron were used as the 
colouring materials.—J. Bougault : The dioxytriazines. 
The synthesis of substituted semicarbazides. A method 
for preparing asymmetrical dioxytriazines has been 
given in a previous paper. These behave as acids 
towards alcohols, and give mono- and di-ethers in 
which the alkyl group is attached to nitrogen. The 
mono-alkylbenzyldioxytriazine on hydrolysis with 
boiling allaline carbonate solution gives the alkyl- 
semicarbazone of phenylpyruvie acid, and this, treated 
