OcrToBER 12, 1899] 
NATURE 
585 
Geometry may be regarded as true; from this fact can be de~ 
duced a group of equations typified by : 
da_ f(b) db : dy 
i ee Ri,)\ 
da siny ada ROS 7, aa da.” 
where a, 4, ¢, are the sides of a triangle, and a, B, 7, the cor- 
responding angles. From these, by appropriate eliminations 
and transformations, the differential equation 
(F(a) = — ett — (f(a) 
can be found for the function # Solving this, we have 
f(a)=« sinh ©, 
K 
and thence can derive the fundamental equations of non- 
Euclidian measurement. 
sinh® /sinh a=sinh o /sin B=sinh < /sin 7: 
K K K 
This was followed by the communication of a Report on 
the Problem of Three Bodies, which Mr. E. T. Whittaker was 
commissioned to prepare at the Toronto meeting. In a 
general sketch of the results, Mr. Whittaker explained the 
transformation which has taken place in dynamical astronomy 
as a result of the researches of Newcomb, \Hill, Lindstedt and 
Poincaré. Formerly the subject might be said to consist of. two 
departments—the planetary and lunar theories; now the dis- 
tinction between these was becoming less prominent, as the 
Problem of Three Bodies was treated in greater generality. 
Among the advances referred to were Dr. Hill’s introduction 
of periodic orbits as a substitute for Keplerian ellipses in the 
first approximation to the solution, Newcomb’s proof that the 
problem can be solved by series in which the time occurs 
only in the arguments of trigonometric functions, Poincaré’s 
theorem that these series are only asymptotic expansions, and 
Bruns’ result that the system possesses no algebraic integrals 
other than those already known. 
A second paper by Prof. Forsyth, ‘‘On Singular Solutions 
of Ordinary Differential Equations,” described some properties 
of the /-discriminant and c-discriminant of an ordinary dif- 
ferential equation of the first order. The two last papers on 
the list were ‘*An Application and Interpretation of In- 
finitesimal Transformations,’’ by Dr. E. O. Lovett, of Princeton 
University, N.J.; and ‘‘On Fermat’s Numbers,” by Lieut. - 
Colonel Cunningham. In the absence of their authors the 
papers were communicated by title, and the session was closed. 
Looking at the papers as a whole, they were of just that 
character which makes the B.A. meeting useful to mathema- 
ticians ; that is, they related not so much to abstruse 
continuations of well-known theories as to new and little- 
known subjects, suggestions of improved notations, reports on 
the recent progress of different branches of mathematics, and 
generally all those topics for which discussion at a real meeting 
is more important than the publication of a paper. 
PHYSICS AT THE BRITISH ASSOCIATION. 
THE attendance of physicists at Dover was rather smaller 
than usual, on account of the occurrence of the Volta Cen- 
tenary celebrations at Como and the simultaneous meetings of 
the French Association for the Advancement of Science at 
Boulogne. Several of those who in past years have been leaders 
in the discussions of Section A were this year conspicuous by 
their absence. Nevertheless, the papers read maintained a 
high standard of excellence, and the reports presented indicate 
that good work is being done by the committees appointed for 
scientific research. 
The address delivered by Prof. Poynting, as President of the 
Section, was the subject of many conversations, not only among 
physicists but with biologists also ; the existence of the sharp 
line which he indicated between the psychical and physical 
methods and the phenomena to which each is applicable, was 
acknowledged on all sides. The physicists were divided on the 
question of the danger of too much hypothesis, and especially 
on the possibility of the propagation of electromagnetic waves 
in air being due to the air as much as tothe ether. All, how- 
ever, were agreed in the expression of thanks to the President, 
proposed by Sir George Stokes and seconded by Sir Norman 
Lockyer. 
In a paper on the spectroscopic examination of contrast 
phenomena, Mr. G. J. Burch described experiments which lend 
NO. 1563, VOL. 60] 
great support to the Young-Helmholtz theory of colour-vision. 
If the eye is fatigued by exposure to a very intense red light, 
such as sunlight filtered through red screens and focussed on the 
eye, and a spectrum be then looked at, the red is invisible ; but 
the rest of the spectrum, green to violet, appears in its ordinary 
colours. Red-blindness is therefore not accompanied by green- 
blindness, as Hering’s theory requires. Further experiments on 
the blue and violet portions of the spectrum have led Mr, 
Burch to the conclusion that we have separate primary sens- 
ations for blue and violet, in addition to those for red and green, 
taking four altogether instead of the three postulated by the 
Young-Helmholtz theory. The experiments are the more con- 
vincing because carried out with spectral colours, thus avoiding 
allerrors due to the impurity of pigment colours. In the dis- 
cussion on the paper several members took part; Sir George 
Stokes said experiments led him to believe that lobelia blue is 
a primary sensation, and Principal Glazebrook suggested that 
the theory should be tested by colour-matches on a spectro- 
photometer. 
Prof. Callendar gave the preliminary results of a research on 
the variation of the specific heat of water with temperature, 
which he commenced in Montreal with Mr. H. T. Barnes, and 
which is now being continued by the latter. The method of 
experiment consists in allowing water to flow steadily through a 
narrow tube along which a platinum wire runs axially; on 
passing a constant electric current through the wire the water 
finally acquires a steady temperature-difference between the 
inlet and outlet of the tube, which is measured by platinum 
thermometers and automatically recorded. Radiation cor- 
rections are reduced to a minimum by surrounding the tube 
with a vacuum-jacket, and the electrical energy supplied is 
measured by observing the current and the potential-difference 
between the ends of the wire in the tube. The results show 
that the specific heat of water has a minimum value of 0°995 in 
the neighbourhood of 40° C., it rises to 1°000 as the temperature 
falls to 10° C., and continues to rise rapidly as the temperature 
decreases. On increasing the temperature above 40°C. the 
specific heat rises to 0°997 at 60°C. Further experiments will 
be made in the neighbourhood of the freezing point and on 
either side of it. 
The committee on electrolysis and electro-chemistry has 
undertaken the comparison of the variation of electrical con- 
ductivity with concentration, and the variation of freezing point 
with concentration for identical very dilute aqueous solutions of 
electrolytes. The electrical measurements have been success- 
fully carried out by Mr. W. C. Whetham, but the freezing point 
determinations, undertaken by Mr. E. H. Griffiths, have been 
delayed by the discovery of errors arising from the presence of 
dissolved gases in the solutions. Incidentally Mr. Griffiths re- 
marked that he was able to measure temperatures to within 
three or four parts in a million. 
Dr. R. A. Lehfeldt, at a subsequent meeting, called attention 
to a flaw in Nernst’s theory of electrolytic solution pressure. 
According to this theory, when a metal is immersed in an 
electrolyte ions are torn either from the metal or from the solu- 
tion according as the solution-pressure is greater or less than the 
osmotic pressure of the ions in solution. It is usually supposed 
that the mass of the ions deposited or dissolved is so extremely 
small that it cannot be detected ; the author showed, however, 
by considering the electrostatic tension due to the ionic charges, 
that the amount dissolved should be easily weighable, at any 
rate in the case of zinc. 
The stability of an ether containing long, thin, empty vortex 
filaments was discussed in a communication by Prof. Fitz- 
Gerald on the energy per cubic centimetre in a turbulent liquid 
transmitting laminar waves. Lord Kelvin considered this sub- 
ject in 1887, and concluded that rapid diffusion would make 
the structure unstable. The author held the opinion (though 
possibly Lord Kelvin would differ from him) that the turbulency 
of a sufficiently fine-grained irregularly turbulent liquid would 
ultimately diffuse so slowly that Lord Kelvin’s investigation 
could be applied to it. 
Until the meeting of the Association in 1893, it was generally 
supposed that the absence of an atmosphere from the moon, and 
of hydrogen from our own atmosphere, is due to the high 
average velocity of the gaseous molecules, which is sufficient to 
carry them beyond the range of the moon’s or earth’s attraction. 
On that occasion Prof. Bryan demonstrated the incorrectness of 
this view for the case of the moon, and he has since extended 
his calculations to the cases of hydrogen and helium in the 
