500 

NATURE 
[Jue 15) Toms 

factor is biological. Search was therefore made for 
organisms fulfilling these conditions and numbers of 
protozoa were found. Definite evidence has been ob- 
tained that trophic forms occur as normal inhabitants 
of the soil, and the estimates of numbers so far avail- 
able show that they are considerable. There is the 
closest possible relationship between the extinction of 
the protozoa and the extinction of the limiting factor, 
and also between the re-establishment of the protozoz in 
fauna and the setting up of the limiting factor after 
reinfection with small quantities of soil—Prof. W. M. 
Hicks: The enhanced series of lines in spectra of the 
alkaline earths. A discussion of the enhanced series 
of the allkaline earths is carried out in order to deter- 
mine their relation to the sun. For this purpose the 
results given for Mg, Ca, Sr by Fowler in his recent 
Bakerian Lecture are used, and, in addition, the corre- 
sponding series in Ba and Ra are considered. It is 
found that the quantity A’, giving the doublet separa- 
tions, is given with great accuracy in terms of the 
oun, as follows:—Mg, 5633; Ca, 688; Sr, 585; Ba, 
5636; Ra, 6036; w here 8 is four times the correspond- 
ing oun for the element. The satellite separations are 
also found as functions of the same quantity. Further 
it is shown that these series strongly support the 
general relations given in a former communication 
that the first p-sequence depends on a multiple of the 
atomic volume, and that the diffuse sequence is such 
that the denominators of the first lines, when the wave 
number is expressed in the form A—N/(den)?, are 
themselves multiples of A’ or of the oun.—Prof. H. F. 
Baker; Certain linear differential equations of astro- 
nomical interest. This paper is written to exemplify 
the application of a general method for the solution 
of linear differential equations given by the author 
some years ago. The method furnishes solutions in 
a form valid for an indefinitely extended region. It is 
here applied (1) to establish a result as to the con- 
vergence of the solution of a particular equation, 
apparently in disagreement with a conclusion reached 
by Poincaré in his ‘‘Méthodes Nouvelles de la 
Mécanique Céleste’’; (2) to place the general method 
given by Laplace for the absorption of the time in 
astronomical series under trigonometrical signs in 
connection with the ordinary theory of characteristic 
exponents; (3) to discuss in general terms the oscilla- 
tions of a dynamical system about any given possible 
state of motion; (4) to furnish a regular calculus for 
the solution of the equation used by G. W. Hill for the 
motion of the moon’s perigee, and similar equations. 
The earlier part of the paper discusses particular 
equations from a less formal point of view, and has 
seemed necessary in order to place the matter in proper 
light. One particular problem discussed is that of 
the stability of three bodies of any masses moving in 
ellipses at the angular points of an equilateral triangle, 
a matter of which the discussion has recently been 
revived.—Prof. Karl Pearson: The partial correlation- 
ratio. The general theory of mutiple correlation has 
been long established, and is summed up in the dis- 
cussion of two constants—the partial correla- 
tion coefficient and the multiple correlation 
coefficient. If there be m variates, 1,2,3...m, then 
the partial correlation coefficient of the (m-—-2)2¢ order 
is related to the multiple correlation coefficients of the 
(m—1)th and (m—2)24 orders by the equation :— 
2 —1-R*-934---m 
TRA een 
The object of the present paper is to give the corre- 
sponding equation for show-regression. It is known 
that the value of the above relation is exactly com- 
mensurate with the linearity of the regression, a con- 
dition not synonymous with but embracing as a special 
NO. 2383, VOL. 95] 

case gaussian or normal distributions of frequency. 
When the regression is not linear, nor the partial» 
variations homoscedastic in distribution, then the 
statistician has to use, in order to represent by a 
single coefficient the association of two variables, the 
correlation-ratio, usually symbolised by 7. The use of 
the correlation-ratio has been hampered by the absence 
of any generalised theory in the case of multiple 
variates. If 34...-m-2 be the partial correlation- 
ratio of the first variate on the second for constant 
third, fourth... mth variates and H,.., 7 benthe 
multiple correlation-ratio for 1 on 2, 3...m, then the 
fundamental formula is— 
J “m 
The paper shows that there are only three independent 
first order partial correlation-ratios and gives the 
formula for these, and for higher order correlation- 
ratios in terms of the multiple ratios and lower order 
partial ratios.—S. Skinner and F. Entwistle : The effect 
of temperature on the hissing of water when flowing 
through a constricted tube. The experiments deal 
with the temperature coefficient of the effect described 
by Osborne Reynolds before the British Association at 
Oxford, 1894. It is shown that the velocity at which 
hissing just occurs between 0° and 100° C. suffers a 
diminution which may be expressed by a formula 
V,=—c(t—6), where V, is the velocity of the stream 
at a temperature t, and @ the critical temperature of 
water, and c a constant. It is argued that this result 
forms a measure of the tensile strength of the liquid, 
and consequently it brings the phenomenon of hissing 
into relation with the other properties of a liquid.— 
J. C. McLennan and J. P. Henderson ; Jonisation poten-- 
tials of mercury, cadmium, and zinc, and the single 
and many-lined spectra of these elements. (1) It is 
shown that a spectrum consisting of a single line is 
obtainable for mercury, for zinc, and for cadmium. 
(2) The wave-lengths of these lines are, for mercury, 
N=2536-72 A.U.; for zinc, A=3075-99 A.U.; and for 
cadmium, A= Beto: 17 A.U. (3) The minimum ionisation 
potentials for mercury, zinc, and cadmium are shown 
to be 4-9 volts, 3-74 volts, and 3-96 volts respectively. 
(4) Some considerations are presented which support 
Sir J. J. Thomson’s theory of the two-type ionisation 
of atoms of mercury, and others which suggest that 
the theory is applicable as well to the ionisation of 
atoms of zinc and cadmium. (5) The minimum arcing 
potential differences which will bring out the many- 
lined spectra of mercury, zinc, and cadmium vapours 
are found to be 12-5 volts, 11-8 volts, and 15-3 volts 
respectively. These voltages are also probably the 
minimum ionisation potentials of the second type for 
the atoms of these three elements. (6) Considerations 
are presented which suggest the possibility of 
analysing the spectrum of an element in such a way 
as to enable one to correlate different portions of the 
spectrum with disturbances in definite portions of the 
atomic structure of that element.—Dr. A. E. H. 
Tutton; The monoclinic sulphates containing ammo- 
nium.—Completion of the double sulphate series. In 
this communication are described the five remaining 
double sulphates of the series R,M(SO,),..6H,O, in 
which R is ammonium and M is nickel, cobalt, man- 
ganese, copper, and cadmium. The present memoir 
completes the author’s work on the double sulphates 
of this series. The main conclusions are the follow- 
ing :—(1) These ammonium salts are truly isomorphous 
with the similarly constituted potassium, rubidium, 
and czesium salts of the generic formula above given, 
but are not eutropic with them; the potassium, rubi- 
dium, and cesium salts alone form the exclusive 
eutropic series in which the crystallographical proper- 

