510 
layer of varying temperature had thickened to about 20 fathoms. 
The deep temperatures in the groups w2re now very different :— 
I. IT. Ill. IV. 
r : 5 
4u8 4U3 415 415! 
45°7 439 43°38 45°3' 
AiQ: 2:6" | 2:3 RBis 
To groups ITI. and IV. analogues a-e found ina deep and a 
shallow basin of Loch Lomond, in both of which the bottom 
temperature rose between April and June. From this it is 
inferred that land-influences, especially drainage en metsse, 
produce most of the effect noticed in ILI. and 1V. The great 
rise in the North Channel and southern plateau is evidently due 
to a warm oceanic current. The rise in temperature in group 
II. is due to the incoming of warm water from without. As 
the water between 30 and 75 fathoms in this group is very 
uniform in temperature, and as the south plateau is 25 fathoms 
below the surface, it is supposed that the dense plateau water is 
carried into the open basins (group II.), and through convection 
mix2s thoroughly the water below 3) fathoms there. Loch Goil 
is specially remarkable for its isolation and the small rise of 
bottom temperature —o°’6 F. in two months. In Upper Loch 
Fyne a lenticular mass of water below 43°'0 F. was found in 
June to float between two warmer layers. Its greatest thick- 
ness, 30 fathoms, wis opposite Inverary. The bottom layer of 
44°°0 F, was not found to be in connection with any equally 
war.n layer either inside or outside of the loch, 
On the Critical Curvature of Liquid Surfi-es of Revolution, 
by A. W. Riicker, M.A., F,R.S.—Let a mass of liquid film be 
attached to two equal circular rings, the planes of which are 
perpendicular to the line joining their centres. It will form a 
surface of revolution the equation of which is, according to 
Beer, — 
Deep temperature in April 
» ” June 
Rise of temperature ... 
Ip 
a 
where F and E are elliptic integ-als of the first and second 
kinds respectively, the amplitude beinz @, and the modiu;s 
« = Ja”—B*/a =sin @. If@b2 conceived as increasing from 
0, when it is in the first quadrant the figure will be an undaloid 
lying being the cylinder and the sphere, in the second quadrant 
a nodoid, the limits of which are the sphere andacircle. In 
the third and fourth qualrants the figure will be dice-box- 
shaped with a contraction in the middle, being a nooid in the 
third and an uaduloid in the fourth quadrant. The one passes 
into the other through the catenoid. If now we suppose the 
rings to be at a fixed distance apart, and the volume of the sur- 
face to be altered, the curvature will change, and the direction 
of the chanze will depend on the diameter and distance apart of 
the rings, and on the magnitude of the maximum or minimum 
ordinate (the principal ordinate), which lies half-way between 
them. The object of the paper is to investigate the general 
relation between these quantities when the curvature is a maxi- 
mum or minimum, if the changes in the form of the film take 
place subject to the conditions that the diameter and distance of 
the rings a-e constant. It has been recently shown by Prof. 
Rein5ld and the author that, if these conditions hold, 
(a°E — B°F + a A, cot p,)5a + a°(F — E + A, tan g,)38 =0, 
where 4; is the upper limit of the integrals and 
AY= J1= sin? @ sin? @,. 
Writing this in the form A5a + B38 = 0, it is proved that the 
curvature has in general a critical value when A — B = 03 so 
that 
2E — F(r + cos? @) + 2A, cot2p, = 0 
is a condition which must be satisfied by @ and ¢,. To find 
values of @, corresponding to given values of @ the equation 
must be solved by trial ; but it is prove that, if a pair of co-re- 
sponding values is given when @ lies (say) in the first quadrant, 
the values of , can be at once found which correspond to 7 — 6, 
a + 6, and 2m — 9. The value sof , corresponding to @ and m- @ 
re equal, and, if , be the value corresponding to m + @ and 
m — 6, it is given by the equation 
tan ¢, tan (7 — ,) = sec 0. 
By means of these equations a curve can be drawn, showing the 
relation s between , and @, and thence are found the values of 
2/Y, X/f, and X/Y, where 2Y, 2X, and 2 are the diameter 
* Average temperature of first few fathoms above bottom. 
NATURE 
[ Sept. 23, 1886 
and distance of the rings and the magnitude of the principal 
diameter. If we now conceive the two rings gradually to approach | 
or recede from each other, and the principal diameter to be | 
altered so that the condition of critical curvature is always ful- 
filled, it is proved that the changes in its form would be as fol- 
lows :—Beginning with the cylinder, the distance of the rings 
would (as has been shown by Maxwell, Art. ‘ Capillarity,” 
“Enc. Brit.”) be half their circumference. As the diameter 
increases, the rings would move apart, and the distance between 
them would be a maximum when @ = 64°'2, being 17 per cent. 
greater than in the case of the cylinder. When 6 = 90°, the 
figure is a sphere, and the distance between the rings i; about 
4 per cent. less than in the case of the cylinder. The sphere 
has a larger diameter than any other figure of critical curvature. 
The surface next becomes a nodoid, and the distance between 
the rings diminishes till when @ = 180° they touch, and thus 
the surface reduces to a circle. In the next quadrant the rings 
separate, but the figure is now dice-box-shaped, and the pressure 
exerted by the film is outwards. When @ = 270°, the figure is 
the catenoid. The principal ordinate is then less than that of 
any other figure of critical curvature, and the radius of the rings 
is a mean proportion between this minimum ordinate and the 
maximum which was attained in the case of the sphere. The 
same relation holds between the principal ordinates of any two 
figures which correspond to values of 6 which differ by 180°,. In 
the fourth quadrant the figure becomes an unduloid, the pressure 
isinwards, the rings continue to separate, and the ratio of the 
distance between the rings to the principal ordinate is a maxi- — 
mum when 6 = In the paper tables and curves are given to 
illustrate the ‘‘ march” of these functions. To secure con- 
tinuity, the problem is discussed without reference to the ques- 
tion as to whether the surfaces are in stable equilibrium, though 
those i1 the first and fourth quadrants and figures corresponding 
to values of @not much >z/2 and not much <3z/2 certainly 
are. In conclusion it is shown that by means of the curves we 
can solve a number of problems with sufficient accuracy for 
practical purposes. Thus, if any two of the three quantities, 
the diameter of the rings, the distance between them, and the 
diameter of the surface of critical curvature, are given, the third 
can be found. 
7 
SECTION B—CHEMICAL SCIENCE 
Absorption Spectra of Uranium Salts, by Dr. W. J. Russell 
and W. J. Lapraik.—This paper wis communicated by Dr. 
Russell, who pointed out that well-marked absorption bands in: 
the visible spectrum are produced by the different salts of this 
metal ; the bands produced by the uranous salts are distinct from ~ 
those given by the uranic salts ; both consist, however, of three’ 
distinct bands or groups of bands. The bands produced by the 
uranous salts are at the red end of the spectrum, whilst those 
due to the uranic salts are at the blue end; and when both 
classes of salts are mixed in solution there are three series of 
bands distributed with tolerable regularity over the whole of the 
spectrum. Exp2rirsents with different salts show the nature of 
the acid radical to have no influence on the spectrum, whereas 
in the case of other metals, such as cobalt, it has been found that 
different radicals produce different spectra. The spectrum’ 
common to all uranic salts is slightly altered by the addition of 
free acid ; a diminution in intensity in the least refrangible bands 
and a slight shift in others has been observed. Crystals of 
uranic nitrate give an absorption spectrum similar to that pro- 
duced by its solutions. The spectrum of the uranous salts if 
less refrangible than that of the uranic salts ; the examination of 
the spectra produced by the uranous salts in the solid state was 
found to be more complex than those given by these salts in 
solution. r 
The Air of Dwellings and Schools, and its Relation to 
Disease, by Prof. Carnelly.—The author gave an account of an — 
elaborate series of experiments conducted by him and Dr. Hal- 
dane at Perth and Dundee, in connection with the sanitary and 
school authorities, the object being to determine the relations 
between the composition of the air and the death-rate in houses — 
and schools, and also the effect of various systems of ventilation. 
For this purpose the carbon dioxide, organic matter, and micro- 
organisms were determined, both in the outside air and in the 
room to be examined. In the air of the towns of Perth and 
Dundee a distinct increase of impurities could be detected in 
close parts of the towns as compared with the open spaces. In 
examining the dwelling-houses, the experimenters had authority 
