366 
—— 
The case of exception is the 
biquadratic equation, for which it is impossible to 
assign an invariantive criterion that shall serve to dis- 
tinguish between the case of all the roots being real and 
all imaginary. ab 
It is proper to notice that it follows, from the definition 
of the symbol 7z.p, that its value is zero whenever 72 1S 
less than 2. Thus, inthe matrix written out above, the 
symbols 3'2, 4°3, 5°3, 5°4; 64, 74 may be replaced by zeros. 
The above general result for a curve of any order is 
actually obtained by a far less expenditure of thought 
and labour than was employed by Monge, Halphen, and 
others to obtain it for the trifling case of a conic. I touch 
a secret spring, and the doors of the cabinet fly wide 
open. J. J. SYLVESTER 
New College, Oxford, August 6 
by means of invariants. 
CAPILLARY ATTRACTION * 
III. 
N these other diagrams, however (Figs. 13 to 28), we 
have certain portions of the curves taken to represent 
real capillary surfaces shown in section. In Fig. 13a solid 
sphere is shown in four different positions in contact with 
a mercury surface; and again, in Fig. 14 we havea section 
of the form assumed by mercury resting in a circular V- 
groove. Figs. 15 to 28 show water-surfaces under different 
conditions as to capillarity ; the scale of the drawings 
for each set of figures is shown by a line the length of 
Fic. 13.—Mercury in contact with solid spheres (say of glass). 
which represents. one centimetre ; the dotted horizontal 
lines. indicate the positions. of the free water-level. The 
drawings are sufficiently explicit to require no further 
reference here save the remark that wafer is represented 
by the lighter shading, and so//d by the darker. 
We have been thinking of our pieces of rigidified 
water as becoming suddenly liquified, and conceiving 
them inclosed within ideal contractile films; I have here 
an arrangement by which I can exhibit on an enlarged 
Fic. 14.—Sectional view of circular y-groove containing m2rcury. 
scale a pendant drop, inclosed not in an ¢dead film, but in 
a veal film of thin sheet india-rubber. The apparatus 
which you see here suspended from the roof isa stout 
metal ring of 60. centimetres. diameter, with its aperture 
closed by a sheet of india-rubber tied to it all round, 
stretched uniformly in all directions, and as tightly as 
_1 Adopting the convention for degree and weight of a differential coeffi- 
cient usual in the theory of, reciprocants the deg : weight of the differential 
criterion of the 7th order will be easily found to be— 
2 WT. IDb2 HTM. M+ YD, TD 2 
6 ; Ser Sle weal 
except that for # =2 itis.3:.3 instead of 4:3. 
* Lecture delivered at the Royal Institution. 
the Author. Continued from p. 294. 
Revised and extended by 
NATURE 
[ dugust 19, 1886 
could be done without special apparatus for stretching it 
and binding it to the ring when stretched. 
I now pour in water, and we find the flexible bottom 
assuming very much the same shape as the drop which 
you saw hanging from my finger after it had been dipped 
into and removed from the vessel of water (see Fig. 16). 
Fics. t5-21.—Water in glass tubes, the internal diameter of which may be 
found from Fig. 22, which represents a length of one centumetre, 
I continue to pour in more water, and the form 
changes gradually and slowly, preserving meanwhile the 
general form of a drop such as is shown in Fig. 15, 
until, when a certain quantity of water has been 
poured in, a sudden change takes place. The sud- 
Fic. 23.—Water resting in the space between a solid cylinder and a con- 
centr.c hollow cylinder. 
den change corresponds to the breaking away of a 
real drop of water from, for example, the mouth of a 
tea-urn, when the stopcock is so nearly closed that a 
very slow dropping takes place. The drop in the india- 
rubber bag, however, does not fall away, because the 
tension of the india-rubber increases enormously when 
yee ue ES ee eel ee we rer er eee ee 
