200 

NATURE 
[FEBRUARY 10, 1923 
Can Gravitation really be absorbed into the Frame of Space and Time? 
By Sir Jos—rpH Larmor, F.R.S.1 
AN answer to this question in the negative has 
been advanced in a previous paper on the 
gravitational deflection of light (Pil. Mag., Jan.). 
The destructive paradoxes concerned with the recent 
gravitation theory, which were unfolded by M. Jean 
Le Roux, professor at Rennes, in three notes in 
the Comptes rendus (Nov. 6, Dec. 4 and 22), after 
that paper was completed, were referred to in a 
footnote in support of this departure from the familiar 
answer. These objections require to be further con- 
sidered ; for at first sight they are destructive to 
all such theories, including the modification ‘there 
substituted. If an orbit is postulated to be a curve 
of minimal length in a fourfold expanse of space-time, 
the element of length (or distance-interval) must be 
expressed for it locally, and can involve as variables 
only its own co-ordinates and their differentials. Yet 
in the cases that have been worked out, the element 
as determined involves also the concurrent co- 
ordinates of the other interacting masses; with all 
these variables present, it could not belong to a curve 
in a fourfold at all. This destructive dilemma applies 
very. widely. : 
There may be a suggestion to evade it, in the 
theory as modified into one of dynamical Action, 
along the line (already indicated by A. A. Robb) that 
the idea of distance cannot subsist in the pseudo- 
space at all. For within an infinitesimal fourfold 
spherical domain with radius a very small interval ds, 
the co-ordinates would have an infinite range of values. 
The idea of locality, essential to real space, is thus 
absent. The fourfold expanse could still be utilised 
to express conveniently the domains of integration : 
but where distances have to enter they must be in 
threefold real space, though it can be variable and be 
associated with time also variable. Such real spaces 
and times would be locally not unique; they con- 
stitute a Lorentz group of interchangeable forms. 
The modified gravitational scheme of the previous 
paper, with its reduction of the influences on radiation 
to one-half of the accepted values, might, merely by 
avoiding the idea of fourfold interval interpreted as a 
geometric distance, possibly still manage to evolve as 
a dynamical formulation. 
But this train of ideas need not be pursued ; for in 
fact the criticism, which seems destructive of a quasi- 
z 1 Abstract of a paper read on January 22 at the Cambridge Philosophical 
Society. 
geometric scheme for gravitation, does not inhere at 
all in the dynamical domain of Action. The type of 
procedure for minimising the total Action, when more 
closely exhibited, would run in_principle as follows. 
Assume some approximate specification for the orbital 
paths in the fourfold, close of course to the Newtonian 
solution. The orbits thus assumed will determine the 
nature of the fourfold space-time expanse (namely 
ds*) already adjusted to minimal Action, in which they 
exist. For each such specification calculate the 
density of Action in this fourfold expanse, after the 
manner of approximate modifications as developed 
by Einstein ; and thence find by integration the total 
Action of the system corresponding to these assumed 
orbital forms. The forms of the orbits would enter 
in the expression for the linear element ds defining 
the space determined by these orbits and necessarily 
containing them. By taking varied forms of the 
orbits, different forms of ds and different values of 
the total Action would be obtained. The aim would 
be to adapt the forms of the orbits so that the Action 
thus determined from them should remain stationary 
for all slight variations. The way to carry this out 
would be to minimise the Action further for joint 
variation of all the orbits, exactly on the lines of the 
previous paper. The spaceitself, being determined by 
the orbits, also changes as the orbits are varied ; and 
it is not at all involved that ds remains the elemental _ 
distance in the same space throughout the procedure. 
It would appear then that the Minkowskian method 
of fourfold spatial analysis as generalised by Einstein 
for adaptation of gravitation into the optical and 
electrodynamic group of frames, can be saved from 
the destructive criticism of M. Le Roux. But to this 
end the postulate of absorption of gravitation into 
the spatial frame must be abandoned; and the 
principle of equivalence of gravitation and accelera- 
tion would disappear. The application of the mathe- 
matical spatial analysis to astronomy and optics 
would be reconstructed as a dynamical theory of 
normal type, unfolding itself in terms of a distribution 
of Action located ultimately throughout the region of 
the problem: but the results as modified would still 
require actual confirmation. If, however, any gravita- 
tional influence on light is finally established by the 
astronomical observations, this type of analysis by 
aid of a varying spatial frame may remain the most 
effective way to include it in theory. 
The Nature of Gels. 
By Dr. S. C. BRADFORD. 
[? has been known, probably from the earliest 
times, that when sufficiently concentrated solu- 
tions of certain substances, such as gelatin and agar- 
agar, are allowed to cool, instead of depositing crystals 
of the dissolved substance, the whole liquid turns 
into a jelly. It is natural, therefore, that specula- 
tions on the nature of jellies should have been rife 
long before Graham, in 1861, first pointed out the 
slow rate of diffusion of colloid substances which 
distinguished them from bodies which separate from 
solution in the ordinary crystalline form. 
The many theories of gel structure fall naturally 
under three heads: (1) One-phase or molecular 
systems, (2) two-phase liquid-liquid systems, and (3) 
two-phase liquid-solid systems. To the first class 
belongs Proctor’s hypothesis that a gel is a more or 
NO. 2780, VOL. 111] 

less solid solution of a liquid in the colloid substance, 
in which both constituents are within the range of 
molecular attractions. This view is very similar to 
the “‘ super-cooled liquid ’’ theory of glass, and, like 
that, has difficulty in explaining the loss of mobility 
which occurs on setting. Proctor suggests that the 
transformation consists in the formation of tenuous 
crystals, which interlace and possibly anastomose. 
Later experiments! show that gelation is really an 
extreme case of crystallisation, but this suggestion 
would bring Proctor’s theory into the third class. 
In either case, however, his experiments are im- 
portant, as they show that the swelling of gelatin in 
1 Bradford, Science Progress, 1917, 12, 62; Biochem. Jour. 1918, 12, 
3573 1920, 14, 91; 1921, 15, 553; and ‘‘The Physics and Chemistry of 
Colloids,’ Discussion by the Faraday Society, etc., London, 192r. 
