ro 
“systematic 
_ January 6, 1923] 
But the main result is the establishment of a 
correspondence between the  electro- 
dynamic fields of a material system at rest in the 
aether and the same system convected with a uniform 
velocity v. The result in its simple form holds only 
up to the first order of u/c. The fields are not identical, 
unless certain of the vectors are ignored as being un- 
real and merely mathematical expressions. But he 
points out that all relations concerned with the inter- 
actions of matter, such as alone experiment could test, 
are unchanged by the convection. This is the first 
systematic appearance of the electrodynamic principle 
of relativity. It can be extended in modified form with 
confidence to the second order of u/c, at any rate on 
an electric theory of matter, for the electrons within 
the atom are still small enough compared to their 
distances apart to be treated as point charges ; and 
that covers the whole practical field except the domain 
of P rays. But when, as Prof. Lorentz noted in 1904, 
the truth of the result as thus extended is found to hold 
for the field up to all orders, the completion of this 
exact correspondence to include the atomic structure 
has to become a postulate or assumption : that was 
the birth of the modern efforts towards unrestricted 
convective relativity as an abstract formulation hold- 
ing far beyond experimental verification. 
There is a striking formal analysis near the end for 
the effect of convection on rotational optical media. 
For an isotropic medium the ordinary rotational 
modulus will be altered, and also a new rotational 
effect involving interaction of the vector velocity of 
convection with the vectors of the field can arise. 
As the result is of the first order in u/c, it is difficult to 
see how it could exist on a purely electric theory of 
atomic structure; so that the two formal effects 
should cancel. It appears that the experiments of 
Mascart (1872) were scarcely adequate to verify this 
absence of effect. Anyhow the principle of electro- 
dynamic relativity repudiates any effect altogether. 
Hitherto the transformation, up to the second order, 
for convection was ascribed to the molecular system, 
the frame of reference of space and time remaining 
invariable. For steady states of the system, in which 
time does not come into consideration, it meant a 
shrinkage along the direction of convection : changes 
so rapid that the alteration of the measure of time 
could be effective scarcely occurred, and were put 
aside. When Prof. Lorentz pointed out that the 
transformation, which is now known by his name, was 
exact as regards electrodynamic fields in free space, 
and also exact to some extent when there are electric 
densities in the field, the subject took on a new and 
wider trend. The transformation was transferred by 
Einstein (in recent years attached to Leyden as part-time 
NO. 2775, VOL. 111] 


NATURE 5 
Professor) to the frame of space and time instead of the 
molecular aggregations of matter, each taken separately, 
which accidentally occupied it. The question is then 
no longer confined to shrinkage of the material frames 
of terrestrial experiments: effects must be expected 
over astronomical distances across empty ~ space. 
Adaptation of the Newtonian law of gravitation into 
a form invariant for the fourfold space-time frame of 
Minkowski, which was the final analytical consolida- 
tion of this aspect of the subject, was effected by 
Lorentz and by others with a view to search for astro- 
nomical indications, and in particular to find out 
whether the outstanding minute secular rotation of 
the orbit of the planet Mercury, already the standard 
test for modified laws of gravitation, became amenable. 
The changes thereby introduced proved to be of small 
account. 
Meantime Einstein seems to have been struggling 
to get rid of the Minkowskian uniform universal space- 
time, which was just as absolute in its combined four 
dimensions as was the Newtonian scheme of separate 
space and time. By identifying locally the essential 
features of a physical field with intrinsic differential 
constructs in the fourfold expanse, named tensors, 
of which a formal calculus had already been fully 
developed by Ricci and Levi-Civita, he was able finally 
to select a group of related local tensors as the result of 
tentative adaptations so as to exhibit the now famous 
view of gravitation as represented by warping of the 
fourfold pseudo-spatial expanse around the material 
nuclei. Though this can scarcely be said to have 
explained gravitation, it has been widely held to have 
explained (or abolished) space and time: it merely 
forced gravitation, just as it happens to exist, into 
the electrodynamic frame with its property of insensi- 
bility to uniform convection, with no detriment to 
the results of Newtonian physical astronomy and a 
rather better account of the problem of the Mercury 
perihelion. 
This empirical building up of a field of gravitation 
out of tensorial constructs belonging to*a space-time 
expanse, now differentially heterogeneous, was com- 
pleted by adapting the Minkowskian vector potential 
of the pervading electrodynamic and optical field to 
the same conditions. The need for a more physical 
setting, at any rate to those who believe in minimal 
Action as the ultimate and necessary binding principle 
in physical analysis of a molecular world, seems to 
have been met immediately to a considerable extent 
by Lorentz and soon after by Einstein himself and by 
Hilbert. “‘ The discussion of some parts of Einstein’s 
theory of gravitation may perhaps gain in simplicity 
and clearness, if we base it on a principle similar to 
that of Hamilton. . . . Now that we are in possession 
Al 
