448 SECTIONAL TRANSACTIONS.—A. 
space-times as general relativity, but with a law of gravitation different from 
Einstein’s. Otherwise the two theories will differ onlyinmethod. I believe, 
however, that all Prof. Milne’s results so far derived are included amongst 
those of general relativity. 
M. VAbbé Lemairre——The cosmical significance of the clusters 
of nebula. 
The theory of the expanding universe seems to indicate that the universe 
is not older than a few thousand million years, i.e. not much older than the 
earth. On the other hand, the generally accepted theory of evolution of 
the stars with transformation of matter into radiation needs a period one 
thousand times greater. The conflict between these two theories could be 
solved if the mechanics of the expanding universe provided some means of 
substituting for the slow evolution of the stars a rapid evolution which would 
explain the formation of stars, nebulz and clusters of nebulz in a period of 
a few thousand million years. 
Progress of the theory of the behaviour of local condensations in the 
expanding universe show, at least in the case of spherical symmetry, that 
each concentric shell of matter would obey the same law as a universe. But 
they need not all follow the law of the same universe. ‘The universe at 
large, starting with a very small radius, would expand with a diminishing 
velocity, slow down to pass over the equilibrium radius, and then expand 
again for ever with an accelerated velocity. On the contrary, interior regions 
of a somewhat greater density might fail to attain equilibrium and contract, 
collapsing towards their centre, while the universe at large continues to 
expand. This is a new typical case of instability, very small differences in 
the initial density being followed in the long run by extremely great 
modification of the motion. 
This property of the universe seems to be able to explain the rapid forma- 
tion of nebula. But when we try to follow up this idea in more detail, we 
meet a very essential difficulty. For a condensation of a thousand million 
suns, as seems required to build up a normal nebula, the equilibrium radius 
would be about 80,000 light-years, although the radius of a typical elliptical 
nebula is not much greater than one thousand light-years. Now, although 
the condensation must first collapse, it will evidently rebound and cannot 
adjust itself to a permanent radius of one thousand light-years unless some 
vigorous stopping process takes place in the course of the contraction. The 
energy which must be taken off is really enormous, and at first sight it seems 
difficult to understand what mechanism would account for it. Actual 
computation shows that the loss of energy must be equal to the total heat 
content of the stars contained in the nebula. This gives the solution of the 
puzzle. The stopping process, which prevents the nebule from rebounding 
too far, is the formation of the stars. Before the contraction the matter was 
formed of gas, dust or meteorites. When the whole mass collapses towards 
its centre, powerful encounters take place ; the diffuse matter agglutinates 
suddenly into stars and the energy turned into heat by this process explains 
together how the new-born stars have the necessary heat to start on the sub- 
atomic processes which provide their continuous output of light, and why 
the nebulz can adjust themselves to their present radius. 
Stars and nebule are born together in an astronomical instant. Sudden 
evolution of the universe takes the place of slow evolution of the stars, with 
the same net result, even with equipartition of energy among the stars. 
The shape of the nebula depends on its initial moment of momentum, 
elliptical nebulz or spiral nebulze being born together. Here evolution 
