305 
273, 274 ] Disturbances from Passing Stars 
of the eccentricity and the period. Temporarily denoting the eccentricity by 
e (to avoid confusion with e = 2*7182), we have 
so that, keeping E" constant, 
and eccentricities. 
274. This law of distribution falls naturally into two parts, one of which, 
P. This shews that in the final steady state which is obtained after a suffi 
cient amount of interaction between different systems, there will be no 
correlation between the periods and eccentricities of binary systems. 
A very different state of things is disclosed by the tables given in § 258, 
periods and eccentricities of orbits increasing together in a very marked way. 
tained a statistical steady state. 
This result is not altogether disadvantageous to the progress of cosmogony. 
If the theoretical law of steady-state distributions had been exactly obeyed 
by actual stellar orbits, we should have obtained a result which, while strik 
ing and concise, would have closed the door against all further progress 
in the direction in which we are now working. As it proves, the law is far 
from being obeyed, and the deviations from the law, which come from the 
stars not having interacted for a sufficient time, must represent surviving 
vestiges of the initial conditions of the stars : they provide material, then, for 
discussing the origins and early histories of binary systems. If the present 
distribution of eccentricities and periods had agreed with the theoretical 
steady-state law, the problem of discussing these origins and early histories 
would have been comparable only to that of trying to decipher the writing 
on a slate after a wet sponge had been rubbed over it. Our discussion has 
shewn that the sponge was not thoroughly wet ; the writing, although doubt 
less smudged, is not wholly obliterated. The eccentricities and periods have 
not yet been levelled to the extent required by the theoretical steady-state 
7 2 E"hdh 
ed€ = -— 
Using this and the further relation 
the law of distribution (273‘7) takes the form 
which gives the law of distribution of orbits classified according to periods 
2 ede, involves only the eccentricity e, while the other involves only the period 
which reveal a pronounced correlation between these two quantities, the 
We must conclude that the orbits of binary stars are still far from having at-