It is, indeed, further objected that some of the resulting fragments ought to have retrograde motions. It turns out on calculation, however, that this is not the case. Assuming as true the velocity which Lagrange estimated would have sufficed to give the four chief planetoids the positions they occupy, it results that such a velocity, given to the fragments which were propelled backwards by the explosion, would not have given them retrograde motions, but would simply have reduced their direct motions from something over 11 miles per second to about 6 miles per second. It is, however, manifest that this reduction of velocity would have necessitated the formation of highly-elliptic orbits--more elliptic than any of those at present known. This seems to me the most serious difficulty which has presented itself. Still, considering that there remain probably an immense number of planetoids to be discovered, it is quite possible that among these there may be some having orbits answering to the requirement. NOTE V. Shortly before I commenced the revision of the foregoing essay, friends on two occasions named to me some remarkable photographs of nebulæ recently obtained by Mr. Isaac Roberts, and exhibited at the Royal Astronomical Society: saying that they presented appearances such as might have been sketched by Laplace in illustration of his hypothesis. Mr. Roberts has been kind enough to send me copies of the photographs in question and sundry others illustrative of stellar evolution. Those representing the Great Nebulæ in Andromeda and Canum Venaticorum as well as 81 Messier are at once impressive and instructive--illustrating as they do the genesis of nebulous rings round a central mass. I may remark, however, that they seem to suggest the need for some modification of the current conception; since they make it tolerably clear that the process is a much less uniform one than is supposed. The usual idea is that a vast rotating nebulous spheroid arises before there are produced any of the planet-forming rings. But both of these photographs apparently imply that, in some cases at any rate, the portions of nebulous matter composing the rings take shape before they reach the central mass. It looks as though these partially-formed annuli must be prevented by their acquired motions from approaching even very near to the still-irregular body they surround. Be this as it may, however, and be the dimensions of the incipient systems what they may (and it would seem to be a necessary implication that they are vastly larger than our Solar System), the process remains essentially the same. Practically demonstrated as this process now is, we may say that the doctrine of nebular genesis passes from the region of hypothesis into the region of established truth. FOOTNOTES: