There can be no doubt that astronomers have been startled into something like general protest against the rigid uniformitarianism of Sir Charles Lyell. Differing as they do very widely in their conceptions of the probable manner in which planets are formed, they seem to agree that those bodies have their beginning in heat and in fusion. The phenomena of variable stars, taken in connection with the revelations of spectrum analysis, demonstrate that the combustion and the cooling of starry masses are occurrences not unknown in the economy of the universe. If Sir Charles declines to contest the astronomical position of the original fluidity of the planet, considerable plausibility will continue to attach to that geological doctrine which connects the crystalline rocks with the fluidity in question. Those rocks, from the most ancient granites to the most recent clay-slates, occupy a large proportion of the earth's surface. Their great general antiquity is indisputable. The theory that they furnish the link between the past and the present of the earth's crust--that they furnish the point where the lights of geological and of astronomical science meet--strongly commends itself to the mind. These observations derive additional force from the circumstance that Sir Charles Lyell's doctrine of the modern and chemical origin of all crystalline rocks is dependent upon considerations which must be allowed to possess not a little of a hypothetical and precarious character. The phenomena of metamorphism, as arising from heat, from thermal springs, and so on, are well-known and important; but there is nothing like adequate evidence that they are capable of giving the crystalline rocks that structure and aspect under which we behold them. The chemical substances in the crust which Sir Charles presumes to be capable of forming seas of molten matter, five miles deep and 5,000 miles long, have never placed before human eyes a lake of fire three miles across; is there not a trace of arbitrary hypothesis in supposing that, during hundreds of millions of years, those chemical agencies have been providing, beneath the surface of the world, cauldrons of fire to melt the granites of all known ages, from the Laurentian to the Tertiary, to produce the twistings, undulations, contortions of the metamorphic strata throughout hundreds of thousands of cubic miles of rock, and to feed every volcano that ever flamed on the planet? Not even to that proposition which is avowedly at the basis of Sir Charles's theory, namely, that the solidified shell of the earth is at least from 800 to 1,000 miles thick, can absolute certainty be said to belong. We are willing to admit the distinguished ability of Mr. Hopkins; but it is a fatal mistake to impute to solutions of problems in mixed mathematics that character of certainty which belongs to the results of purely mathematical reasoning. Into every problem of mixed mathematics one element at least enters which