(Thursday, October 19, 1871)
Lindsay, W. Lauder
Leighton's lichen-flora of Great Britain, pp. 482-484
vA TURF [Ocd. 19, 187! the distance of the motion is less, which only amounts to the truth, that a small portion of an ellipse is ulti- mately undistinguishable from a circle. The truth of the Axioms of Geometry never really comes into question at all, and Helmholtz has merely pointed out circum- stances in which the figures treated in plain geometry could not always be practically drawn. It is a second question whether the dwellers in a spherical world could acquire a notion of three dimen- sions of space. We must remember that such beings could bear no analogy to us, who have solid bones and flesh, and live upon a solid globe, into which we can penetrate a considerable distance. These beings have no thickness at all, and live in a surface infinitely thinner than the film of a soap bubble, in fact, not thin or thick at all, but devoid of all pretensions to thickness. There would be nothing at first sight to suggest the threefold dimensions of space, and yet I believe that they could ultimately develop all the truths of solid geometry. They could not fail to be struck with the fact that their geometryof finite figures differed from that of infinitesimals, and an analysis of this mysterious difference would cer- tainly lead them to all the properties of tridimensional space. Indeed, if Riemann, prior to all experience, is able to point out the exact mode in which a curvature of our space would present itself to us, and can furnish us with analytical formulae upon the subject, why might not the Riemann of the spherical world perform a similar service, and show how the existence of a third dimension was to be detected ? It might well be that the inhabitants of the sphere had in the infancy of science never suspected the curvature of the world, and, like our ancestors, had con- sidered the world to be a great plain. In the absence of any experience to that effect, it is certain that the notion of thickness could not be framed any more than we can imagine what a fourth dimension of our space would be like. We have some idea what a world of one dimension would be, because as regards time we are in a world of that kind. The characteristic of time is that all intervals beginning and ending at the same moments are equal. But suppose that some people discovered a mysterious way of living which enabled them to live a longer time between the same moments than other people; this could only be accounted for by supposing that they had diverged from the ordinary course of time, like travellers taking a round- about road. Though in one sense such an occurrence is utterly inconceivable, yet in another sense we can probably anticipate the character of the phenomenon, and the 47th proposition of Euclid's first book would doubtless give the most important truth concerning times thus differing in direction. With all due deference to so eminent a man as Helm- holtz, I must hold that his article includes an ig-noratio elenchi. He has pointed out the very interesting fact that we can conceive worlds where the Axioms of our Geometry would not apply, and he appears to confuse this conclu- sion with the falsity of the axioms. Wherever lines are parallel the axiom concerning parallel lines will be true, but if there be no parallel lines in existence, there is nothing of which the truth or falsity of the axiom can come in question. I will not attempt to say by what pro- cess of mind we reach the certain truths of geometry, but I am convinced that all attempts to attribute geometrical truth to experience and induction, in the ordinary sense of those words, are transparent failures. Mr. Mill is another philosopher whose views led him to make a bold attempt of the kind. But for real experience and induction he soon substituted an extraordinary process of mental experimentation, a handling of ideas instead of things, against which he had inveighed in other parts of his " System of Logic." And the careful reader of Mr. Mill's chapter on the subject (Book II. chapter 5) will find that it involves at the same time the assertion and the denial of the existence of perfectly straight lines. Whatever other doctrines may be true, this doctrine of the purely empirical origin of geometrical truth is certainly false. W. STANLEY JEVONS LEIGHTON'S LICHEN-FLORA OF GREAT BRITAIN The Lichen-Flora of Great Britain, Ireland, and the Channel Islands. By the Rev. W. A. Leighton, F.L.S. (Published for the Author. Shrewsbury, I87I.) T falls so rarely to the botanical reviewer in this country I to notice works on Lichenology, that we gladly avail ourselves of the present opportunity of introducing to our readers a little unpretentious volume which has the excel- lent object primarily-" of elevating the knowledge of our insular lichens to a level with that of other branches of our country's flora," and which, moreover, completely vindicates the title of Britain's lichens to at least equal study with the other families of her cryptogamia. Since the publication of Mudd's excellent "Manual" in i86i, the additions made to the lichen-flora of Great Britain and Ireland have been both so numerous and important, that lichenological students have felt the want of some sys- tematic work containing a complete list of the British lichens up to the present date, along with specific diag- noses and other aids to their identification. It was gene- rally felt, moreover, that no fitter authority could undertake so intricate a labour than Mr. Leighton, whose name is identified with lichenological progress in this country by the publication of many important papers of a mono- graphic character, and who is justly regarded, both by home and foreign botanists, as the representative and father of lichenology and lichenologists in Britain. The present work, which we are glad to find is to be followed, in due time, by another which is even more urgently required - a Conspectus of all known lichens throughout the world-is a convenient 1 2mo volume of about 470 pages, which confines itself mainly to a systematic enumeration, with specific diagnoses, of all the lichens at present known to occur in " Great Britain, Ireland, and the Chan- nel Islands." The nomenclature and classification followed are those of Dr. Nylander, of Paris, who is described as " the facile frinceps of modem microscopic lichenologists." Succeeding the specific diagnoses, the author cites the leading synonyms; gives references to published plates and fasciculi of dried specimens; narrates the general geographical distribution of species through- out the world, on the one hand, and throughout the three kingdoms on the other; specifies the particular loca- lities of growth in each of these latter kingdoms; and gives, so far as possible, the date of original discovery in Britain, with the name of the discoverer. 482 ,.. .
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