30 



NATURE 



\Nov. ir, 1875 



assumption, and we also ask him how he gets the last 

 line on p. 27. These crucial points occur in "inde- 

 pendent proofs " of the same theorem ; they are pure 

 " beggings of the question," we believe. This is all we 

 have to say on Part I. Part II. opens with an admirable 

 motto (reminding us herein of Mr. James Smith), " Prove 

 all things ; hold fast that which is good." Having proved 

 then the previous theorem, he holds fast to that, and pro- 

 ceeds to the "construction of the circle ;" his object being 

 " to make manifest the great importance of the circle as 

 one of the fundamental facts belonging to the Plan of 

 Creation." As we consider the foundation wrong, until 

 Prop. A is proved, we shall not follow the writer through 

 the twenty-four pages of rather obscure mathematics 

 devoted to this subject. We come next to " Mathematics 

 and the Art of Computation." Starting from what he has 

 (as he thinks, we will say) just proved, viz., that " the 

 difference of the quadrant and the chord of the quadrant 

 is an aliquot part of the quadrant and of the chord, and 

 that the number of those equal parts contained in the 

 chord being nine —the quadrant contains ten" : because he- 

 finds in this "conclusive evidence that the (so-called) 

 Arabic system of notation is is not an artificial human 

 contrivance, but a great natural fact of a primary cha- 

 racter, a fundamental part of the Science of Creation." 

 Further down he speaks of many persons preferring 

 " with a strange, and, as it would seem, with an increasing 

 perversity, to cultivate the thorns and thistles, leaving 

 the good seed as not worth utilising." He is then careful 

 to state that by " thorns and thistles " he does not mean 

 the modern methods of mathematical analysis. Still, " is 

 it, or is it not, true that the language of mathematics is 

 fast becoming an unknown tongue to ordinarily educated 

 men, and that those to whom it is known can scarcely 

 hold converse with their fellows (on any scientific sub- 

 ject) in ordinary language without a feeling of conde- 

 scension, and scarcely without a feeling of impropriety ? 

 .... Is it true that the mathematician does now, in 

 some degree, regard his fellow-worker who is unprac- 

 tised in the calculus and non-conversant with differ- 

 ential methods as but little better than a publican 

 and heathen ? " We will not undertake to answer 

 this question, but perhaps our author's ground for this 

 opinion is the reputed division of the human species by 

 the " Cambridge Wrangler " into those who understand 

 the differential calculus and those who do not. He him- 

 self goes on to say, "If it be true that such a result does 

 manifest itself in any considerable degree, it may be pro- 

 nounced decidedly unwholesome and bad — bad for science 

 and bad for civilisation— because mathematical know- 

 ledge is a necessity to science and a necessity to civilisa- 

 tion." This we admit. He then reiterates the statement 

 that he knows that examination will show his demonstra- 

 tion of the quantitive {sic) ratio of the perimeters of the 

 circle to the diameters is " mathematically incontestable." 

 He then goes into an examination of Prop. XIII., Book V., 

 of Brewster's Legendre : " The surface of a regular in- 

 scribed polygon and that of a similar polygon circum- 

 scribed, being given, to find the surface of the regular 

 inscribed and circumscribed polygons having double the 

 number of sides." Among other objections, he objects to 

 the italicised statement (Prop. XIV., " Legendre "), " We 

 shall infer that the last result expresses the area of the 

 circle, which, since it must always lie between the inscribed 

 and circumscribed polygon, and since these polygons 

 agree as far as a certain place of decimals, must also 

 agree with both as far as the same place," His objection 

 to the whole method is " in the omission to observe that 

 comparison has to be made between a continuous curved 

 line (the circle) and a continuous straight line (the dia- 

 meter)." And then, as elsewhere, he indulges in meta- 

 physics. Part III. begins with Curvature and ends with 

 Theology. " A human science which does not distinctly 

 recognise the primary truths of theology as its ultimate 



basis, is not based on reality ; it has not and cannot have 

 any actual and secure foundation. If the science of Eng- 

 land is not so based, no matter what seeming progress 

 may for a time be made, whenever the trial comes it will 

 be as the house built on the shifting sand, and, if not de- 

 stroyed by sudden catastrophe, will eventually become a 

 ruin, together with the civilisation which rests upon it." 

 Our safety then, we presume, Kuklos would have us 



believe, is to believe in tt = ^2^. The supplement has 



" Supplementary Illustrations " and Tables. The work is 

 printed at Montreal. 



The conclusion of the matter is, that there are Cyclo- 

 meters and Cyclometers. We have endeavoured to give a 

 fair presentment of the several kinds by giving as far as 

 possible their views in their own words. The majority of 

 their writings evidence great waste of ingenuity, which, 

 had it been otherwise directed, might have resulted in 

 works of utility instead of in such utterly trivial work as 

 it has done. 



To any who may be thinking of taking up this 

 " curiosity of literature," not having done so hitherto, we 

 say emphatically, " Don't." 



I 



SCIENCE IN GERMANY 

 {From our own Correspondent^ 



N Wiedersheim's recently published book, " Salanian- 

 drina perspicillata und Geotriton fuscus," two very 

 little-known tailed amphibians (Urodela) are described 

 and compared anatomically, which, by their entire organi- 

 sation, stand at the two opposite limits of the Salaman- 

 drinse that are known to us, representing the highest and 

 the lowest form of these. Salamandrina perspicillata, 

 which is rather a land than a water animal, seems to be 

 found only in the western half of Italy ; it is a prettily 

 coloured, small, and slender animal, which lives on insects, 

 and during the dry summer months continues in a kind 

 of summer sleep, but in winter it is found in full vital 

 activity. In its skull are almost entirely wanting the 

 cartilaginous parts denoted as the " primordial cranium," 

 so that in this it rises above all other Salamandrince, and 

 comes near the Reptiles. In accordance with this, also, 

 is the existence of a cavity in the base of the skull (sella 

 turcica), the prolongation of the frontal bone (frontale) 

 into the eye cavity, and a roofing-over of the latter; 

 lastly, the absence of a special nose-partition (which, 

 again, quite characterises the Reptiles). On account 

 also of the course of development of its vertebrse, and 

 the numerous bones of its carpus and tarsus, Salainan- 

 drina perspicillata must stand at the top of the Salaman- 

 drinae ; its divided kidneys, again, suggest the reptile, so 

 that we must look on this animal as a form rendering 



Tongue of Geotriton fuscus. 



possible the transition from the Amphibia to the Reptilia, 

 and which, on account of its peculiarities, might repre- 

 sent a separate family. Geotritofi fuscus, on the 

 other hand, holds quite a different position. If, in 

 view of the numerous anatomical relations adduced, 

 we are able, commencing with Salamandrina pe.rspicil- 

 lata, and passing through the various water salamanders 

 (Tritons), to the land z2iXz.ra.z.-a.6ji,x{Salamandra maculata), 

 to form a descending series of ever less-developed forms, 

 Geotriton fuscus comes at the lower end of the series, for 

 in many respects it ranks with the lowest Amphibia gene- 

 rally, the Perennibranchiata. Indications of this appear 

 in the fewness of bones in the skull and the tarsus, the 

 extended double cone form of the soft-cartilaged vertebrae ; 



