268 



NA TURE 



{Jan. 17, 1889 



to find his way readily to any part of it. In the one 

 before us this want is met by an admirable index, and an 

 equally complete table of contents, and by the liberal use 

 of clarendon type in the body of the book. The printing 

 is clear and generally correct, but we notice the following 

 errata : — 



P.x. line 8 from top, for "1885- 1 888 "read "1883- 1 888." 

 P. no, in the heading of Chapter VI., for " 641-1543 " 

 read "641-1453." 



P. 168, line 4 from bottom, for "Act iv. sc. 3 "read 

 " Act iv. sc. 2." 



P. 358, line 8 from bottom, for " 1728 " read " 1738." 

 All the salient points of mathematical history are given, 

 and many of the results of recent antiquarian research : 

 but it must not be imagined that the book is at all dry. 

 On the contrary, the biographical sketches frequently 

 contain amusing anecdotes, many of the theorems men- 

 tioned are very clearly explained, so as to bring them 

 within the grasp of those who are only acquainted with 

 elementary mathematics, and there is a very interesting 

 account (in a footnote) of the early history of the Uni- 

 versities of Paris, Oxford, and Cambridge. For those 

 who wish to study mathematical history in detail there is 

 a long list of authorities at the beginning, and many 

 references to other works are made in different parts of 

 the book. We would suggest that in future editions 

 reference should be made to " Les Fondateurs de 

 I'Astronomie Moderne Copernic— Tycho Brahd, Kdpler, 

 Galilee, Newton," by Joseph Bertrand (8vo, Paris, n.d.), 

 and to the article " Viga Ganita " in the " Penny Cyclo- 

 paedia " (which contains the opinions of Colebrooke, the 

 translator of the " Lilavati," &c., on many points connected 

 with Hindu mathematics). 



Finally, we would suggest that the following motto 

 should be printed on the title-page of the second 

 edition : — 



"Habetis originis ac progressionis mathematics his- 

 toriam brevem. Ex qua matheseos antiquitas, praestantia, 

 ac dignitas apparet." 



The quotation is taken from the concluding paragraph 

 of the " Historica Narratio " prefixed to Andrew Tacquet's 

 "Euclid" (2nd ed., by Whiston, 1710). It describes 

 perfectly the contents of the present treatise. 



Mr. Ball promises us a supplementary volume contain- 

 ing a list of mathematicians and their works, which is to 

 be as complete as possible. It will be a most import- 

 ant contribution to mathematical bibliography, and we 

 sincerely hope that the reception that this volume meets 

 with will encourage him to \4^rite the supplement. 



THE BUILDING OF THE BRITISH ISLES. 

 The Building of the British Isles : a Study in Geo- 

 graphical Evolution. By A. J. Jukes-Browne, B.A., 

 F.G.S. (London : George Bell and Sons, 1888.) 



IT is now thirty-three years since Godwin-Austen, in 

 a paper which glows with the instinctive perception 

 ithat is one of the marks of genius, suggested to geolo- 

 gists an application of their science which lifts it out of 

 the region of technicalities, gives it a human interest, and 

 attracts all those who care to follow the long chain of 



events of which the present state of things is the outcome. 

 It was an attempt to go back to Mesozoic and Palaeozoic 

 days, and mark out the main outlines of the physical 

 geography of Great Britain and the adjoining parts of 

 Europe during those epochs. To enable its conclusions 

 to be more easily grasped, the paper was accompanied by 

 a map, almost bewildering in its complexity and some- 

 what hazy in its outlines, but full of the masterly gener- 

 alization that marshals into one compact body a crowd 

 of isolated facts, and of the intuition that foresees the 

 complete meaning of imperfectly ascertained data. 



Many a geologist has since been tempted to try his 

 hand at similar tasks, but few have mustered courage, 

 when it came to the point, to embody their conclusions in 

 a map. And no wonder : everyone who has speculated in 

 this direction knows how easy it is to clothe his conceptions 

 in words, and soon finds out how hard verbal descriptions 

 of physical geography are to follow. So he becomes 

 keenly alive to the fact that, if he wishes to be listened 

 to, he must make the road easy by presenting his restora- 

 tions to the eye in the pictoral form of a map. But if 

 he be haunted by any sense of accuracy, and any horror 

 of vagueness and hasty reasoning, he finds himself beset 

 on all sides, when he begins to plot out his map, with 

 uncertainties and hesitations that give him pause. It 

 may be easy to say that land lay on this side and sea on 

 that, but when a coast-line is actually to be laid down, 

 though it may be possible to fix the limits between which 

 it must lie, these limits are often so wide apart that the 

 feeling of uncertainty as to the actual position of the 

 boundary becomes unbearable, and the prospect of making 

 a map that shall be even approximately accurate grows 

 hopeless. Worse still is it— and this not unfrequently 

 happens— when there are not even bounding limits, and 

 the coast-lines can be no better than such guess-work 

 as rashness delights in and the logical temperament 

 abhors. 



But even those who reahze most clearly the difficulties 



of the task of making maps which show the distribution 



of land and sea during past geological epochs, welcome 



\ with keen delight attempts, such as those in the book 



before us, which are made in the right spirit ; and it would 



ill become me to carp at the author's restorations, even 



I were they less satisfactory than is the case, for I believe 



j that, in noticing a former work of his, I ventured to take 



him to task for not having appended maps to his verbal 



j descriptions of the old physical geography of our islands. 



I Mr. Jukes-Browne has explained, in the introduction, 



I the principles which have been his guide ; and the words 



with which he concludes his opening remarks show how 



fully he is aware of the difficulties that attend the task 



he has undertaken, and how much uncertainty hangs over 



many of his results. Even where we cannot agree with 



him, we feel sure thait he has never been hasty and 



has spared no pains to arrive at the most probable 



conclusions. 



With commendable caution no attempts are made to 

 depict on a map the physical geography of Archaean and 

 Cambrian times ; but preference is given to Prof. Hull's 

 conjecture that the great mass of Cambrian land " lay to 

 the north-west of Europe, and occupied a large part of 

 what is now the North Atlantic Ocean." The words 

 "large part'' are vague, but a partiality for filling up the 



I 



