404 



NA TURE 



[March 25, 1875 



deposited, as the rocks strike with the line of fault ; " or a 

 map, in which many of the faults upon which the form of a 

 lake is said to depend are drawn altogether below the 

 waters of the lake, and the direct evidence of their direc. 

 tion or even existence is not given in the text (p. 123, 

 and pi. ii. p. 15). Again, anyone who wished to see for 

 himself whether it was possible that " streams have run 

 over pohshed, scratched, and etched surfaces of rock for 

 ages without having been able to obliterate the ice- 

 marks " (p. 87), could hardly be sure of finding the places 

 referred to by the author from the vague description that 

 they were " among the ice-dressed hills of Galway, Kerry, 

 and Cork " {ib.) 



We cannot see what right our author has to assume 

 because the " outlines — river-valleys, lake-basins, and 

 bays — occur in systems, the general bearing of which may 

 be indicated by lines," that " if such systems are not 

 caused by breaks in the subjacent rocks, they must be due 

 to chance " (p. 99), when we kn ow that other authors 

 have appealed to this very same fact in support of the 

 theory that the leading features of the country referred to 

 are due to a body of ice moving from the N.E. 



It does not seem unreasonable to suppose that valleys 

 which appear to have been shifted (p. 175) may have 

 been formed along lines of fracture or of softer rock which 

 had been previously shifted, or were for any reason not 

 opposite to one another. 



That an unfinished plain of marine denudation should 

 have an irregular margin (p. 177) does not prevent our 

 believing that the sea can in time cut back most of the 

 hard promontories as well as the softer rock, or arrest at 

 a uniform level the sub-aerial action'which is reducing 

 both hard and soft. That a river should deposit sedi- 

 ment on a slope at any part of its course, even out into the 

 estuary (p. 187), seems to present fewer difficulties than 

 the supposition that the rock ddbris resulting from the 

 denudation of Loch Lomond was carried out through a 

 hole in the bottom of the lake (p. 215). 



Although, however, such statements lead us to distrust 

 somewhat the author's judgment, we must allow that 

 the work contains much that is useful and suggestive, 

 and should be read by all who are engaged in the study of 

 earth-sculpture. 



OUR BOOK SHELF 



The Cone and its Sections treated Geometrically. By 

 S. A. Renshaw. Pp. 148. (London : Hamilton, Adams, 

 and Co., 1875.) 

 " What so intricate and pleasing withal, as to peruse and 

 practise ApoUonius's Conies ? " The author of the pre- 

 sent work has evidently the same admiration for this Old 

 World writer that Burton had. He remarks of him that 

 his work has apparently maintained its superiority over 

 every subsequent treatise on the subject. Like Apollonius 

 in one respect, Mr. Renshaw derives the sections from the 

 Scalene Cone, and rebuts the possible charge of " consider- 

 able prolixity " by affirming his belief that " the reader 

 will be well repaid for the time and patience expended in 

 the investigation." Upon this point opinions will most 

 likely differ. The subject, though of considerable interest 

 to all minds of a geometrical cast, is yet only a subordi- 

 nate one, and we question if many can find time in these 

 days of " high pressure " for the extra time and patience 

 demanded. However, the student need not so occupy 



his time, for our author has also derivedf'the principal 

 well-known properties from the right cone independently. 

 Further, he establishes a proposition by means of which 

 the scalene-cone properties may be derived from the 

 right cone. 



We have, in former numbers of Nature, given in our 

 adhesion to the principle of deriving the properties of 

 these curves from the cone, and so are glad to see that 

 the latest work on the subject is grounded on this prin- 

 ciple. Robertson (1802), following Hamilton (1758), takes 

 as his fundamental proposition the following ; — If there 

 be four lines in the plane of a conic which are parallel, 

 two and two, then the ratio of the rectangles under the 

 segments from one point of section to the rectangles under 

 the segments from the other point of section is constant. 

 Mr. Renshaw builds upon the proposition that in the 

 ellipse and the hyperbola the tangent at any point on the 

 curve makes equal angles with the focal distances of the 

 point (with modification for the special case of the para- 

 bola). These and the other primary properties are, as 

 we have said, proved from the cone, and this " it is 

 believed to a greater extent than in any previous treatise." 

 A great portion of the work, however, is taken up with 

 the treatment of the curves in piano, and here a funda- 

 mental proposition is that of the generating circle. The 

 properties are neatly derived by this means. We should 

 mention that the generating circle (which in a particular 

 case becomes the auxiliary circle of modern treatises) is 

 said to have been first employed in Walker's work on 

 Conies (1794), and is thus defined : If we have a focus 

 and corresponding directrix of a conic, and in the same 

 plane take any point and from it let fall a perpendicular 

 on the directrix, then the circle required is that described 

 fi'om the above point as centre with a radius equal e times 

 the above perpendicular {e being the eccentricity of the 

 curve). We have been thus explicit, as this circle appears 

 to have dropped out of recent text-books. We must refer 

 for application to the work under review. The subject is 

 ably treated, and the book copiously illustrated by well- 

 drawn figures (in most cases) ; these latter, however, have 

 been sadly marred in the engraving. Indeed, it is matter 

 of regret that the paper, the ink, and the engraving are 

 of an inferior character. The work was printed at 

 Nottingham. 



A Whaling Cruise to Baffin's Bay and the Gulf of 

 Boothia. By A. H. Markham, F.R.G.S., Commander 

 R.N. With an Introduction by Rear Admiral Osborn, 

 C.B., F.R.S. Second Edition. (London : Sampson 

 Low and Co., 1875.) 

 Commander Markham has done well to issue a cheap 

 edition of his attractive narrative at the present time. 

 The author, in the summer of 1873, went out to Baffin's 

 Bay in the whaler Arctic, with the deliberate intention ot 

 acquiring experience in ice-navigation ; consequently from 

 his book a reader is likely to obtain a better idea of the 

 real nature of the dangers attendant on pushing through 

 the frozen ocean, than from a book whose chief aim is to 

 narrate discoveries. Commander Markham, it is evident 

 from the work before us, took such excellent advantage of 

 the opportunities afforded him while cruising about in the 

 Arctic seeking for whales, and finding them plentifully, 

 that his knowledge of the " ways " of the ice must be of 

 great advantage to the expedition of which he is second 

 in command. 



To those who wish to have a full and accurate idea of 

 how the whale-fishing is prosecuted at the present day, 

 we recommend this delightful narrative, which we should 

 think is likely to become an established favourite with 

 boys. There is a wonderful amount of information 

 packed into the small volume concerning the regions 

 visited, the nature of the ice and icebergs, currents, 

 coasts, natives, fauna, flora, &c. He visited some of the 

 spots rendered classical by former explorers, and actually 





