November 3, 1892] 



NATURE 



where vol (ABC) denotes the volume of the parallelopiped 

 of which ABC are three adjacent edges. The only ob- 

 jection to this name lies in its suggesting that A, B, C 

 are linear vectors. 



Here appears the defect in the author's cos and sin 

 notation, in that it cannot be applied to the products of 

 three vectors, or at least that the special reason for its 

 use has disappeared, and the author does not suggest 

 so applying it. 



But there is a certain perspicuity attained by this very 

 limitation of the cos and sin notation to the products of 

 only two vectors, inasmuch as there can be no ambiguity 

 in the meaning of an expression in which they occur, even 

 if brackets are omitted or placed differently. Indeed, 

 instead of cos (Sin AB . C) the author writes cos (Sin AB)C, 

 -which seems a curious use of the bracket. But 

 cos Sin AB. C, or preferably cos C Sin AB, is just as 

 explicit, and even cos Sin ABC, though wrong to write as 

 being puzzling, can only have the same meaning. 



The author concludes with short sections on dyads and 

 matrices, on scalar- and vector-differentiation, including 

 scalar-differentiation of a quaternion. On the last page 

 are a series of propositions relating to the addition of 

 scalar and vector quantities situate at, or passing through, 

 specified points. 



The pamphlet is confined solely to statements of 

 principles and the section devoted to dyads and matrices 

 is very condensed, so that it is not in any sense a text- 

 book for students. It is rather a synopsis of the subject, 

 with the introduction of a special notation which the 

 author has found useful. A text-book of vector algebra, 

 with examples showing its application to problems in 

 geometry, mechanics, and general physics, and contrast- 

 ing the method with the Cartesian method of treating the 

 same problems, is much needed, as many physicists are 

 becoming interested in the new algebra, owing in great 

 measure to Mr. O. Heaviside's able exposition of its 

 principles and applications in the Electrician and else- 

 where. 



THE LAKE OF GENEVA. 

 Le Ldman : Monographic Limnologique. F. A, Forel. 



Tome Premier. (Lausanne : F. Rouge, 189-.) 

 JpROF. FOREL has been for some years occupied in 

 studying the Lake of Geneva, and has now published 

 the first instalment of the fruits of his labours. The work, 

 when finished, is intended to be a complete monograph of 

 the history of a single lake, and will be a most important 

 contribution toaninterestingbranch of physical geography. 

 In the present volume the geography, the hydrograpliy, 

 the geology, the climatology, and the hydrology of Lake 

 Ldman are discussed, after some introductory matter 

 relating to the instruments employed in sounding with 

 other preliminaries. But, though only a single volume, 

 the work embraces so many questions that we must, for 

 want of space, confine our notice mainly to one, which, 

 of late years, has attracted the most attention, at any rate 

 in this country, viz. What has been the origin of the 

 lake basin ? Was it formed by the old Rhone glacier or 

 in some other way ? The especial value of Prof. Forel's 

 memoir is the number of new facts which it brings to 

 bear on the problem thus propounded. 

 NO. I 20 1, VOL. 47] 



The Lake of Geneva, however it may have been 

 caused, is more modern than the middle of the Miocene 

 period : " Le lac n'existait pas encore, la valine du Ldman 

 n'dtait pas mcme indiqude quand la mer helvdtienne 

 ddposait les moUasses d'Epalinges et du Mont." Its 

 slopes, and almost certainly its bed, are covered with 

 glacial deposits, of later date than the formation of its 

 basin. Terraces around its shore indicate that its waters 

 once reached a higher level, the greatest elevation which 

 can be identified with certainty, being about 30m. above the 

 present surface. The next pause was at lom. ; after that 

 the lake sank (the fall always being rapid) to its present 

 level. Traces of still higher terraces are to be found on 

 the north shore, but as these neither can be identified on 

 the opposite side, nor correspond with any natural bar- 

 rier in the course of the Rhone below the lake. Prof. 

 Forel doubts whether they indicate old levels of its waters. 

 Lake Leman consists of two basins. The first and 

 larger extends from the embouchure of the Rhone to ihe 

 narrow of Promenthoux. At the east end the slope of the 

 cone of alluvium deposited by the Rhone in no part ex- 

 ceeds 25''. First comes a zone of very shallow water 

 off the actual shore line ; to this succeeds a more rapid 

 slope, which gradually eases off as it descends. The 

 current of the Rhone has made and maintains a well- 

 marked channel in this mass of detritus, and the contour 

 lines are affected down to 250m. At the embouchure of 

 the Dranse, on the south shore, another alluvial cone has 

 been deposited. This, however, is rather steeper, but it 

 is much smaller, and does not perceptibly affect the 

 course of the subaqueous contour lines below about 2::;om. 

 On the north side of the basin the slope varies. Under 

 the walls of Chillon the descent is rapid, amounting to 

 137 in ICO ; it is nearly the same near St. Gingolph on the 

 opposite shore, doubtless indicating submerged crags ; 

 but it is generally more moderate. West of Vevay it is 

 about one in four, whence it changes gradually to one in 

 ten opposite to Ouchy. 



West of this port the descent is still more gentle, and 

 so it continues round the western end of the basin, the 

 lip of the latter being 7Sm. below the surface. The con- 

 tours of the south side correspond generally with those of 

 the north, and the form of the basin is evidently related 

 to the geology of the district, being narrower and steeper 

 among the harder rocks at the eastern end. The deepest 

 part is a large rudely triangular area, the apex pointing 

 towards the west, and the base lying roughly north and 

 south, extending from almost opposite to the embouchure 

 of the Dranse to near Lutry. All this area is an almost 

 level plain, for it is wholly below the 300m. contour line, 

 but the greatest depth obtained was only 3097m. 



The Petit Lac may be described as a comparatively 

 narrow and shallow trough, rising very slowly from a 

 depth of about 70 to 50 metres, and then gradually 

 mounting to the embouchure of the Rhone, its bed being 

 slightly interrupted by five small shallow basins, which 

 roughly speaking, have a linear arrangement, but their 

 floors only sink four or six yards at most below the 

 general level. 



The lake to some extent is still held up by the huge 

 mass of gravel brought down by the Arve, through which 

 the two rivers have now cut their channels on either side 

 of the plateau of La Batie below Geneva. But it is 



