May 30, 1889] 



NATURE 



01 



to attack with success the subject of modern analytical 

 geometry. Mr. Dupuis looks at a triangle not as "the 

 three-cornered portion of the plane inclosed within its 

 sides, but the combination of the three points and three 

 lines forming what are usually termed its vertices and 

 its sides and sides produced." His object is to lead up 

 to the idea of a figure as a locus, with a view to preparing 

 the way for the study of Cartesian geometry. Here the 

 necessity for a careful distinction between congruence and 

 equality arises. He introduces freely the principle of 

 motion in the transformation of geometric figures, and 

 devotes some space to the principle of continuity. Further, 

 he connects geometry with algebraic forms and symbols, 

 " (i) by an elementary study of the modes of representing 

 geometric ideas in the symbols of algebra, and (2) by 

 determining the consequent geometric interpretation which 

 is to be given to each interpretable algebraic form." The 

 subject of proportion is treated on the method of measures, 

 and the term tensor is freely used. The first part (pp. 

 1-90) traverses the point, line, parallels, the triangle 

 and circle. The second part (pp. 91-146) considers the 

 measurement of lengths and areas : each part closes with 

 a section devoted to illustrative matter drawn from 

 constructive geometry. The third part (pp. 147-177) 

 consists of two sections— the first on proportion amongst 

 line-segments, and the second on functions of angles and 

 their applications in geometry. Some instruments are 

 described, as the proportional compasses, the sector, the 

 pantagraph, and the diagonal scale. In the fourth part 

 (pp. 178-251) there are seven sections, which are taken 

 up with such matters as the centre of mean position, 

 inversion and inverse figures, pole and polar, radical 

 axis, and centres and axes of perspective. The closing 

 part (pp. 252-290) introduces the student to harmonic and 

 anharmonic properties, polar reciprocals and reciprocation, 

 and to homography and involution. The author discusses 

 all these points in a lucid style, and illustrates them with 

 full store of carefully selected solutions : in addition there 

 are a great number of unworked exercises in all the 

 subjects. These good results are the otitcome of many 

 years' teaching of geometry to the junior classes in the 

 University of (2ueen's College, Kingston, Canada. Tiie 

 book is closed with a full index, and clearly drawn figures 

 accompany the te.xt. 



A Vertebrate Faung. of the Outer Hebrides. By J. A. 

 Harvie-Brown, F.R.S.E., F.Z.S., and T. E. Bucklev, 

 B.A., F.Z.S. (Edinburgh: David Douglas, 1889). 



This is a sister volume to " A Fauna of Sutherland, 

 Caithness, and West Cromarty," which was published by 

 the same authors in 1887, and reviewed in Nature at 

 that time. It may be remembered that in the preface to 

 this work, the authors expressed their intention of follow- 

 ing it up with others, dealing in a similarly exhaustive 

 manner with the vertebrate faunas of other parts of Great 

 Britain. We are glad to receive at so early a date so 

 substantial a fulfilment of this intention ; for we cannot 

 give higher praise to " A Fauna of the Outer Hebrides " 

 than by saying that it is in all respects worthy of its 

 predecessor. Moreover, when we have regard to the 

 immense amount of labour which the production of these 

 volumes must have involved, we cannot refrain from con- 

 gratulating the authors on the rapidity with which their 

 works have followed one another. This second member of 

 the series runs to over 250 pages, and, like the first member, 

 is embellished by a few beautifully executed drawings of 

 landscape scenery. Like the first member, also, it gives 

 an exhaustive account of all the Vertebrata which occur 

 within the area specified, together with several introductory 

 chapters dealing with the topography of the district, and 

 the relation (palaeontological and otherwise) of its fauna 

 to that of the rest of Great Britain. As the value of such 

 a work consists mainly in the number and the accuracy 

 of its details, Uttle need be said of it in a review, save in 



general terms. And, as we have already indicated, the 

 painstaking labour which has been bestowed upon this 

 Fauna appears to us to leave nothing that can be desired 

 in the way either of addition or subtraction. We heartily 

 recommend both these Faunas to all systematic 

 zoologists, and sincerely hope that their authors may be 

 able to continue their researches through other areas ot 

 Great Britain. G. J. R. 



Dictionary of Photography. By E. J. Wall. (London : 

 Hazell, Watson, and Viney, Limited, 1889.) 



This work is practically a complete encyclopaedia o 

 photography, and will form a very useful addition to 

 photographic literature. It is written throughout in 

 plain and straightforward language, each heading being 

 thoroughly treated. The subject-matter under the head- 

 ing of "Lens "is accompanied by excellent illustrations 

 of the various forms of lenses, showing by shaded lines 

 the dififerent combinations of crown and flint glass. 

 Developing, printing, &c., receive their full share in the 

 work, and under" toning "no less than twenty-nine differ- 

 ent baths are discussed. At the end there is a collection 

 of miscellaneous tables that have not been inserted in the 

 dictionary part of the book, such as sizes of French and 

 Italian dry plates, a list of dry plates and sensitometer 

 numbers, solubilities, freezing mixtures, &c. 



For photographers in general this work ought to prove 

 most useful. It will make it unnecessary for them to 

 refer to other works for a hint or remedy, or anything 

 else that may be wanted at a moment's notice. 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents . Neither can he umlertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE, 

 No notice is taken of anonymous communications.^ 



Upper Wind Curren's over the Equator in 

 Atlantic Ocean. 



the 



1 ^J January last I addressed you a letter from the Straits of 

 Magellan, with an account of the upper wind currents observed 

 over the equator during a voyage to South America in the 

 month of December. Then I described how the northeast and 

 south-east trades both turned into a common light surface 

 easterly current along the line of the doldrums ; how low clouds 

 from south-east drove over the north-east trade up to 15" N. ; 

 how the highest clouds moved from south-west, north of the 

 equator ; and how, from 300 miles south of the line, a very high 

 current from north-west prevailed over the south-east trade. 

 No high observations were obtained in that l-elt of 300 miles, 

 nor were any middle-level, clouds seen over the south-east 

 trade. 



Now, I have just crossed the same route in the month of May, 

 under a somewhat different wind system. The north-east trade 

 turned to north as it approached the doldrums, instead of 

 towards the east, as in the previous voyage. In the calm belt, 

 it met a light easterly current, without much conflict in the way 

 of rain ; while further south the regular south-east trade was 

 experienced as far as 8" S. , when the north-east monjoon of the 

 Brazilian coast prevailed nearly down to Rio Janeiro. 



No signs of south-east wind could be discovered at any level 

 over the north-east trade, which wind, on the other side, blew 

 at low or middle levels over the south-east trade, till surface, 

 low, and middle currents combined to form the Brazilian 

 monsoon. 



Very few observatiois were obtained of the highest clouds, 

 but in 6" S. a high north- west prevailed ; from 2° S. to the 

 equator, both the middle and highest clouds came from the 

 east ; and nothing more could be determined till a high south- 

 west current was found over the north-east trade, in 7^ N. 

 latitude. 



These results confirm in a most striking manner the discovery 

 which I have announced from time to lime in your columns, 

 apfi which was most conclusively proved by the labours of the 



