100 



SCIENCE. 



[N. S. Vol. III. No. 55. 



equal good in its line. Electricians are alive to 

 the importance of this work also, and the indi- 

 cations are that they will have much influence 

 in its settlement. 



But since at the present time there are writers 

 on space analysis who see nothing but vectors, 

 and other writers who identify vectors with 

 quadrautal quaternions, and since the princi- 

 ples commonly accepted by Quaternionists are 

 not free from fundamental errors, it is evident 

 that much time is still required for the discus- 

 sion of principles before definite decisions about 

 notation can be arrived at. The notation which 

 is adopted must be built on an adequate analysis 

 if it is to be lasting. And here the ^r muddle in 

 the system of electric and magnetic units ought 

 to act as a warning to make haste slowly. 



The logical harmony and unification of the 

 whole of mathematical analysis ought to be kept 

 in view. The algebra of space ought to include 

 the algebra of the plane as a special case, just 

 as the algebra of the plane includes the algebra 

 of the line. And as the algebra of space in- 

 cludes the spherical and higher forms of trigo- 

 nometry, it ought to be made to harmonize as 

 much as possible with the existing notations 

 and conventions of trigonometrical analysis. 

 When vector analysis is developed and pre- 

 sented so as not to contradict, but, on the con- 

 trary, to include the ordinary branches of anal- 

 ysis, we may expect to see many zealous culti- 

 vators, many fruitful applications, and, finally, 

 its universal diflusion. Then there will be no 

 need of arguments to prove its utility. May 

 the movement initiated by Messrs. Molenbroek 

 and Kimura hasten the realization of this happy 

 result. Alexander Macfaelane. 



Lehigh Univeesity. 



SCIENTIFIC LITERATURE. 

 De Saint Louis a Tripoli par le lac Tchad. Par 

 le Lieutenant-Colonel P. L. Monteil. 

 Paris, Alcan. 1895. Pp. x. and 463. Fifteen 

 itinerary charts and one general map. Pro- 

 fusely illustrated by Riou. 

 This book may be considered as the fruit of 

 the treaty between England and France which 

 was entered into on August 5, 1890. The 

 reason for the treaty was the necessity of fixing 



a boundary between the regions subject to their 

 respective influences along an imaginary line 

 drawn from Say on the Niger to Lake Tchad. 



Monteil proposed to the French government 

 to traverse this region, starting from St. 

 Louis, in the French possessions on the west 

 coast of Africa. His object was to obtain 

 treaties with as many of the native potentates 

 along the route as possible, and thereby fix the 

 boundary as far as France was concerned. 



He left St. Louis on October 9, 1890, with one 

 white companion, Adjt. Badaire, and twelve 

 natives, four of the latter deserting him quite 

 promptly. For twenty-seven months from this 

 time his experiences are given with considerable 

 minuteness. He had the regulation ' ups and 

 downs ' Avhich are the lot of the explorer every- 

 where, particularly in Africa. As far as Wago- 

 dogho he followed the itineraries of Binger and 

 Crozat. Beyond this point everything was rel- 

 atively vmknown, except where light had been 

 thrown upon various points along the line 

 when his path crossed the track of his prede- 

 cessors, Denham and Clapperton, Barth, Nachti- 

 gal and others. 



His occupations were numerous, as he was at 

 various times soldier, engineer, physician, bot- 

 anist, astronomer, cartogTapher, pharmacist, 

 trader, diplomat and magician. Photography 

 did not prosper with him. His Early attempts 

 were crushed in Paris; where his plates going 

 to one office and his letter of instructions to 

 another, they were both opened separately with 

 the consequent disastrous result to the negatives. 

 A final blow was struck at this portion of his 

 work when a native stole his camera, plates and 

 all. One can imagine the 'joy and perplexity ' 

 of the average native while examining this 

 piece of apparatus, as well as the feelings of the 

 rightful owner under the circumstances. 



The loss, however, is made good by the 

 superb set of ilkistrations by Eiou, which are 

 one of the charms of the volume. The artist 

 has so thoroughly caught the spirit of the 

 author that, much as we regret the absence of 

 the true copies of nature, we feel satisfied by 

 the insight which the skillful sketches give us 

 on the subject. 



Another feature of the book which cannot be 

 too highly praised is the series of itinerary 



