302 



SCIENCE. 



[N. S. Vol. I. No. 11. 



It is to be remembered that the secretions 

 of Orya barbarica are acid, thus in this case 

 excluding the explanation of Eadziszewski. 

 William Hallock. 



mathematics. 

 The Principles of Differentiation in Space-Ana- 

 lysis.'^ By A. Macfarlane, D. Sc, LL. D. 

 According to Hamilton the differentiation 

 of a function of a quaternion presents novel 

 difficulties due to the non-commutative 

 character of a product of quaternions. 

 There is in general no derived function, and 

 it is necessary to define the differential in a 

 new manner. Under certata conditions 

 there is an analogue to Taylor's Theorem, 

 but it is very complex, and no use is made 

 of it. Hamilton does not differentiate the 

 general transcendental functions, but only 

 these functions restricted to a constant 



The author shows that these anomalies 

 are true of products of vectors, but not of 

 functions of versors. In versor analysis 

 there is a derived function, satisfying a gen- 

 eralized form of Lagrange's definition ; and 

 Taylor's Theorem takes on a form similar 

 to that in ordinary analysis, only the order 

 of the two quantities must be preserved. 

 Let X and h denote two versors, then 



f (x+]i)=f (x)-|-{' (x)h-l-* f" (x)h2+, etc., 

 provided the order of the x and h be pre- 

 served throughout. 



The author finds the derived functions of 

 various transcendental functions in space. 

 He also shows that there are two essentially 

 different meanings of V ~-l ; one, when made 

 definite, means a quadrant of rotation 

 round a specified axis ; while the other has 

 no reference to direction, but distinguishes 

 the area of a hyperbolic angle fi-om the 

 area of a circular angle. He also re- 

 marks that the theory of functions must be 

 imperfect, because it is based upon a complex 



* A paper read before the meeting of the American 

 Mathematical Society, January 26, 1895. (Abstract.) 



number which is restricted to one plane; no 

 account is taken of the two essentially 

 different meanings of V~-l, and the idea of. 

 the versor is not distinguished from that of 

 the vector. 



meteorology. 

 Neudnicke von SeJiriften und Karten ueher 

 Meteorologie und Erdmagnetismus. 

 Dr. Gr. Hellmann, of Berlin, has under- 

 taken the republication of certain old and 

 rare writings relating to meteorology and 

 terrestrial magnetism which have an im- 

 portant bearing on the historj^ and develop- 

 ment of these sciences. Very rare or typo- 

 graphically interesting works are printed 

 in facsimile. Each reprint is preceded by 

 an introduction, containing a general de- 

 scription of the book and its author. Al- 

 though facsimile publications generally are 

 so dear that only connoisseurs are able to buy 

 them, yet, owing to the aid of the German 

 Meteorological Society and its Berlin 

 branch, the reprints are offered at a relative- 

 ly low price by A. Asher & Co., Berlin. A 

 few copies may also be had of A. L. Eotch, 

 Blue Hill Observatory, Readville, Mass., at 

 the publishers' prices. Each j^ear one or 

 two of the reprints will be issued, but the 

 whole number will not exceed twelve. The 

 following have already appeared : 

 No. 1. Wetterbuechlein von imhrer Erkennt- 

 niss des Wetters. Reynman, 1510. 41 

 pages introduction and 14 pages fac- 

 simile. Price 6 M. = $1.50. 

 This is the oldest printed meteorological 

 work in the German language and was 

 verj'^ popular, having 34 editions in seven- 

 teen years. Nevertheless, it is now so 

 scarce that hardly thii-ty-six copies can be 

 found. 



No. 2. Jtecit de la Gfrande Experience de VEquil- 

 ibredes Liqueurs. Blaise Pascal. Paris. 

 1648. 10 pages inti-oduction and 20 

 pages facsimile. Price 3 M. ^ 75 cents. 

 This little work is of the greatest impor- 



