524 



SCIENCE. 



[N. S. Vol. II. No. 42. 



Verehrer steht es fest, dass der seltene Tag nicht 

 vorbei gehen darf ohne ein dauerndes Zeichen 

 der Erinuerung. Wir gedenken von einem 

 hervoiTagenden Bildhauer ' Leuekart'sMarmor- 

 biiste ' herstellen zu lassen und sie zugleich mit 

 einer kiinstlerisch ausgestatteten Adresse zu 

 iiberreichen. 



" Wir ■wen den uns an alle, welche in ihrem 

 geistigen Entwickelungsgange .seiu Wirken und 

 seinen Einfluss verspiirt liaben, dass sie zu einer 

 wiirdigen Ebruug des Jubilars beisteueru. 



' ' Da es unmoglich ist, die Adressen aller 

 seiner Scbiiler, namentlich derer, die nicht Zo- 

 ologen von Each geblieben sind, zu erlangen, so 

 bitten wir diejenigen Herren, welche der allge- 

 meinen Anregungen, die sie aus Leuckart's Vor- 

 lesungen in ihren Beruf mit hinausgenommen 

 haben, in Dankbarkeit gedenken, dass sie in 

 ihren Kreisen durch Verbreitung dieses Aufrufs 

 in unserem Sinne thatig sind. 



" Betrage warden erbeten an Herru Carl 

 Graubner (C. F. Winter's Verlag, Leipzig, 

 Johannesgasse 8), welcher das Amt des Schatz- 

 meisters freundlichst iibernommeu hat. ' ' 



Within a few weeks of the receipt of the cir- 

 cular by American zoologists I received a num- 

 ber of inquiries froni various sources asking for 

 further information regarding the subject, but 

 was unable to reply to these inquiries, as I had 

 not learned the detailed plans of the Leipzig 

 Committee. At present, however, I can furnish 

 some of the desired information, and, as the time 

 is very short, will utilize the columns of Science 

 for this purpose. 



It is the intention of the Leijizig Committee 

 to have a life-size marble bust of the Geheimrath 

 made and to present it to him on December 

 13th, and it is understood that the bust will 

 eventually be deposited in the University at 

 Leipzig or in the Leipzig Gallery. The statue 

 will be made by one of the most prominent 

 sculptors of Germany, who attended Leuckart's 

 lectures this last semester, unbeknown to the 

 lecturer, in order to study his expression. The 

 estimated cost is 4,000 marks, of which about 

 1,000 marks had been subscribed before Sep- 

 tember 1st. Should more money be collected 

 than is necessary it will probably be spent for 

 photographs of the bust which will be sent to 

 persons who have forwarded subscriptions. 



The subscrij)tions thus far made vary from 10 

 to 200 marks, most of them being in sums of 20 

 to 50 marks. 



It is not intended to confine the subscriptions 

 to Leuckart's pupils, for a number of other 

 persons have expressed their desire to contribute. 

 The Leipzig Committee therefore extends a 

 cordial invitation to all admirers of the Geheim- 

 rath to join in the celebration, and I would there- 

 fore urge all of Leuckart's pupils in this country 

 to bring this circular to the attention of their 

 scientific and medical friends. 



Subscriptions can be sent to Carl Graubner, as 

 announced in the original circular, or to me. 

 At the reqviest of Dr. Simroth, the moving spirit 

 in the undertaking, I have agreed to receive 

 American subscriptions and forward the same 

 in one sum to Leipzig. 



Ch: Waedell Stiles. 



U. S. Depaetjient of Ageicultuee, 



WASHIIfGTON, D. C. 



TO THOSE INTEEESTED IN QUATEENIONS AND 

 ALLIED SYSTEMS OF MATHEMATICS. 



Deae Sies : The mathematical ideas asso- 

 ciated with the direct treatment of vectors and 

 vector functions are daily becoming more fa- 

 miliar to the scientific mind. Half a century 

 ago the broad principles of vector theory were 

 laid down in the Quaternions of H[amilton and 

 the Ausdehnungslehre of Grassmann. In his 

 second monumental work Hamilton developed 

 a vector calculus of great power and flexibility, 

 peculiarly appropriate to geometry and phjrsics ; 

 while both systems, in their richness of trans- 

 formations, generality of treatment, simplicity 

 of expression and interpretation, surpass any 

 other known forms of mathematics. Neverthe- 

 less, these systems have not received the atten- 

 tion that is surely their due, and remain still 

 in a comparatively undeveloped state. 



Meanwhile, in connection chiefly with the re- 

 markable advance in electrical theory, the 

 growing necessity for a vector calculus, or at 

 least for a compact vector notation, has induced 

 more recent investigators to invent new sj'S- 

 tems, which have very much in common with 

 those already established by Hamilton and 

 Grassmann. 



