396 



Mr. E. J. Nanson on 



but agrees very well with the results obtained by Volkmann, 

 Hall, Sentis, Rayleigh, and others. 



In conclusion I wish to thank Professor Rowland and 

 Dr. Ames for their suggestions and encouragement through- 

 out the entire course of this work. 



Johns Hopkins University, 

 June 1897. 



L. On Determinant Notation. By E. J. Nanson, M.A* 



^HE notation for a determinant introduced in 1861 by 

 H. J. S. Smith has baen almost universally adopted on 

 account of its extreme simplicity and clearness. That nota- 

 tion is that the determinant 



«11 



«2 1 



a 12 

 «2 2 



an\ a 



n'2 



a nn 



n). 



is denoted by 



I a Pi I (P,9 = h- 



Now just as it is convenient to have this simple notation for 

 the determinant, so also is it convenient to have a simple 

 notation for the array of symbols used to form the deter- 

 minant, or, more generally, for an array in which the number 

 of rows is not necessarily the same as the number of columns. 

 It is therefore proposed to use the notation 



( a pq) (p=l,...m; j=l, ...n); 



for the array 



'12 



This notation is particularly convenient in dealing with 

 determinants which can be divided by horizontal and vertical 

 lines into blocks, such that all elements in the same block 

 follow the same law. For instance, the bordered deter- 

 minant 



«n 



Cll 



»i 



. a x 



. a„ 

 • c h 



b lt . . . b ln 



Kx 



7.ni n 



* Communicated bv the Author. 



