1888 — 89 .] Dr A. James on Muscle Contraction. 
389 
rapidity of clonus in a given muscle varies inversely with its distance 
from its centre in the cord, the ankle being slower than the knee, 
the knee than the elbow, &c., indicates that in the production of 
each jerk, nerve cell and nerve fibres are concerned equally with the 
muscle, and that the length of the motor nerve fibres seems to be 
the element of most importance in conditioning the rapidity of the 
clonus. 
The Theory of Determinants in the Historical Order 
of its Development. By Thomas Muir, M.A., LL.D. 
Part I. Determinants in General (1836-41). 
(Continued from p. 234 of Yol. XVI.) 
GRUNERT (1836). 
[Supplemente zu Georg Simon Klugel’s Worterbuch der reinen 
Mathematik. Art. Elimination (I. Gleichungen des ersten 
Grades), ii. pp. 52-60.] 
With Grunert it is necessary to take a long step backward. 
Although the memoirs of Bezout, Vandermonde, and Laplace were 
known to him, in addition to those of Hindenburg, Rothe, and 
Scherk, he advances only a short distance into the subject; his' 
aim, indeed, is little more than the establishment of Cramer’s rule 
for the solution of a set of simultaneous linear equations. His 
mode of presenting the subject, however, is fresh and interesting, 
the method of “undetermined multipliers” being taken to start 
with. 
Writing his equations in the form 
(l)i^i + (2)pr 2 + (3)^ + •••• + (n\x n = [1] 1 
(l) 2 aq + (2) 2 x 2 + (3) 2 x 3 + .... + (n) 2 x n = [1] 2 
(l) 3 aq + (2) 3 x 2 + (3) 3 x 3 + ....+ ( n\x n = [1] 3 [ 
(1)^1 + (2)n^2 + ( 3 )«^3 +>•••+ (»>A = [1], 
