272 Proceedings of the Royal Society of Edinburgh. [Sess. 
Jacobi, C. G. J. (1845, August). 
[Ueber ein leichtes Verfahren die in der Theorie der Sacular-storungen 
vorkommenden Gleichungen numerisch aufzulosen. Crelle’s 
Journ., xxx. pp. 51-94: or Gesammelte Werke, i. pp. 227-270: or 
Nouv. Annates de Math., x. pp. 258-265.] 
This long memoir being intended for astronomical mathematicians and 
computers, there is little of it that concerns us except two of the intro- 
ductory sections (§§ 2, 3, pp. 52-56); and even these need not detain us, as 
they are in effect but a well-constructed abstract of Cauchy’s paper of 1829, 
the starting-point being the set of n + 1 equations 
(«n - 0)x i + 
a n x 2 + . 
. . + a ln x n = cr 
a^x x + (« 22 
- 6)x 2 + . 
• • 4" Ct>2 n,Xn = 9 
> 
a nl x x + 
CK rt 2^2 "h . . 
• +(a n n-0)x n = 0 
x\ + 
x\+ . . 
+ 
si 
II 
i— ‘ 
considered without any regard to the mode in which they may have 
originated. 
Cayley, A. (1846). 
[Sur quelques proprietes des determinants gauches. Crelle’s Journ., 
xxxii. pp. 119-123: or Collected Math. Papers, i. pp. 332-336.] 
There is clear evidence that Rodrigues’ paper of 1840 made a strong 
impression upon Cayley. In a paper published in 1843 * he introduces his 
subject by speaking of Rodrigues as having “given some very elegant 
formulse for determining the position of two sets of rectangular axes with 
respect to each other, employing rational functions of three quantities only”; 
and he proceeds at once to demonstrate these formulae as a necessary 
preliminary to the essential part of his paper. In another paper published 
in 1845,f the first part of which deals with a quaternion identity, he makes 
the important observation that a set of nine coefficients which occur in the 
identity is precisely the same as the set of nine given in Rodrigues’ trans- 
formation ; and he adds, “ It would be an interesting question to account a 
* Cayley, A., “ On the motion of rotation of a solid body.” Cambridge Math. Journ., iii. 
pp. 224-232 : or Collected Math. Papers, i. pp. 28-35. 
t Cayley, A., “On certain results relating to quaternions.” Philos. Magazine, xxvi. 
pp. 141-145 : or Collected Math. Papers, i. pp. 123-126. 
