1916-17.] The Square Roots of a Linear Vector Function. 355 
linear vector functions, arises in the solution of linear differential equations 
of the second order. If p and < p are commutative the equation depends 
for its solution on the extraction of the square root of a linear vector 
function.* The non-commutative case must be reserved for treatment 
in a separate paper. 
* See Tait’s fascinatingly suggestive paper, Proc. Roy. Soc. Edin., vii, p. 311. 
(. Issued separately December 10, 1917.) 
