Professor Tait has considered the question of finding the square root of a strain, or what is the same thing, that of a matrix of the third order— A mode of doing this is indicated in my “Memoir on the Theory of Matrices” (Phil. Trans., 1858, pp. 17–37), and it is interesting to work out the solution.

The notation and method will be understood from the simple case of a matrix of the second order. I write to denote the two equations, x 1 = ax + by, y 1 = cx + dy.