706 X. ON THE STRUCTURE OF 'MATTER' 

theory. The problem was not to discard the numerical data, which, whatever they mean structurally, represent quite solidly established data, but to find new equations which would be satisfied by these facts. Now 'new equations' really mean languages of new structure, and therefore new formulations had to be discovered.
Dealing with tables which give special theoretical data, it was natural to start with a calculus which deals with such numerical special tables. Such a calculus had been developed long ago, and was called the matrix calculus. Later on, when matrices themselves were treated as complex quantities, and still later, as operators, we were enabled to pass to the more developed calculi which use ordinary differential equations. The new quantum theories give us a unique case, in which several mathematical methods have been used at once and of which the results are fairly in accord. 







called determinants of the second order.
The numbers in the first, second . , horizontal lines are called the first, second . , rows, respectively; the vertical lines are called first, second . , columns.
The above definitions and method can be applied to any number of equations with an equal number of variables, and in each case our determinant would have «^{2} numbers, n rows and n columns.
We may use another notation which employs one letter for the coefficients of our variables, with indexes or suffixes to indicate that their values are 




