Regarding your historical note, the reason why the formula in Bartlett's paper doesn't have -1 is due to the fact that (confusingly enough!) n is not the sample size in Bartlett's notation. As Bartlett writes in a previous paper: "Let the total number of degrees of freedom available from the original observations be n; we shall usually have n = r - 1, when deviations from the general mean are employed for each variable, where r is the total number of observations for each variable, i.e., in the present context r is the total number of persons tested." (Bartlett, 1950, p.77)

The 1951 paper is not as clear on what exactly n denotes, only stating "Thus in the canonical analysis the elimination of real canonical components tends to reduce automatically the dimensions
(degrees of freedom) of the observations (n-space), the dependent variables (p-space) and the independent variables (q-space)." (Bartlett, 1951, p. 337). But it seems reasonable to assume that Bartlett would use the same notation in the 1951 paper as in the 1950 paper as they both are about the same test and the formula looks the same in both cases.

Sources:
Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Psychology, 3(2):77–85.
Bartlett, M. S. (1951). The Effect of Standardization on a χ2 Approximation in Factor Analysis. Biometrika, 38(3/4), 337–344.