## A Contribution to The Aetiology of Manic-Depressive Insanity (1940)

*Natural Rhythm of Mood Variations*

The more one inclines to the view that manic‑depressive illnesses correspond to phasic biological variations, the more one is tempted to look for a biological rhythm in the spontaneously recurring attacks of illness. As far as I know, this problem has not till now been attacked statistically. I have calculated. the difference in time between the dates of admission to clinic or hospital for every patient at every successive attack. For instance, Case 173 had intervals of 35, 46, 33, 11, and 40 months between his various illnesses. It is necessary to consider such figures for every patient singly and for the group of patients as a whole. The procedure is as follows: the sum of the intervals, S(x), is calculated for each patient (e.g. in the above case it equals 165). Similarly, the number of illnesses, n, (in the above case = 5); the mean value of the intervals, (= 33); the sum of the squares of the intervals, S(x^{2}), (=6151); the product of ** ^{.}**S(x), (= 5445); from these figures in each case is calculated the sum of the squared deviations from the mean, S(x‑)

^{2}= S(x)

^{2}‑ S(x), (= 706). This was done for all the patients for whom sufficient data were available, of whom there were 105. Then were summed all values all values of of S(x) = T; all values of n = N; all values of S(x

^{2}) =∑S(x)

^{2}; all values of S(x) = ∑xS(x); alla values of S(x-x)

^{2}= ∑S(x-x)

^{2}. The mean value of all intervals taken together is = T/N = . The sum of the squared deviations of the individual means, , of each individual patient from the general mean, , is S(-)

^{2}= ∑S(x)-T. In this way we obtain the following scheme:

That is to say, the variability in respect of length of interval between attacks for different patients is more than double _{} as great as the variability in length of interval between attacks for individual patients. The statistical reliability of this result can be tested by calculation of the function z.^{1}

The standard error of z can be calculated, when the number of degrees of freedom n2 and. i are large, according to the formula:

It follows that in this calculation z is more than ten times as great as its standard error. This may be taken as a proof that the comparatively small variability in length of interval between attacks for the single patient is not accidentally determined but is a quality of the psychosis. It may be said that every patient has his own mean length of interval between attacks. He has his own rhythm. He has the tendency to fall ill a second time at a definite period after his last illness. It need hardly be said that this tendency is by no means clearly demonstrated by every single patient. The actual variability shown by different patients can be very great. The mean value of this variability in this material reaches the high figure of 44** ^{.}**6 months, and may be exampled by Patient 8: intervals 144, 26, and 193 months; Patient 15: 79, 51, 36, 165, and 15 months; Patient 16: 312, 52, 40, and 34 months, etc. But in general it would appear that the recurrence of the illness is determined among other causes by a biological rhythm. It is to be regretted that I was unable totest the material as to the way in which the intervals between onset were divided between illness and health. Unfortunately, sufficiently accurate data on the duration of illness were not available for the examination of this interesting point.

(1) This statistical method is discussed by R.A. Fisher in "Statistical Methods for Research Workers", Edinburgh and London, 1930.