and more compensate each other and thereby be swallowed up in the central value around which they occur. And the final result of combining the values will be approximately the same as if the actually changeable causes had remained the same not only conceptually but also numerically. Thus, the average value is in these cases the adequate numerical representative of a conceptually definite and well limited system of causal connections; if one part of the system is varied, the accompanying changes of the average value again give the correct measure for the effect of those deviations on the total complex.
On the other hand, no matter from what point of view statistical constants may be considered it cannot be said of them that each separate value has resulted from the combination of causes which by themselves had fluctuated within tolerably narrow limits and in symmetrical fashion. The separate effects arise, rather, from an oftimes inextricable multiplicity of causal combinations of very different sorts, which, to be sure, may share numerous factors with each other, but which, taken as a whole, have no conceivable community and actually correspond only in some one characteristic of the effects. That the value of the separate factors must be very different is, so to say, self evident. That, nevertheless, approximately constant values appear even here by the combining of large groups—this fact we may make intelligible by saying that in equal and tolerably large intervals of time or extents of space the separate causal combinations will be realised with approximately equal frequency; we do this without doing more than to acknowledge as extant a peculiar and marvellous arrangement of nature. Accordingly these constant mean values represent no definite and separate causal systems but combinations of such which are by no means of themselves transparent. Therefore their changes upon variation of conditions afford no genuine measure of the effects of these variations but only indications of them. They are of no direct value for the setting up of numerically exact relations of dependence but they are preparatory to this.
Let us now turn back to the question raised at the beginning of this section. When may we consider that this equality of conditions which we have striven to realise experimentally has been attained? The answer runs as follows: When the average values of several observations are approximately constant and
