seen that this cuts off each corner of the high column of any maximum year and contributes those corners to the adjacent lower column, so that the ordinary bent line of the rainfall record has thus been twice smoothed—once in the yearly sum and once in the method of plotting.
In speaking of the above records, I have in mind the smoothing in time intervals, but I would like to note also that whenever a district is averaged as a whole the average thereof is a smoothing in space. The temperature at any one time in a city station is a single definite record; but if the mean temperature in a valley or a State, for example, is tabulated, there is at once a spacial smoothing. In the minds of many students of solar variation and weather, the reason why a large group of meteorologists fail to get evidence of the relationship is because they take the average of the whole earth at once in their test of temperature changes or of rainfall. It is evident, therefore, that the reason they do not get results is because they do too much smoothing of the curves. Studies in connection with the present investigation have given some indication that small districts balance each other in their reaction to solar stimuli.
The fundamental data tabulated in the appendix are the means of the actual measures of the various groups. They, therefore, contain the effects of the two chief arboreal constants, which are (1) the nearly universal big growth at the center of the tree and (2) the increased size in some entire trees due to specially favorable environment. In producing a perfectly normal record of tree-growth over long periods, one desires to have it expressed throughout in terms of the normal adult growth of an average tree. This is the kind of record most suitable for analytical study. In the present study, in which so much time has been spent in finding how the work should be done, on account of the great labor involved no attempt has been made to apply these corrections to individual trees; but in comparing groups with one another it has seemed worth while to apply both corrections in a simple manner. Each group supplies an approximate curve of its decreasing growth with age. So, after plotting the means, a long average line as nearly straight as possible is drawn through them. This gives the factor by which individual rings may be reduced to the standard adult growth; at the same time this line enables us to reduce the different groups to a common standard of size. Both corrections are done at once by calculating for each year the percentage departure of the plotted mean from this line. In actual tabulation this works out very easily, for under each mean is placed the reading of this line, and below that the quotient obtained by dividing the former by the latter. The line of quotients then becomes the desired group curve corrected for age and for mixed sizes. This process is the standardizing process referred to in previous descriptions.