DETAILS OF CURVE PRODUCTION. 63 
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 tem- 
perature changes or of rainfall. It is evident, therefore, that the rea- 
son 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. 
STANDARDIZING: 
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 standard- 
izing process referred to in previous descriptions. 
