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. 



