PROCEEDINGS: WASHINGTON ACADEMY 239 



The negative answer he offers to this question in the immediate con- 

 text is based in part on very indirect evidence drawn wholly from 

 Clayton's work itself. This is too much in the nature of reasoning in 

 a circle to carry conviction and can not outweigh the very direct adverse 

 evidence derived from a critical examination of the simultaneous data 

 showing atmospheric transmission and solar radiation intensities. A 

 study of this kind has been carried on at the Weather Bureau for the 

 past several months by Mr. Clough, whom I regard as a most con- 

 scientious and astute student of questions of this nature, and I am 

 unable to refute the results of the studies he has thus far shown me, 

 and these seem to me to indicate that in at least some of the observa- 

 tions employed by Mr. Clayton the value of the solar constant comes 

 out high for low atmospheric transmission, and the value is low for 

 high transmission. This question of the accuracy of the data must 

 be removed before Mr. Clayton's views can be established. 



(3) Finally, I must express skepticism as to the conclusiveness of a 

 demonstration resting mainly or alone on correlation coefficients and 

 the comparison of somewhat similar curves. Correlation coefficients 

 are quite meaningless without the probable error of the coefficient, and 

 I notice the probable errors of the correlation coefficients have been 

 completely omitted from Mr. Clayton's last account of his work. This 

 makes it impossible to properly weigh the evidence submitted. 



Every problem in the correlation of two variables can be graphically 

 represented by a so-called dot chart in which the position of each dot 

 with reference to the conventional coordinate axes represents the simul- 

 taneous values of the two variables. In nearly all problems of this 

 kind with which I have any acquaintance the dots fall in a widely 

 scattered "star cluster" sort of arrangement, signifying a large measure 

 of inconsistency. The correlation coefficient serves simply to define the 

 straight line of least-square best fit for the given cluster of dots. The prob- 

 able error of the correlation coefficient is an index of the amount of scatter 

 of the dots. In a great many cases the clusters of dots are nearly 

 as broad as they are long, and the direction of the straight line of 

 best fit in such cases is determined almost wholly by a small number 

 of pairs of the variables which have extreme high or low values. The 

 great bulk of the dots serve no other purpose than to fix the origin of 

 the coordinate axis at the center of gravity of the system. We may 

 use results of this sort with a high probable error as a basis for rough 

 estimations, approximations, or even forecasts. But I cannot feel 

 justified in accepting them as demonstrations of cause and effect re- 

 lations. 



Summarizing my views, I may say, first, I am not convinced of the 

 entire physical soundness of Mr. Clayton's first and second conclusions 

 stated. Second, I think it is still possible there may be some residual 

 error in measurements of solar radiation intensities by which a portion 

 of those values, sufficient to influence final conclusions, are system- 

 atically high with low atmospheric transmission and low with high 



