6 EFFECTS OF WINDS AND OF 



METHODS OF THIS INVESTIGATION. 



In general, both in this investigation of wind effects and barometric effects 

 and in the larger investigation of evaporation from the Great Lakes, of which 

 it is a part, the procedure has been as indicated in the following numbered 

 paragraphs : 



(1) The immediate problem to be attacked was studied in the light of all 

 available information. A theory was developed as to the relations of the 

 various quantities involved. The theory was expressed in the form of a 

 general equation. The equations were then set up for a least-square solu- 

 tion to test that theory. Each equation expressed an observed quantity, 

 a change in elevation of the water surface, in terms of other known or ob- 

 served quantities, in conformity with the theory which was on trial. The 

 solution was then made by the least-square method of computation. The 

 principal outcome was (a) a set of computed values of the unknowns, 

 assumed to be constants, which were supposed ' to express the relations 

 between the observed quantities, and (6) a set of residuals which are the 

 discrepancies between the tentative theory and the observed facts. 



(2) The outcome of the least-square solution was then studied in the light 

 of all available internal and external evidence. As the theory expressed in the 

 observation equations of such a solution approaches more closely to perfec- 

 tion and to completeness, the computed probable errors are smaller, the 

 residuals as a rule are smaller, and the distribution of the residuals as to sign 

 and magnitude follow the laws of accidental errors more closely. These 

 tests furnished the main portion of the internal evidence. The external 

 evidence was derived mainly (a) from comparisons of the outcome of the 

 solution with that from other solutions already made, (6) from a study of 

 apparently abnormal residuals, and (c) from general checks on the reliability 

 of the various items of outcome of the solution which were derived from 

 any available information which was independent of the least-square 

 solutions. 



(3) In some cases, especially in the later portions of the investigation, the 

 observed fluctuations in elevation of the water surface were plotted in graphs, 

 and the fluctuations as computed from the constants derived from the least- 

 square solutions were plotted, superposed, on the same scale. The graphs 

 were then studied to secure further checks, contradictions, or suggestions. 



(4) In the light of all evidence a new set of observation equations was then 

 set up and the whole process repeated of making a least-square solution and 

 then studying the outcome from it. In general, each new set of observation 

 equations involved one or more of the following: (a) a change in the tentative 

 theory, expressed as a change in the form of the observation equations; (6) 

 a change in the data used, brought about by rejecting certain observation 

 equations or by combining certain others (two or more in a group) to form 

 one; (c) the addition of a considerable amount of data, so as to increase the 

 number of observation equations to at least double what it had been, or (d) 



