BAROMETRIC PRESSURES ON THE GREAT LAKES 61 



The observation equations were arranged in groups, one group for each 

 day. The groups were studied separately as well as in combination with 

 each other as a single set of equations for one whole solution. 



EXAMPLES OF NORMAL EQUATIONS FOR WIND EFFECTS. 



In each least-square solution for wind effects a set of normal equations 

 was first formed in the usual way from the observation equations for each 

 day. Then these sets of normal equations, one set for each day, were com- 

 bined by addition to form the final set of normal equations for the whole 

 solution. 



The normal equations for August 5, 1910, in solution W25, formed from 

 the observation equations for that date, as shown on page 58, are as follows : 



+252168C p +134728C a -21619 = 0\ . 



+ 134728Cp+260143C a - 12627 = J 



The final normal equations for solution W25 for 22 days, formed by 

 combining 22 such sets of normal equations as are shown in (67), are as 

 follows : 



+2914495C P + 5881 19C a -205977 = 01 ( 



+ 588119Cp+3343518C'a- 178350 = / 



This final set of normal equations for solution W25, (68), depends upon 

 470 observation equations, covering 500 hours, which formed parts of 22 

 days. 



The solution of the final normal equations for solution W25, (68), gave 

 the following values for the unknowns : 



Cp=+0.0622.0064 C a = +0.0425.0060 



The probable errors shown were computed rigorously from these normal 

 equations and from the residuals, v, of the 470 observation equations of 

 solution W25. 



THE FOUR FINAL WIND SOLUTIONS. 



In this investigation, made by methods outlined on pages 6-8, several 

 separate least-square solutions were usually made on the basis of each 

 group of observational data. The form of each successive solution from 

 one group of data was based upon all the information available up to the 

 time that said form was adopted, including the information from earlier 

 solutions based upon the same data. 



The four final solutions for wind effects were those designated as solutions 

 W25, W26, W20, and W29. Each of these solutions was the culminating 

 one of a series of solutions based on the same group of observational data. 

 The principal facts for these four solutions are shown in tabular form 

 following : 



