BAROMETRIC PRESSURES ON THE GREAT LAKES 73 



shown, computed rigorously from the normal equations and the residuals of 

 the four solutions. If all errors affecting the value +0.088 were of the ac- 

 cidental class, the chances would therefore be even that said value is correct 



.... 1 /0.006 1\ 

 within part = . 



15 V0.088 157 



The four separate least-square solutions are, as indicated in table No. 12, 

 page 62, based on four separate and independent sets of observed data, 

 elevations of the water surface at two different gages Buffalo and Cleveland 

 and including 2,291 hours of observation scattered over 100 days. If 

 any systematic or constant errors affected the computed values of C x from 

 the separate solutions, they would be apt to appear in the comparison of 

 those four values which is shown in table No. 13. If the errors are all of the 

 accidental class, each of such residuals as are shown in the last column of 

 that table should have an even chance of being less than the probable error 

 written in the same line in that table. Note that the residual for solution 

 W29, +0.009, is much less than the corresponding probable error, 0.0175; 

 that the residual for solution W26, +0.016, is very slightly greater than the 

 corresponding probable error, 0.0142; and that the residual which is largest 

 in proportion to its corresponding error is that for solution W25, 0.017, 

 which is 1.9 times the corresponding probable error, 0.0087. According 

 to the laws of probability, such a residual, 1.9 times the probable error, 

 should occur on an average once in five times. It appears, then, that the 

 agreement of the four values of C x from the four solutions is so close as to 

 furnish no indication of systematic or constant errors. The degree of 

 agreement indicates that all errors are of the accidental class, and therefore 

 that the degree of accuracy of the value +0.088 is that indicated by its 

 computed probable error, 0.006. 



The same rules as to rejections and combinations were used in the com- 

 putation of wind effects as have already been stated in connection with 

 the computation of barometric effects (see pages 65-66). 



The same considerations which led there to the conclusion that there was 

 no danger that a fictitious accuracy had been imparted to the computed 

 barometric effects as a result of the rejections and combinations also led to 

 the same conclusion with respect to the computed wind effects. 



As shown in table No. 12, of the total of 2,377 hours of observation avail- 

 able, 2,291 hours were used. That is, only 86 hours, or less than 4 per cent, 

 were rejected. 



The total number of separate observation equations was 2,173 118 less, 

 or 5 per cent less, than the total number of hours used. That is, the combi- 

 nations of equations which were made were such as to combine 5 per cent 

 of the hours with adjacent hours instead of using them in separate inde- 

 pendent equations. 



In addition to the rejections and combinations made under the regular 

 rules, referred to above, in solution W29 at Cleveland, a few other combi- 

 nations and rejections were made on the basis of evidence external to the 



