BAROMETRIC PRESSURES ON THE GREAT LAKES 65 



computed probable error as shown. For example, B n z for Buffalo = 11.69, 

 and its probable error is only 0. 43. This means that the chances are even 

 for and against the proposition that the true value of B nZ for Buffalo lies 

 within . 43 of 11 . 69. In other words, there is one chance in two that the 



value 11 . 69 is correct within one twenty-seventh of itself ( - - = 27 ). 



If for each of the five stations this comparison be made between the 

 largest constant for the station and its probable error, it will be found that 

 in each case the probable error is as small as one-twentieth part, or 5 per cent 

 of the value. The largest constant is selected because it is the one which 

 tends to have most influence upon the computed barometric effect at the 

 station. 



On this basis the conclusion is that the computed barometric constants 

 are subject to errors which stand one chance in two of being less than 5 

 per cent as large as the largest one of said constants at each station. 



Note that the computed probable errors at each station are of approxi- 

 mately the same size for all constants, regardless of the size of the constant 

 itself. The extreme uncertainty, judged by the probable errors, occurs 

 in the constant B n3 for Harbor Beach, of which the value is +0. 47, only 1 . 8 

 times its own probable error, . 26. On the supposition that all the errors 

 are accidental in character, there is less than one chance in four that this 

 derived value, +0.47, for B n3 at Harbor Beach is entirely fictitious. For 

 the few cases in table No. 6 like this one, in which there is a small chance 

 that the constant is entirely fictitious, the main reliance must be placed 

 on other tests than that furnished by the probable error when one is at- 

 tempting to determine the accuracy and reliability. 



If in making any least-square solution a large number of rejections is 

 made of observations which show large residuals, a fictitious appearance of a 

 high degree of accuracy may thereby be given to the remaining observations, 

 which necessarily agree more closely with each other than did the original 

 observations before any rejections were made. That danger has been 

 guarded against in this investigation by the adoption of a cautious rejection 

 limit and by a careful study of each rejected value to determine from ex- 

 ternal evidence if possible whether the value may properly be rejected. The 

 external evidence has in a large percentage of cases been clearly in favor of 

 the rejection. It is believed, therefore, that there is no danger that any 

 fictitious accuracy has been introduced by the rejections. 



THE REJECTION RULE. 



The rejection rule has been that an observation shall be rejected if its 

 residual is larger than five times the probable error of the observation, and 

 that no other observations shall be rejected. 



If all the errors were strictly accidental in character, this rule would 

 reject less than one observation per thousand observations. 



