[bowman] fundamental PROCESSES IN HISTORICAL SCIENCE 503 



umn, he could obtain the correct total, 1,628 only if, in adding the 

 next column, he made a further mistake which would counterbalance 

 exactly his previous omission, e.g., if he called the sum of 3 and 4, 

 erroneously, 8 instead of 7. The occurrence of such an exactly counter- 

 balancing error could be only accidental; therefore, if the student 

 made the first omission and still obtained a correct result, such result, 

 though correct, would not be properly ascertained and for that reason 

 it would be unscientific. 



iii. If a correct and an incorrect process coincide in part, 



CORRECT RESULTS OBTAINED BY THE APPLICATION OF THE IN- 

 CORRECT PROCESS WITHIN THE COINCIDENT PART ARE ONLY 

 ACCIDENTAL AND AFFORD NO GROUND FOR ACCEPTING AS CORRECT 

 THOSE RESULTS WHICH ARE OBTAINED BY THE APPLICATION 

 OF THE INCORRECT PROCESS WITHIN THE NON-COINCIDENT PART. 



Illustration: — If a student in taking the sum of a series of numbers 

 omits habitually to carry the numbers from one column to their 

 proper denomination in the next column but observes in all other 

 respects the requirements of the correct process of addition, he will, 

 notwithstanding his incorrect process, add correctly such a series of 

 numbers as the following: 



111 

 354 

 413 



878 



His success in obtaining this correct result is due to the circum- 

 stance that in adding these numbers, there happens to be nothing to 

 carry from one column to another. Aside from this point his method 

 coincides with the correct process; therefore, in this particular prob- 

 lem in addition, he happens to use only that part of his incorrect pro- 

 cess which coincides with the correct. His success in obtaining 

 accidentally a correct result under these circumstances affords no 

 ground for accepting as correct the results which he will obtain where 

 he must apply that part of his incorrect process which does not coin- 

 cide with the correct. 



