66 BELL SYSTEM TECHNICAL JOURNAL 



and the publication of the necessary tables by Fisher -" and Glover " 

 makes the study of such a curve more feasible. The author finds, for 

 example, that this series furnishes a much closer fit to the distribu- 

 tion of shots, Fig. 5, referred to abo\e than any other that he has 

 tried. 



riu'iiri-ticalh' wc should be able to inijiniM' the approximation by 

 taking a large number of terms of the scries. Such a procedure, 

 however, involves the use of moments higher than the first four, 

 and the errors in these moments are so large as to make their use 

 impractical. 



In spite of the uncertainty attached to the interpretation of the 

 physical significance of fitting any of these curx-es to data, one very 

 practical observation has been made : that is, if an observed series of 

 frequencies could not be fitted by a theoretical curve in any of the 

 ways already mentioned, careful consideration of the possible reasons 

 for the obser\-ed poor fit have in practically cver\- instance suggested 

 the cause or causes thereof. We shall relcr to onl\- one j)ractical 

 example. 



The data have already been given abo\e in Table II. It has been 

 noted that in this instance the variations in the averages of groups 

 of several thousand observations showed that the difTerences were 

 significant. If the observed distributions had been normal, it would 

 have been necessary to assume either that the nu'thods of making 

 the measurements were different for the differtiu i;rou|)s of observers, 

 and for the different machines, or tluii the manufacturing methods 

 were experiencing a trend. Altlimiiih the ()bser\ed frecjuency curves 

 for the different groups were found to be sniooih, the observed fre- 

 quencies could not be readih' lilted 1)\- an\ curve previously de- 

 scribed. This naturally led to a search for the existence of any one 

 of a number of causes affecting the ob.scrvations which might produce 

 such a divergence between theory and practice. One !>>■ one these 

 causes were found and eliminated and as they were the degree of fit 

 between the results of theory and practice increased. For example, 

 it was found that some of the groups of observations were for trans- 

 mitters assembled from onK iwo or three lots of carbon. Trans- 

 mitters assembled from one loi ol carbon had a different average 

 efficiency from those assembled from another lot. jNaturally the 



'•• Fisher, Anic — Loc. cit. As imtcil liy Mr. Fislicr, page 214, the values of 

 <ji (x) ami its first 6 derivatives to 7 decimal places for values of .v up to 4 

 and i)rogressing by intervals of 0.01 were given by Jorgcnsen in his "Krekvens- 

 flader og Korrelation." 



^{"ilover, J. W. — Tables of Compound Interest, I'nnclions, etc. -1923 Editimi 

 published by George Wahr, Ann Arbor, Michigan. 



