024 A D O L F F. V O I G T 



law is frequently assumed to appl}^ If the number of counts is 

 more than a very few, the two give essentially the same results. 



The reliability of a measurement of the strength of a radioactive 

 source depends on the number of counts observed. The function 

 involved is the square root of the number of counts, which is mul- 

 tiplied by a factor that depends upon the accuracy limits one wishes 

 to set up. According to the distribution laws, a definite probability, 

 P, exists that the true value of a measured quantity, such as the num- 

 ber of counts recorded by a counter, is within the limits stated as 

 the limits of error of the quantity. The probability that the true 

 value is outside these limits is obviously 1— P. In order that the 

 limits express a particular probability a factor, K, is chosen by which 

 the square root of the number of counts is multiplied, the result being 

 expressed as C ± A' -\/C, where C is the number of counts recorded in 

 time t. For the standard deviation, K = I and P == 0.683, that is, 

 there is a probability of 0.683 that the true value will be within the re- 

 gion C ± \/C and of 1-0.683 (= 0.317) that it will be outside this re- 

 gion. For the "probable error" P is chosen as 0.5 and A' is 0.6745. If 

 90% certainty is desired (P = 0.90) A is equal to 1.64 and for 99% 

 certainty (P = 0.99) A = 2.58. In the following discussion the 

 standard deviation will be used but any other degree of certainty 

 could be substituted, by inserting the factor A' l)efore the square root 

 sign. 



Since the standard deviation in the niunber of counts, C, is -s/C, 

 that of the counting rate, C/t, will be -s/C/t and the fractional stand- 

 ard deviation in either will be y/C/C or \/\/C- Table II shows the 

 per cent standard deviation for various total counts observed. 



TABLE II 

 ytandard Deviation 



If murt; than one measurement involving some uncertainty is 

 involved, the statistics rules for determining the uncertainty in the 

 tinal answer should be applied. For example, each counter has a 

 background in the absence of a source which must be subtracted 

 from the measured counting rate to obtain the true counting rate 

 due to the source. If the number of counts recorded in taking the 



