Sec. 10.18] GEIGER-MULLER COUNTERS 325 



With data thus obtained the coefficients are calculated which make the 

 quantity 



(TV! + N 2 - N 12 - ntf 



a minimum. This is simply an expression of the principle of least squares 

 stating that the curve which best fits the data is that for which the sum 

 of the squares of the differences between the observed points and the curve 

 is a minimum. 



When only two terms of the series are used, the single coefficient is cal- 

 culated [33] by the formula 



5 



(tii + n 2 — n\i — n b )(n\ + n\ — n? 2 ) 

 t = — min 



I 



— (n\ + n\- n? 2 Y 



«12 



in which the sum is taken over the 5 sets of measurements of tii, n 2 , and n\ 2 

 When three terms of the series are desired, the two coefficients r and v are 

 calculated from the 5 sets of data [33] by the formulas 



mm 



min 2 



where 



H = / — =■ (»i + n 2 — »i2 - n b )(n\ + n\ - n? 2 ) 

 L-l >i{ 2 

 s 



J = / -o («i + th - »i2 - n b )(n\ + n\ - n&) 

 K = y A (»? + < - »A)(*5 + n l - n ® 



s 



L = y 4 (n\ + nl - n? 2 y 



S 



m = y a (»f + »5 - ^i 3 2 ) 2 



Z_Y ^12 



10.18. Coincidence Counting Corrections. As is done for single counters, 

 coincidence counting measurements must be corrected for background, in 



