of u-P articles per Second emitted by Thorium C. 1043 



The final ratio of. p jz for equal 7-activities w s 



<x radium O x 



computed as the mean of the group ratios, each weighted by 

 the root of the number of a-particles included in the group. 



Probable Error in Mean Patio. 



The probable error in the ratio '75 arises from two factors. 

 First, the error due to the finite number of particles counted. 



This is 100 (,.,]-.-. + tt7^kV = 1-22 per cent. The other 

 \132bo looOO/ x 



source of error is the electroscope and the plotting of 

 the curves from the electroscope readings. The number 

 of readings taken during a count was, on the average, 12. 

 The probable error from a combination of 12 readings was 



/ 2d 2 . 

 computed by the formula 2/3 \/ sff^ — 7y from a large 



number of 7-ray measurements made on a radium standard. 

 The highest value of the probable error obtained in this way 

 was *G percent. The error in drawing the logarithmic decay 

 line through the plotted points is unfortunately impossible to 

 calculate. It was certainly not greater than 0*5 per cent. 

 Both these last errors enter twice, so that the probable error 

 is given by { (l'22) 2 -f 2 x '6 2 + 2 x -5 2 p= 1*65 percent. The 



probable error calculated by the formula 2/3 \/ vr/ix ■. \* 



using the group values, is *9 per cent., which is well within 

 the error calculated above from the various factors separately. 

 It is of interest to note in this connexion the agreement 

 between counts by the two observers. We differed by as 

 much as 9 per cent, within groups, but our final ratios are 

 only '3 per cent, apart. The agreement is excellent evidence 

 of the accuracy of the counting of both observers. 



y-Ray Absorption Measurements. 



The 7-rays, in order to reach the interior of the electro- 

 scope used in this experiment, had to pass through a thick- 

 ness of glass, lead, and aluminium having an absorbing 

 power for the rays equivalent to 3'3 mm. of lead. In order 

 to extend the application of the ratio of a emissions to com- 

 parisons through different thicknesses of lead, it was 

 necessary to compare the absorptions in lead of the 7 rays 

 from thorium C and radium C. This was necessarv because 



3X2 



