326 Prof. Brao-o- and Mr. Kleeman 



&» 



on 



consider the figure bounded by the vertical line through de 

 and by the curved line dabc to represent the ionization by 

 the Ra C particles over the whole of their course except the 

 first two centimetres. 



This curve is now added to itself, being first lowered 

 through 2*23 cm., and the points represented by dots in 

 circles represent some of the results of the addition. It will 

 be seen how nearly these points lie on the actual ionization 

 curve, on which the experimental readings are marked by 

 crosses. Again the curve dabc is lowered, by 6*0 mm. this 

 time, and added on to the sum already obtained, and the new 

 points which show tbe result of the addition are also marked 

 as dots in circles. These also lie very nearly on the ionization 

 curve. For the last time the curve is added on, being this 

 time lowered 7*3 mm. ; and again the calculated points lie on 

 the experimental carve except just at the peak. Thus the 

 full curve is formed by the superposition of four simple 

 curves, each alike in all respects but that of height ; and the 

 inference is that the four groups of a particles are alike in 

 every respect but that of initial velocity. The differences of 

 the ranges are in this way given with more accuracy than 

 that with which the actual ranges can be found, for it is hard 

 to avoid all uncertainty about the latter because the gauze of 

 the ionization-chamber is not easily made quite flat. If the 

 curve fg is produced to meet the curve Jig also produced, then 

 the meeting-point is at a height 3 '4 cm. This point should 

 represent the arrival of the Ra rays at the middle of the 

 ionization-chamber, which is 1 mm. higher than the gauze. 

 Hence the range of the particles from Ra is 8*50 cm.; and the 

 ranges of the other three groups are 4*23, 4*83, and 7"06. 

 These must be correct to 0*5 mm. 



Since the ionization curve can now be drawn with some 

 accuracy, it becomes reasonable to make an attempt to dis- 

 cover the relation between the velocity of the a particle and 

 the rate at which it spends its energy. 



Let v be the velocity of the particle, and s the distance it 



has yet to run. Suppose that the energy spent per 



cm. = k.v~ n j where k and n are constants. We seek a value 



for n. 



Then , dv* . n 



hm—r = kv~ n . 

 as 



mv n+l dv = kds 



mv n + 2 



n~\-2 



