190 Messrs. E. Marsden and rt. Richardson on the 



the range. Starting from the end of the range, let x 1 be 

 the air-equivalent of a foil of mass per unit area m ; then the 

 incident range is x 1 cm. Let x 2 be the air-equivalent for 

 emergent range « 1? then the incident range is x 1 -\- x 2 cm., 

 and the air-equivalent of the combined foil of mass per unit 

 area 2m is also % 1 -\-x 2 . Thus the air-equivalents for masses 

 per unit area w, 2m, 3m, etc., are x v x x + x 2 , Xi + ^ + ^zi e ^c 

 respectively. In this way by taking the values of x from 

 the above data (fig. 2), a curve can be plotted connecting- 

 mass per unit area and air-equivalent, this being reckoned 

 in all cases from the end of the range. Such curves are 

 given for gold, silver, and aluminium in fig. 3. They were 



Fi$. 3. 



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Auy 





























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At. 

































/llR COU/VALCHT AT 76 CMS /9/VZJ /5°c. 



determined as the means of the observations for the various 

 foils of the same material given in Table II. The curves 

 obtained for the different foils of the same material agreed 

 closely, showing the approximate accuracy of the assump- 

 tions. From the mean curves given, the air-equivalents of 

 any foil at any part of the range can be obtained. For 

 instance, suppose it is required to find the air-equivalent of 

 a foil of mass per unit area m for a particles of incident 

 range R. Let M be the mass per unit area necessary to 

 completely absorb a particles of range R, and R' the range 

 for mass per unit area M-m; then R — R' is the air- 



