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BELL SYSTEM TECHNICAL JOURNAL 



the desired results are attained without forcing the speed to such 

 heights. 



Suppose now that while the ion is describing its consecutive circles 

 each in a time T, its speed is suddenly increased ; it continues to make 

 circles, of a larger radius but with the same duration. Suppose that 

 the increase occurs twice in each cycle, at intervals Tjl ; the path is a 

 succession of semicircles each broader than the one preceding but all 

 described in equal time. Now we arrive at Lawrence's device. The 

 ions circulate in a round flat metal box, sliced in two along one of its 

 diameters (Figs. 3, 4) ; and every time that one of them passes from 



Fig. 3 — Diagram of the Lawrence apparatus for cumulative accelerations of protons 

 and other ions with auxiliary magnetic field. (After Henderson) 



within half-box B to within half-box A it is accelerated by a voltage- 

 difference existing between B and A, and every time that it passes 

 from within A to within B it is again accelerated by a voltage-difference 

 between B and A. Of course if this voltage-difference remained the 

 same, the ion would lose at the latter passage just the energy which it 

 gained at the former; but here is precisely the distinctive feature of 

 the method : the potential-difference between the two half-boxes is reversed 

 in sign between each two consecutive passages. So rapidly do the 

 successive passages follow on one another, that if the intervals between 

 them were unequal it would probably be impossible to devise any 

 mechanism that would perform the potential-reversals at the proper 



