Sec. 9.6] MASS SPECTROGRAPHS 285 



1 + _ sin — -=. + j8 H cos — ^ J cm 



2 a/2 a V2/ 



The relation between the source distance / and the local plane distance L is 



IL - (I + L) JL C os * - £ = 



and the velocity dispersion in the focal plane in terms of linear units is 



d = {ia(l — cos — -p. -\ — \/~2 sin — ^= ] cm-volts 



To achieve complete velocity focusing, the velocity dispersion of the 

 magnetic field must compensate exactly for that produced by the electro- 

 static analyzer. Since the edge of the magnetic field coincides with the focal 

 plane of the analyzer and pi = mvi/eH, this condition is satisfied when 

 d = 2(3p . This condition is exactly met fpr only one radius of curvature 

 in the magnetic field, and all other radii focus imperfectly at the 180-deg 

 position and hence exhibit progressively wider images with greater distance 

 from the focused value of e/tn. The widths of these foci are given by the 

 expression 



d(po — pi) 



8 = 



Po 



It is apparent that when a limiting resolution is required the final focal 

 image width can be made smaller by reducing the dispersion d with a defining 

 vane placed behind the focal plane of the electrostater analyzer, i.e., in the 

 plane AB, Fig. 64. 



9.6. Bainbridge -Jordan Double -focusing Mass Spectrograph. Direc- 

 tional and velocity focusing is accomplished in a mass spectroscope developed 

 by Bainbridge and Jordan [7], first by deflection of ions in an electrostatic 

 analyzing field through an angle of ir/y/l, and then in a uniform magnetic 

 field through a mean angle of x/3 radians. With the geometrical arrange- 

 ment used (Fig. 65) the small dispersion in velocity accompanying directional 

 focusing for ions of a particular value of m/e is canceled by the velocity 

 focusing in the magnetic field. The focal plane over a large mass range is 

 not strictly flat, but over a considerable range about the exactly focused 

 value of m[e it is sufficiently flat to allow accurate comparison of both mass 

 and abundance. A considerable advantage inherent in this design of spec- 

 trograph is derived from the accurately linear mass scale for a broad range 

 about the exactly focused m/e. In some instances this is highly desirable 

 since it greatly facilitates accurate comparison of masses. 



The relation between the voltage applied across the condenser plates of 



