Equations are obtained for the focusing by a system of two magnets with nonuniform fields such that n>0 in the first magnet and n<0 in the second. For each magnet a lens equation is set up, and then the system of the two magnets is itself treated as a thick lens. It is shown that for very large n, there is in general one object distance for which double focusing takes place. The theory is also applied to deflecting systems with moderate values of n, and it is shown that the entrance and exit angles can be reduced to values of the order of 20° even for small deflections (20°) of the charged particle.

1.
R. M.
Sternheimer
,
Rev. Sci. Instr.
23
,
629
(
1952
). This paper will be referred to as I.
2.
Courant
,
Livingston
, and
Snyder
,
Phys. Rev.
88
,
1190
(
1952
).
3.
M.
Camac
,
Rev. Sci. Instr.
22
,
197
(
1951
);
W. G.
Cross
,
Rev. Sci. Instr.
22
,
717
(
1951
).
4.
Shoemaker
,
Britten
and
Carlson
,
Phys. Rev.
86
,
582
(
1952
).
5.
See, for instance, G. S. Monk, Light, Principles and Experiments (McGraw‐Hill Book Company, Inc., New York, 1937), p. 21.
6.
Throughout this paper the subscript 1 refers to vertical focusing, the subscript 2 to horizontal focusing.
7.
At the end of reference 1, the values of D given for $n = ±0.4$ should have been calculated with the appropriate Eq. (93) instead of Camac’s equation for $n = 0.$ This gives $D = 3.19(R/p)$ (instead of $3.64(R/p)$) for the first example $(φ = 90°, S′ = 1, s = 0, n = −0.4)$ and $D = 1.24(R/p)$ for the second example $(φ = 40°, S′ = 3, s = 40°, n = 0.4).$
8.
This effect was pointed out by Dr. A. M. Shapiro.
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