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James Van Allen journal, 1951?-December 1954

Page 20

Long array (P sub (ABC)) counterparts on plateau.

Short array (P sub (LMN))

Counter projected area A event [of? if?] density P  particles/(cm exponent 2).

Probability of no count   ([e?] exponent (-(p)(A)))

Probability of one or more   (1-([e?] exponent (1(p)(A))))

Therefore, ((P sub (ABC))/(P sub (LMN))) = ((1 - (e exponent (-p(A))))/(1 - (e exponent (-[q? g?](p)(A))))) exponent ([-x?]))

[cf?] = 0.8

x has been taken as 2.5 taken as compromise between 2.0 if only two particles involved, 

[sketch/picture]
drawing of 2 lines 3 circles

and 3.0 if three involved.

[sketch/picture]
drawing of 3 lines 3 circles

From curves of Ostrander ((P sub (ABC))/(P sub (LMN)))       versus (e exponent (-P(A)))

For various values of x :

(e exponent (-P(A))) table

{ ((P sub (ABC))/(P sub (LMN))) \ x } {2.0} {2.5} {3.0}
---------------------------------------------------------------------
{ 1.15 } { 0.105 } { 0.075 } { 0.055 }

{ 1.18 } { 0.14 } { 0.10 } { 0.070 }

{ 1.21 } { 0.18 } { 0.12 } { 0.090 }



((1 - (e exponent (-P(A)))) exponent x) table

{ ((P sub (ABC))/(P sub (LMN))) \ x } {2.0} {2.5} {3.0}
---------------------------------------------------------------------
{ 1.15 } { 0.81 } { 0.82 } { 0.84 }

{ 1.18 } { 0.74 } { 0.77 } { 0.80 }

{ 1.21 } { 0.67 } { 0.72 } { 0.75 }

Saving...

Long array (P sub (ABC)) counterparts on plateau. Short array (P sub (LMN)) Counter projected area A event [of? if?] density P particles/(cm exponent 2). Probability of no count ([e?] exponent (-(p)(A))) Probability of one or more (1-([e?] exponent (1(p)(A)))) Therefore, ((P sub (ABC))/(P sub (LMN))) = ((1 - (e exponent (-p(A))))/(1 - (e exponent (-[q? g?](p)(A))))) exponent ([-x?])) [cf?] = 0.8 x has been taken as 2.5 taken as compromise between 2.0 if only two particles involved, [sketch/picture] drawing of 2 lines 3 circles and 3.0 if three involved. [sketch/picture] drawing of 3 lines 3 circles From curves of Ostrander ((P sub (ABC))/(P sub (LMN))) versus (e exponent (-P(A))) For various values of x : (e exponent (-P(A))) table { ((P sub (ABC))/(P sub (LMN))) \ x } {2.0} {2.5} {3.0} --------------------------------------------------------------------- { 1.15 } { 0.105 } { 0.075 } { 0.055 } { 1.18 } { 0.14 } { 0.10 } { 0.070 } { 1.21 } { 0.18 } { 0.12 } { 0.090 } ((1 - (e exponent (-P(A)))) exponent x) table { ((P sub (ABC))/(P sub (LMN))) \ x } {2.0} {2.5} {3.0} --------------------------------------------------------------------- { 1.15 } { 0.81 } { 0.82 } { 0.84 } { 1.18 } { 0.74 } { 0.77 } { 0.80 } { 1.21 } { 0.67 } { 0.72 } { 0.75 }