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  1. Whose thickness is being neglected for the present.
  2. Of course, if a grain (plate) was initially rigorously perpendicular to the base (θ=π2) there would be no tendency to tilt it, thus leaving θ′ = 90°; but it is scarcely necessary to say that the probability of a grain having exactly θ = 90° is zero.

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Whose thickness is being neglected for the present.

Of course, if a grain (plate) was initially rigorously perpendicular to the base (θ=π2) there would be no tendency to tilt it, thus leaving θ′ = 90°; but it is scarcely necessary to say that the probability of a grain having exactly θ = 90° is zero.

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N d θ : π 2 = 2 π N d θ
sin θ = k sin θ ,
tan θ = k tan θ ,
sin θ ( x 2 x 1 ) : l , and sin θ = ( x 2 x 1 ) : l ,
x 1 = k x 1 , x 2 = k x 2 ,
sin θ = k sin θ .
cos θ = 1 k 2 sin 2 θ ,
κ = 2 π 0 π / 2 1 k 2 sin 2 θ d θ .
κ = 2 π E ( k ) .
κ = 1 ( 1 2 ) 2 k 2 1 ( 1.3 2.4 ) 2 k 4 3 ( 1.3.5 2.4.6 ) 2 k 6 5 · · ,
cos 2 θ = 1 : ( 1 + tan 2 θ ) = 1 : ( 1 + k 2 tan 2 θ ) ,
κ = 2 π 0 π / 2 d θ 1 + k 2 tan 2 θ = 2 π 0 π / 2 cos θ d θ 1 ( 1 k 2 ) sin 2 θ ,
κ = 2 π 0 1 d u 1 ( 1 k 2 ) u 2 .
arc sin 1 k 2 1 k 2 = arc cos k 1 k 2 .
κ = 2 arc cos k π 1 k 2 .
2 π = 0.6366
sin α = k ,
N d θ = 2 π N d θ .
N d θ = 2 π N cos θ d θ k 2 sin 2 θ , o θ arc sin k ,
N d θ = 2 π N k d θ k 2 cos 2 θ + sin 2 θ , o θ π 2
n ( θ ) = 0 θ N d θ = 2 π N d ( sin θ / k ) 1 ( sin θ k ) 2 ,
n ( θ ) = 2 π N arc sin ( sin θ k ) , o θ arc sin k ,
n ( θ ) = 0 θ N d θ = 2 π N arc tan ( tan θ k ) ,
θ = arc sin k = α , n ( α ) = 2 π N arc sin 1 = 2 π N π 2 = N ,
n = 2 π N arc sin 1 2 = 2 π N 1 3 π 2 = 1 3 N ,
n ( θ ) ˙ 2 π N arc sin ( θ k ) , α ˙ k .
θ = π 2 , n ( π 2 ) = 2 π N arc tan = N ,
n ( π 4 ) = 2 π N arc tan ( 1 k ) .
n ( 45 ° ) = N 84.3 90 ˙ 0.94 N ,