## Abstract

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F. 1

### Tables (1)

Table 1 Cosines in Terms of Sines(Copied from Proc. Phys. Soc, xxxii, opposite p. 258)

### Equations (21)

$sin α = sin θ + g ⋅ R , sin α ′ = n n ′ sin α , θ ′ = θ + α ′ − α , g ′ = cos α ′ + cos θ ′ cos α + cos θ g .$
$g ′ g = sin α ′ − sin θ ′ sin α − sin θ = sin α ′ − θ ′ 2 ⋅ cos α ′ + θ ′ 2 sin α − θ 2 ⋅ cos α + θ 2 = cos 2 α ′ + θ ′ − α 2 cos α + θ 2 ,$
$g ′ g = cos 2 α ′ + cos ( θ − α ) cos ( α + α ′ ) + cos ( θ − α ′ ) = cos ( α − α ′ ) + cos ( α ′ + θ ) 1 + cos ( α + θ ) ;$
$g ′ g = cos 2 α ′ + cos ( θ − α ) + cos ( α − α ′ ) + cos ( α ′ + θ ) 1 + cos ( α + θ ) + cos ( α + α ′ ) + cos ( θ − α ′ ) = 1 + cos ( α + α ′ ) + cos ( θ − α ′ ) + cos ( θ + α ) + 2 ( sin α − sin α ′ ) ( sin α ′ + sin θ ) 1 + cos ( α + α ′ ) + cos ( θ − α ′ ) + cos ( α + θ ) = 1 + 2 ( sin α − sin α ′ ) ( sin α ′ + sin θ ) 1 + cos ( α + α ′ ) + cos ( θ − α ′ ) + cos ( α + θ ) .$
$g ′ = g + 4 g ( sin α − sin α ′ ) ( sin α ′ + sin θ ) ( sin θ − sin α + sin α ′ ) 2 ( cos θ + cos α + sin α ′ ) 2 − 1$
$sin α k = sin θ k + g k ⋅ R k , n k + 1 ⋅ sin α ′ k = n k ⋅ sin α k , g ′ k = g k + 4 g k ( sin α k − sin α ′ k ) ( sin α ′ k + sin θ k ) ( sin θ k − sin α k + sin α ′ k ) 2 + ( cos θ k + cos α k + cos α ′ k ) 2 − 1 sin θ k + 1 = sin α ′ k − g ′ k ⋅ R k , g k + 1 ⋅ g ′ k + d k ⋅ sin θ k + 1 ( where d k = A k A k + 1 )$
$tan θ 1 = − h 1 υ 1 − r 1 + r 1 2 − h 1 2 , g 1 = − υ 1 ⋅ sin θ 1 .$
$υ ′ 3 = + 092636 inch .$
$p ′ = n n ′ p , sin α = p R , sin α ′ = p ′ R ′ , θ ′ = θ + α ′ − α ;$
$p k + 1 = p ′ k + a k ⋅ sin k + 1 ,$
$a k = d k + r k + 1 − r k .$
$υ 3 = υ ′ 2 − d 2 , sin θ 4 = n 3 sin θ 3 / n 4 , υ ′ 3 = υ 3 ⋅ tan θ 3 / tan θ 4 .$
$n ′ c ′ l ′ = n c l .$
$x ′ : x = l ′ : l ,$
$n ′ c ′ x ′ = n c x ′ .$
$n ′ x ′ = n x + n ′ n e .$
$n ′ u ′ = n u + n ′ − n r .$
$EC : BC = sin / EB _ C : sin / CG _ B ,$
$/ EB _ C = π − ( α + α ′ ) 2 and / CG _ B = π + ( θ + θ ′ ) 2 ,$
$e = cos α + α ′ 2 cos θ + θ ′ 2 r .$
$n c ′ − n ′ c = n ′ − n r ⋅ cos θ + θ ′ 2 cos α + α ′ 2 .$