1 16 10 5 1 2 2.1 a a a 1 1 1
2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2
5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a h a x y x y 5 3
(3) (4) x y (x + e2 tan φ ) 2 y 2 1 e 2 l + 1 e 2 = l 2 ( ) (1 e 2 ) 2 e 2 sec 2 φ 1 6 φ e φ δ 7 e cos φ (6) sin δ e (5) (5) (1 e 2 )x 2 + 2l e 2 tan φ x + y 2 + l 2 (1 e 2 tan 2 φ) = 0 (7) (5) (7) e 1) e = 0,, x 2 + y 2 = l 2 ( ) 2) 0 < e < 1,, x + e2 tan φ 2 ) l 1 e + y 2 = (e l2 2 1 e 2 (1 e 2 ) 2 sec 2 φ 1 2 3) e = 1,, 2l tan φ x + y 2 + l 2 (1 tan 2 φ) = 0 ( ) 4) 1 < e <,, x e2 tan φ 2 l y 2 e 2 1 5) e =,, x = l tan φ e 2 1 = (e l2 (e 2 1) 2 sec 2 φ 1 2 (6) φ e φ δ e ) (5) 2.4.1 e = 0 (φ = 90, δ > 0 ) (φ = 90, δ < 0 ) e = 0 l 2.4.2 e = (δ = 0 ( e = ) x = l tan φ 6 Appendix 7 4
2.4.3 66.5 φ 66.5 23.5 δ +23.5 e e φ δ 2.4.4 ( φ > 66.5 ) 66.5 66.5 δ 23.5 δ +23.5 8 3 2004 8 12 9 3.1 12 2.0 cm 5.0 cm h 12 (1) cot h 12 = L l = 2.0 = 0.4 (8) 5.0 h 12 = 68.2 3.2 10 8 φ δ φ + δ = 90 180 ( e = 1) e = 1 e = 1 66.5 9 9 10, 10 11, 11 12, 12 13, (13 14, (14 16 10 5
1: 135 3.3 2.4 x y (x i, y i ) i 9 i = 1 16 i = 27 11 11 12 2cm 6
(l = 5cm) i x i (cm) y i (cm) X i (= x i /l) Y i (= y i /l) 1 1.47 4.71 0.294 0.941 2 1.61 4.18 0.321 0.835 3 1.71 3.65 0.341 0.729 4 1.79 3.26 0.359 0.653 5 1.86 2.91 0.372 0.582 6 1.88 2.53 0.376 0.506 7 1.91 2.06 0.382 0.412 8 1.93 1.71 0.386 0.341 9 2.00 1.35 0.400 0.271 10 1.96 0.91 0.392 0.182 11 2.00 0.59 0.400 0.118 12 2.01 0.29 0.402 0.059 13 2.00 0.00 0.400 0.000 14 2.06-0.74 0.412-0.147 15 2.03-1.31 0.406-0.262 16 2.06-1.56 0.412-0.318 17 2.06-2.12 0.412-0.424 18 1.91-2.44 0.382-0.488 19 1.94-2.82 0.388-0.565 20 1.88-3.32 0.376-0.665 21 1.76-3.82 0.352-0.765 22 1.71-4.32 0.341-0.865 23 1.47-4.88 0.294-0.976 24 1.41-5.47 0.282-1.094 25 1.29-5.94 0.259-1.188 26 1.06-6.56 0.212-1.312 27 0.88-7.44 0.177-1.488 3.4 (7) (7) X Y X x l, Y y l (9) (7) X, Y (1 e 2 )X 2 + 2e 2 tan φ X + Y 2 + (1 e 2 tan 2 φ) = 0 (10) l (10) 7
(10) φ φ δ e tan φ = 0.734 e 2 2 12 X i, Y i (i = 1, 2,, 27) e 2 e 2 = 27 i=1 {(X2 i 2X i tan φ + tan 2 φ)(xi 2 + Y i 2 + 1)} 27 i=1 (X2 i 2X i tan φ + tan 2 = 10.89 (11) φ) 2 e e( ) = 3.30 (12) 13 8 12 e = 3.30 (6) (12) δ( ) δ( ) = +14 09 (13) (2004 δ( ) δ( ) = +14 56 (14) 4 2004 8 12 14 12 2 Appendix 13 8 12 δ > 0) 14 8
2: 4.1 l 2004 8 12 12 68.2 8 12 12 L = 3.8cm 15 4.2 x y 12 138.3 15 9
4.3 x y (x i, y i ), i = 1, 2,, 27, l (X i, Y i ) 4.4 (11) (X i, Y i ), i = 1, 2,, 27, e 8 12 δ (δ = +14 56 ) 4.5 4.6 4.7 5 (5) : a : h : δ φ 10
l (x, y) x = l cot z cos a y = l cot z sin a (15) x y z a (δ, H) H δ (h, a) (δ, H) cos h sin a = cos δ sin H, cos h cos a = sin δ cos φ + cos δ sin φ cos H, (16) sin h = sin δ sin φ + cos δ cos φ cos H cos δ sin H cot h sin a = sin δ sin φ + cos δ cos φ cos H, cot h cos a = sin δ cos φ + cos δ sin φ cos H sin δ sin φ + cos δ cos φ cos H (17) X x sin δ cos φ + cos δ sin φ cos H = l sin δ sin φ + cos δ cos φ cos H, (18) Y y l = cos δ sin H sin δ sin φ + cos δ cos φ cos H (19) X Y H (sin φ X cos φ) cos δ sin H = Y sin δ (sin φ X cos φ) cos δ cos H = X sin δ sin φ + sin δ cos φ (20) sin H cos H X 2 (sin 2 δ cos 2 φ) + 2X sin φ cos φ + Y 2 sin 2 δ + sin 2 δ cos 2 φ cos 2 δ sin 2 φ = 0 (21) sin 2 δ cos 2 φ sin 2 δ = cos 2 φ 11
5.1 sin 2 δ cos 2 φ ( X + sin φ cos φ ) 2 sin 2 δ + (sin 2 δ cos 2 φ) (sin 2 δ cos 2 φ) Y 2 = sin 2 δ cos 2 δ (sin 2 δ cos 2 φ) 2 (22) 5.1.1 sin δ = 0 X = tan φ = const. (23) (19) Y = tan H cos φ (24) Y X (18) (X = tan φ) sin δ = 0 δ = 0 λ sin δ = sin λ sin ɛ (25) ɛ sin δ = 0 sin λ = 0 λ = 0, π 5.1.2 sin δ 0 (X + e2 tan φ) 2 Y 2 + 1 e 2 (1 e 2 ) = cot2 δ (1 e 2 ) 2 = 1 ( ) (1 e 2 ) 2 e 2 sec 2 φ 1 (26) e e cos φ sin δ e 2 (27) 5.2 sin 2 δ = cos 2 φ Y 2 + 2X tan φ + (1 tan 2 φ) = 0 (28) 12
6 (10) (X i, Y i ) (1 e 2 )X 2 i + 2e 2 X i tan φ + Y 2 i + (1 e 2 tan 2 φ) = 0 (29) (X i, Y i ) (29) ξ i (1 e 2 )X 2 i + 2e 2 X i tan φ + Y 2 i + (1 e 2 tan 2 φ) = X 2 i + Y 2 i + 1 e 2 (X 2 i 2X i tan φ + tan 2 φ), i = 1, 2,, 27 (30) ξ i (30) φ ξ i e 2 S(e 2 ) S(e 2 27 ) ξi 2 (31) i=1 e 2 e 2 (30) ξ i S(e 2 ) = [ 27 i=1 [ 27 2 (X 2 i 2X i tan φ + tan 2 φ) 2] (e 2 ) 2 ] (Xi 2 2X i tan φ + tan 2 φ)(xi 2 + Y 2 + 1) e 2 27 + (Xi 2 + Yi 2 + 1) (32) 2 i=1 i=1 e 2 (e 2 ) 2 e 2 e 2 = 27 i=1 (X2 i 2X i tan φ + tan 2 φ)(xi 2 + Y 2 + 1) 27 i=1 (X2 i 2X i tan φ + tan 2 (33) φ) 2 S(e 2 ) e 2 (33) 13