67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9
68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1
A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10 1/0 1/30 1 mm n n = 10 0 30 1/n mm A.5 1 0 m m + 1 1 1/n mm l 0 l 1/n mm m + l/n mm 1/n A.5: A.5 1 mm n = 0 0.05 mm 0 1 mm
70 A 1 0.05 mm 9 0.45 mm 1 + 0.45 = 1.45 mm 1 A.6(a) AB A B F AB G B G D E G A B C F 0.5 mm F E 1 B 0.5 mm D 0.5 mm E 50 1 0.01 mm A.6(a) 0 5 mm, 0.01 mm 5 mm E 0.01 mm D E E D A.6(b) 1.5 mm 13.0 mm E 0 E D E 46 47 E 1/10 E 0.465 mm 1.5 + 0.465 = 1.965 mm G A B C D E F G D E 0-5 mm 0.01 mm (a) (b) A.6: (a) (b)
A.. 71 Section A. 0.1 cm 1 mm 8.35 cm 8.3 cm 5 8.35 8.350 8.34 8.36 8.35 8.349 8.351 8.350 8.35 8.350 x = 8.35 8.345 x < 8.355 x = 8.350 8.3495 x < 8.3505 8.35 cm 0.0835 m 0.0000835 km 83500 µm 835 3 0 8.35 10 m 8.35 10 5 km 8.35 10 4 µm 8.35 cm π = 3.1415965 S = π (8.35) = 19.039693 [cm ] 8.345 cm 8.355 cm π (8.345) = 18.777449 π (8.355) = 19.30095 19 cm 3 3 π 3
7 A 8.35 0.01 3 8.35 5 0.01 8.36 8.36 Section A.3 x X ε = x X (A.1) 0 0.01 10.3 0.1 10.3
A.3. 73 0 N x 1, x,, x N X ε i = x i X (A.) σ σ ε i = 1 N N (x i X) (A.3) i=1 ε ε + dε ε i N f (ε)dε f (ε) f (ε) = ( ) 1 exp ε πσ σ σ A.7 σ 68.3 % ±σ 3 f (ε) σ 小 (A.4) 0 σ 大 ε A.7: A B 10 A.1 A.8 0.1 A B A.1 3, ±σ 68.3 % ±σ 95.4 % ±3σ 98.8 %
74 A A.1 A/ B/ 1 10.3 10.16 10.35 10. 3 10.11 10.8 4 10.6 10.05 5 10.08 10.14 6 10.34 10.19 7 10.1 10.43 8 10.4 10.36 9 10.19 10.40 10 10.37 10.47 測定回数 4 3 1 0 Aの測定結果 4 Bの測定結果 3 測定回数 1 0 10 10. 10.4 10.6 10 10. 10.4 10.6 時間 ( 秒 ) 時間 ( 秒 ) A.8: 1 1 1 1 10 Section A.4 x, y σ x, σ y z = F(x, y) x i, y i z i ( ) ( ) F F z i Z = (x i X) + (y i Y) x x=x,y=y y x=x,y=y ( ) ( ) F F = ε x,i + ε y,i (A.5) x y X Y Z x y z z {( ) ( ) } F F σ z = (z i Z) = ε x,i + ε y,i x y ( ) ( ) ( ) ( ) F F F F = ε x,i x + ε y,i y + ε x,i ε y,i (A.6) x y
A.5. 75 ε x,i ε y,i x, y 0 ( ) ( ) F F σ z = σ x + σ y x y A. x, y X, Y x, ȳ z ax ± by axy ax/y ae bx A. σ z a σ x + b σ y (aȳ) σ x + (a x) σ y (a/ȳ) σ x + (a x/ȳ ) σ y (abe b x ) σ x a ln(x) (a/ x) σ x a, b x, ȳ x, y (A.7) Section A.5 N σ ε i ε i + dε i ( ) N 1 exp ε 1 + ε + + ε n dε πσ σ 1 dε dε N S = N ε i = i=1 (A.8) N (x i X) (A.9) i=1 S ds N N dx = (X x i ) = NX x i = 0 i=1 i=1 (A.10) X m X m = 1 N N x i = 1 N (x 1 + x + + x N ) i=1 (A.11)
76 A A.1 A X m = 1 (10.3 + 10.35 + 10.11 + 10.6 + 10.08 + 10.34 + 10.1 + 10.4 + 10.19 + 10.37) 10 = 10.56 10.6 [ ] X m X σ m ( σ m = (X m X) ε1 + ε + + ε ) N = N = 1 { } N ε N i + N(N 1) ε i ε j j i = σ N (A.1) 4 1 1/N 1/ N X ε i i = x i X m (A.13) i = (x i X m ) = N 1 N σ (A.14) σ σ = N N 1 i = 1 N 1 N i=1 i (A.15) N X exp X exp = X m ± σ m = xi N ± i N(N 1) (A.16) A.1 A σ = 0.113 σ m = 0.0357 X exp = 10.6 ± 0.04 [ ] X 10.6 0.04 68.3 % 4 N ε i ε j j i 0
A.5. 77 ( X X Y Y = ax (A.17) a X x 1 x x N Y y 1 y y N X x i Y Y i Y i = ax i S = ε i = (y i Y i ) = (y i ax i ) (A.18) a S a = x i (ax i y i ) = (a xi x i y i ) = 0 a xi y i a = xi (A.19) (A.0) x i x i y i a a b X Y Y = ax + b (A.1) S = ε i = (y i Y i ) = (y i ax i b) (A.) a, b x i (ax i + b y i ) = ( ) a xi + b x i x i y i = 0 S a = S b = (ax i + b y i ) = ( a a b a = ( x i )( y i ) N x i y i ( x i ) N x i b = ( x i )( x i y i ) ( x i )( y i ) ( x i ) N x i ) x i + bn y i = 0 (A.3) (A.4) (A.5) (A.6) m a 1, a,, a m X Y m a i
78 A X Y Section A.6 A.9 A4 1 10 cm 1 1 mm
A.6. 79 A4 変数 y / 単位 300 00 100 データ 1 データ 0 0 10 0 変数 x / 単位 図 ( 番号 ) 表題, 説明文 A.9:
80 A 5 0 0 A.9 A.9 A.10) A.11 1 6 cm 10 A.11 0.1 0. 0.3 0.4 1 3 4, 3 10 10 0.1 1 10 100 0 x, y X, Y X Y X = Ax Y = B log 10 y (A.7) (A.8) B 6 cm y = a exp(bx) (A.9) X, Y Y = B log 10 [a exp(bx)] = bb log 10 e X + B log A 10 a (A.30) 5
A.6. 81 10 10 4 /V 5 /V 1 0.4 0 0 1 3 4 /ms A.10: 0. 0.1 0 1 3 4 /ms A.11: A.11 X Y X = B log 10 x Y = B log 10 y (A.31) (A.3) 1 B X Y y = ax b (A.33) x X, Y Y = B log 10 (ax b ) = bb log 10 x + B log 10 a = bx + B log 10 a (A.34) b A.10 A.11 A.4
8 A A.1 1 µ x y y = a exp ( µx) (A.35) Y A.1(b) µ 1/10 (1) () 1 x 0, y 0 y y 0 /10 x 1, y 1 (3) y 1 = y 0 exp { µ(x 1 x 0 )} = y 0 /10 exp { µ(x 1 x 0 )} = 1 10 (4) µ = log e 10 x 1 x 0 =.30 x 1 x 0 A.1 µ =.30 8.1 = 0.8 [cm 1 ] 1/ (1) () 1 x 0, y 0 y y 0 / x, y (3) µ = log e = 0.693 A.1 µ = 0.693 x x 0 x x 0.5 = 0.8 [cm 1 ] 1/e (1) () 1 x 0, y 0 y y 0 /e x 3, y 3 (3) µ = log e e = 1.00 A.1 µ = 1.00 x 3 x 0 x 3 x 0 3.6 = 0.8 [cm 1 ]
A.6. 83.0 10 1.8 1.6 1.4 1. 1.0 0.8 0.6 0.4 1 10 1 x0 x x3 x1 0. 0 0 4 6 8 10 1 14 10 0 4 6 8 10 1 14 A.1: