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  1. W. Einthoven, Ein neues Galvanometer, Annalen der Physik, 4th Series, vol.  12, p. 1059; 1903.
    [Crossref]
  2. Ibid. Weitere Mitteilungen über das Saitengalvanometer, Annalen der Physik, 4th Series, vol. 21, pp. 483–514 and 665–700; 1906.
  3. Ibid. Ueber die Konstruktion des Saitengalvanometers, Pflüger’s Archiv für die gesammte Physiologe etc., vol. 130, pp. 287–321; 1909.
  4. P. Hertz, Zur Theorie des Saitengalvanometers, Habilitationsschrift, Heidelberg, 1909; also Zeitschr. für Math. und Phys.,  58, p. 1; 1909.
  5. R. Foerster, Elektr. Zeitschr. 35, p. 146; 1914.
  6. G. Fahr, Zur Theorie des Saitengalvanometers, Zeitchr. für Biologie, vol.  64, pp. 61–112; 1914.
  7. A. C. Crehore, Theory of the String Galvanometer of Einthoven, Phil. Mag. vol.  28, p. 207–224; 1914.
    [Crossref]
  8. A. Pochettino, Sul galvanometro a corda di Einthoven, Atti Acad. Scienz. Torino, vol.  57, 2a, pp. 71–80; 1921–22.
  9. G. Wiedemann, Die Lehre vom Galvanismus und Elektromagnetismus, vol. 2a, p. 170, quoting from Le Roux, Ann. de Chim. et Phys., vol.  61, p. 409; 1860.
  10. A. Wehnelt, Austritt negativer Ionen aus glühenden Metallverbindungen, etc., Annalen der Physik, 4th Series, vol.  14, p. 463; 1904.

1914 (3)

R. Foerster, Elektr. Zeitschr. 35, p. 146; 1914.

G. Fahr, Zur Theorie des Saitengalvanometers, Zeitchr. für Biologie, vol.  64, pp. 61–112; 1914.

A. C. Crehore, Theory of the String Galvanometer of Einthoven, Phil. Mag. vol.  28, p. 207–224; 1914.
[Crossref]

1904 (1)

A. Wehnelt, Austritt negativer Ionen aus glühenden Metallverbindungen, etc., Annalen der Physik, 4th Series, vol.  14, p. 463; 1904.

1903 (1)

W. Einthoven, Ein neues Galvanometer, Annalen der Physik, 4th Series, vol.  12, p. 1059; 1903.
[Crossref]

Crehore, A. C.

A. C. Crehore, Theory of the String Galvanometer of Einthoven, Phil. Mag. vol.  28, p. 207–224; 1914.
[Crossref]

Einthoven, W.

W. Einthoven, Ein neues Galvanometer, Annalen der Physik, 4th Series, vol.  12, p. 1059; 1903.
[Crossref]

Fahr, G.

G. Fahr, Zur Theorie des Saitengalvanometers, Zeitchr. für Biologie, vol.  64, pp. 61–112; 1914.

Foerster, R.

R. Foerster, Elektr. Zeitschr. 35, p. 146; 1914.

Hertz, P.

P. Hertz, Zur Theorie des Saitengalvanometers, Habilitationsschrift, Heidelberg, 1909; also Zeitschr. für Math. und Phys.,  58, p. 1; 1909.

Pochettino, A.

A. Pochettino, Sul galvanometro a corda di Einthoven, Atti Acad. Scienz. Torino, vol.  57, 2a, pp. 71–80; 1921–22.

Wehnelt, A.

A. Wehnelt, Austritt negativer Ionen aus glühenden Metallverbindungen, etc., Annalen der Physik, 4th Series, vol.  14, p. 463; 1904.

Wiedemann, G.

G. Wiedemann, Die Lehre vom Galvanismus und Elektromagnetismus, vol. 2a, p. 170, quoting from Le Roux, Ann. de Chim. et Phys., vol.  61, p. 409; 1860.

Annalen der Physik (2)

W. Einthoven, Ein neues Galvanometer, Annalen der Physik, 4th Series, vol.  12, p. 1059; 1903.
[Crossref]

A. Wehnelt, Austritt negativer Ionen aus glühenden Metallverbindungen, etc., Annalen der Physik, 4th Series, vol.  14, p. 463; 1904.

Atti Acad. Scienz. Torino (1)

A. Pochettino, Sul galvanometro a corda di Einthoven, Atti Acad. Scienz. Torino, vol.  57, 2a, pp. 71–80; 1921–22.

Elektr. Zeitschr. (1)

R. Foerster, Elektr. Zeitschr. 35, p. 146; 1914.

Phil. Mag. (1)

A. C. Crehore, Theory of the String Galvanometer of Einthoven, Phil. Mag. vol.  28, p. 207–224; 1914.
[Crossref]

Zeitchr. für Biologie (1)

G. Fahr, Zur Theorie des Saitengalvanometers, Zeitchr. für Biologie, vol.  64, pp. 61–112; 1914.

Other (4)

G. Wiedemann, Die Lehre vom Galvanismus und Elektromagnetismus, vol. 2a, p. 170, quoting from Le Roux, Ann. de Chim. et Phys., vol.  61, p. 409; 1860.

Ibid. Weitere Mitteilungen über das Saitengalvanometer, Annalen der Physik, 4th Series, vol. 21, pp. 483–514 and 665–700; 1906.

Ibid. Ueber die Konstruktion des Saitengalvanometers, Pflüger’s Archiv für die gesammte Physiologe etc., vol. 130, pp. 287–321; 1909.

P. Hertz, Zur Theorie des Saitengalvanometers, Habilitationsschrift, Heidelberg, 1909; also Zeitschr. für Math. und Phys.,  58, p. 1; 1909.

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N d l = T r d l
1 r = H I T
r = l 2 8 U
T = H I l 2 8 U
T = 4 l 2 m τ 0 2
H = 32 m U I τ 0 2
2 u t 2 + k m u t - a 2 2 u x 2 = n = 1 n = s = 1 s = H I n m cos n ω t · sin s π x l
u = 2 l e - k t 2 m s = 1 s = [ 1 1 - l 2 k 2 4 m 2 s 2 π 2 a 2 cos ( t s 2 π 2 a 2 l 2 - k 2 4 m 2 - tan - 1 k 2 m s 2 π 2 a 2 l 2 - k 2 4 m 2 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ ] + n = 1 n = s = 1 s = H I n k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2 cos ( n ω t - tan - 1 k n ω m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) ) sin s π x l }
k 2 m = 2 π 1 τ 0 2 - 1 τ k 2             so that - k t 2 m = - 2 π t 1 τ 0 2 - 1 τ k 2
1 1 - l 2 k 2 4 π 2 m 2 a 2 = π 2 a 2 l 2 π 2 a 2 l 2 - k 2 4 m 2 = τ k 2 τ 0 2 = τ k τ 0
π 2 a 2 l 2 - k 2 4 m 2 = 2 π τ k
k 2 m π 2 a 2 l 2 - k 2 4 m 2 = k 2 m × 1 π 2 a 2 l 2 - k 2 4 m 2 = k 2 m × τ k 2 π = 2 π 1 τ 0 2 - 1 τ k 2 × τ k 2 π = τ k 2 τ 0 2 - 1 .
u = 2 l e - 2 π t 1 τ 0 2 - 1 τ k 2 [ τ k τ 0 cos ( 2 π t τ k - tan - 1 τ k 2 τ 0 2 - 1 ) sin π x l 0 l f ( λ ) sin π λ l d λ ]
u = e β t { 2 l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ - 2 β t l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ } }
u t = β e β t { 2 l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ - 2 β t l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ } - 2 β l e β t s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ .
u = n = 1 n = s = 1 s = H I n l 2 s 2 π 2 T + m n 2 ω 2 l 2 cos ( n ω t - tan - 1 2 s π a n ω l ( s 2 π 2 a 2 l 2 n 2 ω 2 ) ) sin s π x l
H I n l 2 s 2 π 2 T
U s U s _ = 1 1 + 4 π 2 n 2 f 2 τ 0 2 4 s 2 π 2 = 1 1 + f 2 n 2 τ 0 2 s 2
s = tan - 1 8 m π 2 f n τ s m ( 4 π 2 τ s 2 - 4 π 2 f 2 n 2 ) = 8 π 2 f n 4 π 2 τ s - 4 π 2 f 2 n 2 τ s = 2 f n τ s 1 - f 2 n 2 τ s 2 .
tan = 2 f n τ 0 1 - f 2 n 2 τ 0 2
u = e β t ( F ( x ) - β t F ( x ) ) = F ( x ) e β t ( 1 - β t )
u = F ( x ) e - 2 π t τ 0 ( 1 + 2 π t τ 0 )
u = U e - 2 π t τ 0 ( 1 + 2 π t τ 0 )
u = U e - 2 π 3 ( 1 + 2 π 3 ) = .1237 U ( 1 + 2.093 ) = .38 U
β 1 = - k 2 m + k 2 4 m 2 - s 2 π 2 a 2 l 2 β 2 = - k 2 m - k 2 4 m 2 - s 2 π 2 a 2 l 2
u = 2 l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ { e β 1 t ( β 2 β 2 - β 1 ) - e β 2 t ( β 1 β 2 - β 1 ) }
( l 2 - x ) 2 + ( u + V ) 2 = r 2 = ( U + V ) 2
l 2 4 - l x + x 2 + 2 u V + u 2 + V 2 = U 2 + 2 U V + V 2
l 2 4 - l x + x 2 + 2 u V = 2 U l 2 8 u = l 2 4 x 2 - l x = - 2 u V ,
u = 1 2 V ( l x - x 2 )
u = 4 U l 2 ( l x - x 2 )
F ( x ) = 2 l s = 1 s = sin s π x l 0 l 4 U l 2 ( l λ - λ 2 ) sin s π λ l d λ ,
F ( x ) = s = 1 s = sin s π x l · 8 U l 3 { l 0 l λ sin s π λ l d λ - 0 l λ 2 sin s π λ l d λ }
F ( x ) = s = 1 s = 32 U s 3 π 3 sin s π x l
F ( x ) = 1.033 U ( sin π x l + 1 3 3 sin 3 π x l + 1 5 3 sin 5 π x l + · · )
F ( l 2 ) = 1.033 U - .0382 U + .0082 U - .003 U + ·
u = sin π x l
l 2 U = ( l 6 ) 2 U 2 or l 2 U 2 = l 2 36 U
U 2 = U 36
F m ( x ) = s = 1 s = 8 U l 3 5 l 12 7 l 12 ( l λ - λ 2 ) sin s π λ l d λ sin s π x l .
F m ( x ) = s = 1 s = { 32 U s 3 π 3 sin s π 12 - 8 U 3 s 2 π 2 cos s π 12 + 280 U 72 s π sin s π 12 } sin s π x l
F m ( x ) = s = 1 s = { 1.033 U s 3 sin s π 12 - .2704 U s 2 cos s π 12 + 1.24 U s sin s π 12 } sin s π x l
F C ( x ) = 2 l s = 1 s = 5 l 12 7 l 12 C sin s π λ l d λ sin s π x l
F C ( x ) = 2 C l s = 1 s = 5 l 12 7 l 12 sin s π λ l d λ sin s π x l = s = 1 s = 4 C s π sin s π 12 sin s π x l
F C ( l 2 ) = .3198 U - .2910 U + .2386 U - .1704 U + ·
F m ( l 2 ) = .3275 U - .2980 U + .2447 U - .1754 U +
F m ( l 2 ) = .3275 U - .2980 U + .2447 U - .1754 U + F C ( l 2 ) = .3198 U - .2910 U + .2386 U - .1704 U + ψ ( l 2 ) = .0077 U - .0070 U + .0061 U - .0050 U +
F ( 1 2 ) = 1.033 U - .0382 U + .0082 U - .003 U + ψ ( 1 2 ) = .0077 U - .0070 U + .0061 U - .0050 U + F ( l 2 ) - ψ ( l 2 ) = 1.0253 U - .0312 U + .0021 U + .0020 U +
F ( l 2 ) = 1.033 U - .0382 U + .0082 U - .003 U +
1 2 ψ ( l 2 ) = .00385 U - .0035 U + .00305 U - .0025 U + F ( l 2 ) - 1 2 ψ ( l 2 ) = 1.02915 U - .0347 U + .00515 U - .0005 U
u = 2 l e - 2 π t τ 0 s = 1 s = s 1 s 2 - 1 cos ( 2 π t τ 0 s 2 - 1 - tan - 1 1 s 2 - 1 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ }
τ s k = 2 π s 2 π 2 a 2 l 2 - k 2 4 m 2
π a l = k 2 m = 2 π τ 0 ,
τ s k = 2 π 4 π 2 s 2 τ 0 2 - 4 π 2 τ 0 2 = τ 0 s 2 - 1
H I n 16 m 2 π 2 τ 0 2 × 4 π 2 s 2 - 4 π 2 τ 0 2 + m 2 ( 4 π 2 s 2 τ 0 2 - ( 4 π 2 s 2 - 4 π 2 ) τ 0 2 ) 2
H I n τ 0 2 4 π 2 m 4 s 2 - 3
U s k U _ = H I n τ 0 2 4 π 2 m 4 s 2 - 3 × π 2 T H I n l 2 = T τ 0 2 4 m l 2 4 s 2 - 3
a 2 l 2 l 2 a 2 4 s 2 - 3 = 1 4 s 2 - 3 = U s k U _
u = e - k t 2 m ( A sin t μ m - k 2 4 m 2 + B cos t μ m - k 2 4 m 2 )
u ˙ = - k 2 m e - k t 2 m ( A sin t μ m - k 2 4 m 2 + B cos t μ m - k 2 4 m 2 ) + e - k t 2 m ( A μ m - k 2 4 m 2 cos t μ m - k 2 4 m 2 - B μ m - k 2 4 m 2 sin t μ m - k 2 4 m 2 ) = 0
u ˙ = - k 2 m B + A μ m - k 2 4 m 2 , or , since B = U , A = k U 2 m μ m - k 2 4 m 2
u = U e - k t 2 m { k 2 m μ m - k 2 4 m 2 sin t μ m - k 2 4 m 2 + cos t μ m - k 2 4 m 2 }
F ( x ) = 2 l s = 1 s = sin s π x l 0 l f ( λ ) sin s π λ l d λ .
2 u t 2 + k u m t - a 2 2 u x 2 = 0 , u = 2 l e - k t 2 m s = 1 s = [ ( k 2 m s 2 π 2 a 2 l 2 - k 2 4 m 2 sin t s 2 π 2 a 2 l 2 - k 2 4 m 2 + cos t s 2 π 2 a 2 l 2 - k 2 4 m 2 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ ]
u = 2 l e - k t 2 m s = 1 s = [ 1 1 - l 2 k 2 4 m 2 s 2 π 2 a 2 cos ( t s 2 π 2 a 2 l 2 - k 2 4 m 2 - tan - 1 k 2 m s 2 π 2 a 2 l 2 - k 2 4 m 2 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ ]
u = 2 l e - k t 2 m s = 1 s = [ ( cos t s 2 π 2 a 2 l 2 - k 2 4 m 2 + k 2 m s 2 π 2 a 2 l 2 - k 2 4 m 2 sin t s 2 π 2 a 2 l 2 - k 2 4 m 2 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ ] }
u = 2 l e - k t 2 m s = 1 s = 1 1 - l 2 k 2 4 m 2 s 2 π 2 a 2 cos ( t s 2 π 2 a 2 l 2 - k 2 4 m 2 - tan - 1 k 2 m s 2 π 2 a 2 l 2 - k 2 4 m 2 ) sin s π x l 0 l f ( λ ) sin s π λ l d λ
u = H I n m ( D 2 + k m D - a 2 D 2 ) n = 1 n = s = 1 s = cos n ω t sin s π x l .
u = H I n k D + m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) cos n ω t sin s π x l .
u = H I n k D - m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) k 2 D 2 - m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2 cos n ω t sin s π x l .
u = H I n - k n ω sin n ω t sin s π x l - m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) cos n ω t sin s π x l - k 2 n 2 ω 2 - m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2
k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2
k n ω k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2 ,             sin
m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2 ,             cos
= tan - 1 k n ω m ( s 2 π 2 a 2 l 2 - n 2 ω 2 )
u = H I n sin sin n ω t sin s π x l + cos cos n ω t sin s π x l k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2
u = n = 1 n = s = 1 s = H I n k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2 cos ( n ω t - tan - 1 k n ω m ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) ) sin s π x l .
H I n k 2 n 2 ω 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2
H I n 4 s 2 π 2 a 2 m 2 n 2 ω 2 l 2 + m 2 ( s 2 π 2 a 2 l 2 - n 2 ω 2 ) 2
H I n m 4 s 2 π 2 a 2 n 2 ω 2 l 2 + s 4 π 4 a 4 l 4 - 2 s 2 π 2 a 2 n 2 ω 2 l 2 + n 4 ω 4
H I n m s 4 π 4 a 4 l 4 + 2 s 2 π 2 a 2 n 2 ω 2 l 2 + n 4 ω 4
H I n m ( s 2 π 2 a 2 l 2 + n 2 ω 2 )
d u d t = β 1 C 1 e 0 + β 2 C 2 e 0 = 0 β 1 C 1 = - β 2 C 2             ( III ) h
U = C 1 - β 1 β 2 C 1 = C 1 ( 1 - β 1 β 2 ) = C 1 ( β 2 - β 1 β 2 ) C 1 = U             β 2 β 2 - β 1 ( IV ) h
U = C 2 - β 2 β 1 C 2 = C 2 ( 1 - β 2 β 1 ) = C 2 ( β 1 - β 2 β 1 )
C 2 = - U ( β 1 β 2 - β 1 )     .             ( V ) h .
u = U { e β 1 t ( β 2 β 2 - β 1 ) - e β 2 ( β 1 β 2 - β 1 ) }
λ sin s π λ l d λ = - l λ s π cos s π λ l + l 2 s 2 π 2 sin s π λ l
λ 2 sin s π λ l d λ = - l λ 2 s π cos s π λ l + 2 l 2 λ s 2 π 2 sin s π λ l + 2 l 3 s 3 π 3 cos s π λ l .
x n sin a x d x = - x n - 1 ( a x cos a x - n sin a x a 2 ) - n ( n - 1 ) a 2 x n - 2 sin a x d x
sin 5 s π 12 = cos s π 12 sin 7 s π 12 = cos s π 12 cos 5 s π 12 = sin s π 12 cos 7 s π 12 = - sin s π 12
1 1 - l 2 k 2 4 m 2 s 2 π 2 a 2 = 4 m 2 s 2 π 2 a 2 4 m 2 s 2 π 2 a 2 - l 2 k 2 = s 2 π 2 a 2 l 2 s 2 π 2 a 2 l 2 - k 2 4 m 2 = s 2 π 2 a 2 l 2 π 2 a 2 l 2 ( s 2 - 1 ) = s 1 s 2 - 1 .