Page:Elektrische und Optische Erscheinungen (Lorentz) 094.jpg

that has a particular location with respect to the light source. Eventually we understand by $f_{1},g_{1},h_{1},f_{2}$ etc. the same function-sign for both cases.

A look upon the formulas (74) and (76) let us recognize, that we are dealing with corresponding states, on which the theorem of § 59 is applicable. If the light is incident on a non-transparent screen with one opening, then the limitation of light and shadow, or the location of dark diffraction fringes behind of it, will be the same in both cases. Also no difference in the spatial distribution of light and dark will be seen, when the rays were mirrored or refracted at an arbitrary transparent body, or when a lens concentrates them, or when some interference phenomena occur.

Of course, motions that are present in the light source itself, which generate these corresponding states, are not quite the same. In one case they will be determined by (73), and in the other case by (75). If we put

$f_{1}\left(t-{\frac {{\mathfrak {p}}_{x}}{V^{2}}}\xi _{1}-{\frac {{\mathfrak {p}}_{y}}{V^{2}}}\eta _{1}-{\frac {{\mathfrak {p}}_{z}}{V^{2}}}\zeta _{1}\right)=f_{1}'(t)$, etc.,

then we may thus also say:

A moving light source, in which ion motions as represented by

$\left.{\begin{array}{c}{\mathfrak {m}}_{x(1)}=f_{1}'(t),\ {\mathfrak {m}}_{y(1)}=g_{1}'(t),\ {\mathfrak {m}}_{z(1)}=h_{1}'(t)\\\mathrm {etc.} \end{array}}\right\}$

(77)

take place, generates the same phenomena as a stationary light source, to which the formulas

$\left.{\begin{array}{c}{\mathfrak {m}}_{x(1)}=f_{1}'\left(t+{\frac {{\mathfrak {p}}_{x}}{V^{2}}}\xi _{1}+{\frac {{\mathfrak {p}}_{y}}{V^{2}}}\eta _{1}+{\frac {{\mathfrak {p}}_{z}}{V^{2}}}\zeta _{1}\right),\\\\{\mathfrak {m}}_{y(1)}=g_{1}'\left(t+{\frac {{\mathfrak {p}}_{x}}{V^{2}}}\xi _{1}+{\frac {{\mathfrak {p}}_{y}}{V^{2}}}\eta _{1}+{\frac {{\mathfrak {p}}_{z}}{V^{2}}}\zeta _{1}\right),\\\\\mathrm {etc.} \end{array}}\right\}$

(78)

apply.

If we are dealing with oscillations, then