. The Bell System technical journal . re precisely, the radii should vary inversely as the momentum of the true formula for the wave-length as function of the electron-speed is probably X = {h/mov)yll -i^Vc- instead of X = h/mov (here v stands for the speed and nto for the mass-at-zero-speedof the electrons); but as yet the speeds employed have not been great enough northe measurements exact enough to distinguish between the formulae. CONTEMPORARY ADVANCES IN PHYSICS 419 indices (/?i, h-i, Jh) is inclined to the primary beam at a certain angle $for which we have found the formula
. The Bell System technical journal . re precisely, the radii should vary inversely as the momentum of the true formula for the wave-length as function of the electron-speed is probably X = {h/mov)yll -i^Vc- instead of X = h/mov (here v stands for the speed and nto for the mass-at-zero-speedof the electrons); but as yet the speeds employed have not been great enough northe measurements exact enough to distinguish between the formulae. CONTEMPORARY ADVANCES IN PHYSICS 419 indices (/?i, h-i, Jh) is inclined to the primary beam at a certain angle $for which we have found the formulae (8) and (9). We may conceivethat this deflection is due to a reflection of part of the incident wave-motion from a mirror or mirrors traversing the crystal, so tilted thattheir plane bisects the angle $. The picture would be legitimateeven if there were nothing physical corresponding to these mirrors;but we shall presently see that they are not imaginary. The normalto their plane makes supplementary angles ^o and 0 = tt â ^o with. Fig. 20âPowder method diffraction-rings obtained with electron-waves and athin film of gold. (G. P. Thomson, Proc. Roy. Soc.) the primary and the diffracted beams, respectively; and (^o â 6) isthe angle of deflection ^J Combining these statements, and choosingthe positive sense of the normal so that it shall make an acute anglewith the diffracted beam, we find: d ^ \tV - H; ^0 = f TT + i$. (10) We wish to deduce the direction-cosines of the normalâdenotethem for the moment by the symbols 71, 72, 73âfrom the conditionsthat it makes the angles Bq and 6 with the rays having the direction-cosines cci, 0:2, 0:3 and /3i, 182, /Ss respectively. These conditions arethus expressed by the aid of equation (9): ai7i + «272+a373 = cos 0o= âsin-$= â â V//l- + /^2^+/^3^ (H) /3i7i + /3272 + /3373 = cos0-+sin^$= + ^V^7+I?+^, (12) and the reader can easily show by means of equations (6a, 6&, 6c)that they are satisfied when: hi h-i hz V1 ^ â â - ⢠Y t&
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