344 
MR. C. GODFREY ON THE APPLICATION OF FOURIER’S 
Accordingly the distribution of energy in the spectrum given by the succession of 
such pulses is that shown in the curve 
sin 2 ucl 
Fig. 1.—Energy Curve of Rontgen Rays. 
If we take the particles of the cathode stream to be at least as great as molecules, 
2(7. the thickness of pulse, is small compared with the wavedength of visible light 
(see Thomson’s paper) ; dj\ may be taken as xo’oo^ where \ 0 is the wave-length of 
yellow light, say. In the scale of tig. 1 2tt/\ 0 is very near to 0. It appears that long- 
waves have the greatest amplitude; practically the same amplitude is maintained 
onwards through the visible spectrum, and in fact till we approach to wave-lengths 
comparable with the diameter of the molecules. 
§ 33. The measure with which we are concerned, however, is not amplitude, but 
integral energy through ranges of wave-length. Considering this, we see at once 
that the short waves are all-important. The total energy of the pulse is of order E 2 d.. 
The energy contained in waves of length from infinity to \ 0 is of order E ' 2 d. (c7/X 0 ). 
Remembering that the visible spectrum includes an octave, we may say, roughly, 
that ! oV o’ °f the energy of the radiation will reside in the visible part of the spec¬ 
trum ; and, of the rest, practically the whole in waves of length comparable with 
the diameter of the molecules. It is noteworthy that waves of length equal to the 
thickness of the pulse or sub-multiples thereof will be excluded from the spectrum. 
§ 34. Inequalities in the thickness of the pulses will slightly modify the features 
of the equivalent spectrum. Such inequalities will arise partly from the fact that 
different pulses arrive in slightly different directions; they come from different parts 
of the glass (an effect diminishing with distance). Furthermore, the particles are 
not stopped at a single impact in the molecules of the glass. 
It also appears that, if Rontgen rays can be made powerful enough, they will 
affect the eye as ordinary white light. 
§ 35. Professor Thomson’s magnetic pulses are all negative. A mixture of negative 
and positive pulses will present the same features except in so far as the long-waves 
are concerned. If the negative and positive are present in equal quantities, the 
amplitude of the infinite wave will vanish. 
§ 36. It is to be remarked that Professor Thomson’s magnetic pulses differ in one 
important respect from the thin pulses by which Sir George Stokes'* has sought to 
* Wilde Lecture, ‘ Proc. Manchester Phil. Soc.,’ 1897. 
