296 BELL SYSTEM TECHNICAL JOURNAL 



maximum frequency, and then and there come to a sudden end; yet 

 apparently it does. There is a high-frequency limit to each X-ray 

 spectrum, and wave-trains of frequencies exceeding that limit are 

 not detected; whereas the spectrum of the hypothetical pulses ought to 

 include wa\e-trains of everj' frequency low or high, the amplitudes 

 indeed declining to infinitely low values as one goes along the spectrum 

 to infinitely high frequencies, but certainly declining smoothly and 

 gradually. To demonstrate this high-frequency limit is a delicate 

 experimental problem, quite like that other problem of demon- 

 strating a sharply definite topmost value for the energies of photo- 

 electrons. That question whether the curves of photoelectric current 

 vs. retarding voltage, the curves of Fig. 2, cut straightly and sharply 

 enough into the axis of abscissae to prove that there are no photo- 

 electrons with velocities higher than the one corresponding to Xo, 

 returns again in a slightly altered form. 



The most reliable of the methods actually used to demonstrate 

 the high-frequency limit depends on the fact that the high limiting 

 frequency (which I will call ;',nax) varies with the energy of the bom- 

 barding electrons, increasing as their velocity increases. Therefore, 

 if the radiant energy' belonging to rays of a certain fixed wave length 

 or a certain fixed narrow range of wave lengths is separated out from 

 the X-ray beam by a spectroscope, and measured for various veloci- 

 ties of the impinging electrons, passing from very high \'elocities step 

 by step to very low ones; it will decrease from its first high \'alue 

 to zero at some intermediate velocity, and thereafter remain zero. 

 But according to the classical theory also, it must decrease from its 

 first high value to an imperceptibly low one; the descent however will 

 be gradual and smooth. Thus the only question which can be settled 

 by experiment is the question whether the descent from measurable 

 intensities to immeasurably small ones resembles the gentle quasi- 

 asymptotic decline of the curve of Fig. 1 or the precipitate slope of 

 the curve of Fig. 2. The data assembled by Duane and Hunt are 

 shown in Fig. 4 plotted in the manner I have described; there is little 

 occasion for doubt as to which sort of cur\'e these resemble most.* 



Fach of the curves in Fig. 4 represents that portion of the total 

 intensity of an X-ray beam, which belongs to rays of wave lengths 

 near the marked value of the frequency v. This frequency is the high 



• Three simple cur\'es of the intensity-distribution in the X-ray spectrum are 

 shown in Figure 5. The abscissa is neither frequency or wavelength, but a variable 

 which varies continuously with either (it is actually arc sin of a quantity propor- 

 tional to wavelength) so that the acute angle between each curve and the axis of 

 abscissae, at the point where they meet, corresponds to and has much the same 

 meaning as the acute angles in Figure 2 — not so conspicuously. 



