THE PRESIDENTIAL ADDRESS II 
noted, as a picture of our knowledge of nature, but as a picture of 
nature itself. The particle-parable is useful as a concession to the 
materialistic habits of thought which have become ingrained in our 
minds, but it can no longer claim to fit the facts, and, so far as we 
can at present see, the truth about nature must lie very near to the 
wave-parable. 
Let me digress again to remind you of two simple instances of 
such conflicts and of the verdicts which observation has pro- 
nounced upon them. 
A shower of parallel-moving electrons forms in effect an 
electric current. Let us shoot such a shower of electrons at a thin 
film of metal, as your own Prof. G. P. Thomson did. The particle- 
parable compares it to a shower of hailstones falling on a crowd 
of umbrellas ; we expect the electrons to get through somehow or 
anyhow and come out on the other side as a disordered mob. But 
the wave-parable tells us that the shower of electrons is a train of 
waves. It. must retain its wave-formation, not only in passing 
through the film, but also when it emerges on the other side. And 
this is what actually happens : it comes out and forms a wave-pattern 
which can be predicted—completely and perfectly—from its wave- 
picture before it entered the film. 
Next let us shoot our shower of electrons against the barrier 
formed by an adverse electro-motive force. If the electrons of the 
shower have a uniform energy of ten volts each, let us throw them 
against an adverse potential difference of a million volts. According 
to the particle-parable, it is like throwing a handful of shot up into 
the air; they will all fall back to earth in time—the conservation 
of energy will see to that. But the wave-parable again sees our 
shower of electrons as a train of waves—like a beam of light—and 
sees the potential barrier as an obstructing layer—like a dirty window 
pane. The wave-parable tells us that this will check, but not 
entirely stop, our beam of electrons. It even shows us how to 
calculate what fraction will get through. And just this fraction, in 
actual fact, does get through ; a certain number of ten-volt electrons 
surmount the potential barrier of a million volts—as though a few 
of the shot thrown lightly up from our hands were to surmount the 
earth’s gravitational field and wander off into space. ‘The pheno- 
menon appears to be in flat contradiction to the law of conservation 
of energy, but we must remember that waves of knowledge are not 
likely to own allegiance to this law. 
A further problem arises out of this experiment. Of the millions 
of electrons of the original shower, which particular electrons will 
get through the obstacle? Is it those who get off the mark first, 
or those with the highest turn of speed, or what ? What little extra 
have they that the others haven’t got ? 
