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PHYSICS: DUANE AND SHIMIZU 
from the hot body to the surrounding enclosure." Now I was wrong in ob- 
jecting to this particular passage, for just here Richardson is speaking of an 
insulated piece of metal which is imagined to give off electrons that do work 
as a gas on a moving piston; and for such a 'virtual' operation his statement 
is doubtless true. But in his experiments he is really taking oiff a stream of 
electrons in the gas state from the metal, and g,n equal stream is constantly 
entering the metal by conduction, yet he assumes that the same $ which occurs 
in the equation above quoted, for his case of virtual emission from an insulated 
body, holds as the heat of emission for his actual case. 
It was this actual case, of electric flow, that I had in mind when I offered 
my criticism that his equation for dS fails when not only heat but substance 
also, that of the incoming electrons, is added to the system during the opera- 
tion under consideration. I believe that this objection holds. 
Bridgman, missing my point through my lack of precision in stating it, 
studied Richardson's argument again and presently made for himself the same 
discovery that I had made, so that he and I are now in agreement regarding 
the inaccuracy of Richardson's reasoning. He finds, moreover, that, when 
this inaccuracy is corrected, Richardson's line of argument leads to precisely 
the same result as Kelvin's. 
Accordingly Bridgman now writes P' instead of P in the equation in ques- 
tion, meaning by P' the total reversible heat effect that accompanies a virtual 
movement of charge from one plate to another of a condenser made of dif- 
ferent metals, though he may not subscribe entirely to my theory as to the 
action of ionization and re-association within the metals. 
I hope that Professor Bridgman's paper, dealing with thermo-electricity 
in a broad way, will be published before long. 
ON THE X-RAY ABSORPTION WAVE-LENGTHS OF LEAD 
ISOTOPES 
By William Duane and Takeo Shimizu 
Jefferson Physical Laboratory, Harvard University 
Communicated by T. Lyman, April 5, 1919 
Researches on the transformations of radioactive substances have lead to 
the conclusion that chemical elements exist which have the same atomic 
number but different atomic weights. Such chemical elements have been 
called isotopes. In the reactions of ordinary chemical analysis isotopes be- 
have in identically the same manner. It has not been found possible to 
separate isotopes from each other by means of purely chemical processes; 
although it seems probable that, since the atomic weights of isotopes differ 
from each other, they will act somewhat differently in those phenomena in 
which the mass of the atom enters as a factor. The ordinary line spectra of 
