Vol. 6, 1920 PHYSICS: DUANE, FRICKE AND STENSTROM 
607 
which is the desired condition, containing one arbitrary constant and 
one arbitrary function, and reducing to Lame's condition when ^ = 0. 
It is easy to show that (12) is satisfied by a set of parallel planes, con- 
centric spheres, or concentric circular cylinders, all these being parallel 
surfaces. It is not satisfied, as is the case with Laplace's equation, by a 
set of confocal ellipsoids. It Was owing to the impossibility of finding 
other sets of surfaces to test the result, together with compunctions about 
Huygens' principle, that caused the writer to hold back the result. Re- 
cently, however, Somiliana has published a proof that these are the 
only sets of parallel surfaces that allow propagation according to Huy- 
gens' principle {Aui Torino, 54, (974-979). SuUe relaziono fra il prin- 
cipio di Huygens e I'ottica geometrica) in which he is obliged to use the 
formulae of differential geometry. I therefore venture to publish the 
above more simple result. 
THE ABSORPTION OF X-RAYS BY CHEMICAL ELEMENTS OF 
HIGH ATOMIC NUMBERS 
By WiIvUam Duane, Hugo Fricke and Wii^helm Stenstrom 
Jkfferson Physicai, Laboratory, Harvard University 
Communicated August 19, 1920. 
Introduction. — A critical absorption wave-length characteristic of a 
chemical element is a wave-length such that the element absorbs X-rays 
longer than the critical value less than it does X-rays shorter than that 
value. Each chemical element has one critical absorption wave-length 
associated with its K series of characteristic emission lines. Duane and 
Hu^ have shown that in the K series of rhodium the critical absorption 
wave-length is about one-fourth of one per cent shorter than that of the 
shortest line (the 7 line) in the K emission series. The authors^ found 
that the critical absorption in the K series of tungsten has a wave-length 
of about one-half of one per cent shorter than that of the Ky emission line. 
Since the other characteristic X-ray series have longer wave-lengths than 
those of the K series, the K critical absorption wave-length is the shortest 
X-ray wave-length now known to be characteristic of a chemical element. 
In the research described in this note the authors have measured the 
critical absorption wave-lengths in the K series of most of the avail- 
able chemical elements from tungsten to uranium, both inclusive. They 
used an ionization spectrometer, and examined spectra of the first, second 
and third orders. In 1918 Duane and Shimizu^ measured four of these 
wave-lengths in spectra of the first order by the ionization method. Mea- 
surements with the same spectrometer of the K critical absorption had 
previously been made for most of the chemical elements down to man- 
