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  1. For aluminium λκ=7.59 A, and for copper λκ=1.38A, so that for these most important filters the jumping-clause would be superfluous within 0.1–1.35A, which is the whole interval of practical interest in our connection.
  2. E.g. by A. H. Compton, "X-rays and Electrons," 1926, p. 189.
  3. According to the cube-formula the ratio of differences Δµ:Δ(λ3) ought to be constant. Now, e.g., for λ=0.1 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.1 1.32 the observed values are µ/ρ=.164 .201 .269 .370 .531 1.05 1.91 3.18 5.00 7.50 10.3 13.8 20.0 31.5 whence one finds for the said ratio of differences between contiguous items (divided by a constant, 10ρ) the values 1.56 1.47 1.32 1.41 1.40 1.41 1.40 1.43 1.48 1.29 1.29 1.49 1.19 which show huge oscillations.
  4. Actually these methods have been constructed mainly for the integral equations of "the second kind," viz. of the type [equation], where σ is a parameter and ƒ(x) the unknown function, whereas not much attention has been paid by the mathematicians (except Volterra) to the equations of the first kind. In the case of the former, power series of the parameter σ are used.
  5. Note added Jan. 30, 1932. Since this has been written the writer has obtained, with the kind aid of Dr. H. Batemau, a rigorous solution of the integral equation (L) for a certain class of functions I(x) which cover quite closely most of the observed filtration curves. This has enabled him to derive with ease the complete spectral curves for radiation samples whose filtration curves are of such a type. This method and its practical applications will be set forth in a paper which is now being prepared.
  6. Neeff, T. C.: cf. Fortschritte a. d. Geb. d. Röntgenstrahlen, XLI, 414, 1930.
  7. Table in A. H. Compton's 'X-rays and Electrons,' 1926, p. 189.
  8. The figures quoted give in each case the maximum potential. Similarly for the Media tube treated below. Cf. Neeff, loc. cit.
  9. A brief reference name of the analyzing set of formulae for three wave lengths with Al as filter.
  10. Radiology, XVI, 302, March, 1931.
  11. Since I1=1 rigidly, by convention, δI1=0.
  12. So far as dependent on the δIk only.
  13. In none of a large number of my trials (various selections of sets of xk and λi was the greatest coefficient below 52.
  14. HWS.-Messungen in Aluminium, Strahlentherapie, 38, 329, 1930, et seq. "HWS."=halfvalue layers.
  15. "HWS" plotted against "Vorfilter" (prefilter).

Compton, A. H.

E.g. by A. H. Compton, "X-rays and Electrons," 1926, p. 189.

Other (15)

For aluminium λκ=7.59 A, and for copper λκ=1.38A, so that for these most important filters the jumping-clause would be superfluous within 0.1–1.35A, which is the whole interval of practical interest in our connection.

E.g. by A. H. Compton, "X-rays and Electrons," 1926, p. 189.

According to the cube-formula the ratio of differences Δµ:Δ(λ3) ought to be constant. Now, e.g., for λ=0.1 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.1 1.32 the observed values are µ/ρ=.164 .201 .269 .370 .531 1.05 1.91 3.18 5.00 7.50 10.3 13.8 20.0 31.5 whence one finds for the said ratio of differences between contiguous items (divided by a constant, 10ρ) the values 1.56 1.47 1.32 1.41 1.40 1.41 1.40 1.43 1.48 1.29 1.29 1.49 1.19 which show huge oscillations.

Actually these methods have been constructed mainly for the integral equations of "the second kind," viz. of the type [equation], where σ is a parameter and ƒ(x) the unknown function, whereas not much attention has been paid by the mathematicians (except Volterra) to the equations of the first kind. In the case of the former, power series of the parameter σ are used.

Note added Jan. 30, 1932. Since this has been written the writer has obtained, with the kind aid of Dr. H. Batemau, a rigorous solution of the integral equation (L) for a certain class of functions I(x) which cover quite closely most of the observed filtration curves. This has enabled him to derive with ease the complete spectral curves for radiation samples whose filtration curves are of such a type. This method and its practical applications will be set forth in a paper which is now being prepared.

Neeff, T. C.: cf. Fortschritte a. d. Geb. d. Röntgenstrahlen, XLI, 414, 1930.

Table in A. H. Compton's 'X-rays and Electrons,' 1926, p. 189.

The figures quoted give in each case the maximum potential. Similarly for the Media tube treated below. Cf. Neeff, loc. cit.

A brief reference name of the analyzing set of formulae for three wave lengths with Al as filter.

Radiology, XVI, 302, March, 1931.

Since I1=1 rigidly, by convention, δI1=0.

So far as dependent on the δIk only.

In none of a large number of my trials (various selections of sets of xk and λi was the greatest coefficient below 52.

HWS.-Messungen in Aluminium, Strahlentherapie, 38, 329, 1930, et seq. "HWS."=halfvalue layers.

"HWS" plotted against "Vorfilter" (prefilter).

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