One year ago the writer reported to this Academy the results of some preliminary calculations of the intensities of the three components assumed by Millikan to compose the cosmic radiation, based upon his last published data.1 At that time the Academy was so kind as to set apart a grant for a continuance of this research. Soon afterward, Dr. Millikan informed me that he was engaged upon a more elaborate series of depth-ionization measurements which promised greater precision, and extended the hope that the results would be available by fall. It was, however, not until February that the new data were received, and it was then found that the results would entail considerably more calculation than had been anticipated from the earlier set

Weld, Le Roy D.

English

The report herein contained is of a preliminary character, and is intended to exhibit only the first steps of the problem in hand. At the Des Moines meeting of the American Physical Society on Dec. 31 last, the writer presented a paper in which were set forth details of a method of treating the observations of Millikan and Cameron upon the absorption of the cosmic-rays, in order to render them susceptible to adjustment by the method of least squares

Weld, LeRoy D.

Name not available

Progress in the Analysis of Cosmic-Ray Observations

University of Northern Iowa

Proceedings of the Iowa Academy of Science Volume 38 Annual Issue Article 53 1931 Progress in the Analysis of Cosmic-Ray Observations (II) Le Roy D. Weld Coe College Copyright ©1931 Iowa Academy of Science, Inc. Follow this and additional works at: https://scholarworks.uni.edu/pias Recommended Citation Weld, Le Roy D. (1931) "Progress in the Analysis of Cosmic-Ray Observations (II)," Proceedings of the Iowa Academy of Science, 38(1), 209-212. Available at: https://scholarworks.uni.edu/pias/vol38/iss1/53 This Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. PROGRESS IN THE ANALYSIS OF COSMIC-RAY OBSERVATIONS (II) LE ROY D. WELD One year ago the writer reported to this Academy the results of some preliminary calculations of the intensities of the three com-ponents assumed by Millikan to compose the cosmic radiation, based upon his last published data.1 At that time the Academy was so kind as to set apart a grant for a continuance of this research. Soon afterward, Dr. Millikan informed me that he was engaged upon a more elaborate series of depth-ionization measurements which promised greater precision, and extended the hope that the results would be available by fall. It was, however, not until Feb-ruary that the new data were received, and it was then found that the results would entail considerably more calculation than had been anticipated from the earlier set. In their previous paper (Zoe. cit.) Milliken and Cameron assumed th!Y'ee components having absorption coefficients 0.04, 0.08, 0.35 per meter, respectively. From the more recent results,2 they now conclude that there are at least four components, the absorption coefficients of which are estimated to be 0.03, 0.10, 0.20, and 0.80, and whose intensities are approximately 33, 80, 130 and 141,000. The exceedingly powerful fourth component, if such exists, is so rapidly absorbed that its effect disappears almost completely with-in a few meters of depth. The theory that the cosmic rays enter the absorbing water uniformly from all directions gives rise to an expression for the intensity i at any depth H : i = 11 G (µiH) + 12 G (µ.H) + Is G (µsH) +I. G (µ.H) + R, (1) in which I is the initial intensity and the function G is the integral :3 G (µH) = f =-2 e-µHxdx. (2) R is a term which is added to represent the leakage of the electro-scope and to cover any feeble residual radiation not included in 1 Millikan and Cameron, Phys. Rev. 31, p. 921 (1928). 2 Millikan and Cameron. Phys. Rev. 37, p. 235 (1931). . . 3 In the paper cited in footnote 1, this integral appears with the coefficient 2:n;, which is an error borrowed, apparently, from Gold's paper (Proc. Roy. Soc. A82, p. 62, 1909). 209 1Weld: Progress in the Analysis of Cosmic-Ray Observations (II)Published by UNI ScholarWorks, 1931210 IOWA ACADEMY OF SCIENCE [VoL. XXXVIII the four principal components. The preliminary estimate of R is 1.2 ions per cc. per sec. The equation ( 1) may be regarded as an observation equation containing nine unknowns, I,, I 2, 13 , 14 , µ,, µ2 , µ3 , µ4 , and R, the observed quantities being H and i. In a paper read before the American Physical Society in December, 1929, the writer showed that this equation may be transformed into a linear one, in which the unknowns are not the quantities immediately sought, but are the small corrections which should be applied to the approximate values already estimated. If for each component, I = I' + c, where I' is the known approximate value of I and c the correction, and likewiseµ=µ'+ k; and if R = R' + r; then the new, linear observa-tion equation may be written A,c, + A.c, + A,c, + A,c. + B,k, + B2k2 +Bak.+ B,k, + r = s, (3) in which A= G (µ'H), B = ~ [ G (µ'H) - e -µ'H]. (4) s = i - [ il'G (µ'H) + R'} In their latest paper (footnote 2), Millikan and Cameron con-clude that the absorption coefficients µ, as measured, are not quite constant, but that they are smaller at first and increase to equilib-rium values as the depth of peneiiation becomes greater. This is attributed to the effect of the Compton secondaries. For this reason the writer thought best to divide the range of the observa-tions into two parts, and to analyze each separately, in order, if possible, to detect this change in absorption rate. Further, the large absorption coefficient estimated for the assumed fourth com-ponent makes it questionable whether the value of the necessary correction k4 is small enough to neglect its higher powers. For small depths H these appear with appreciable coefficients in the complete expansion, from which the linear equation ( 3) is derived by dropping the higher power terms. But at greater depths, these questionable higher terms rapidly die out for all four components. The coefficients of all higher powers of the e's are, in fact, zero; while the terms containing the higher powers of the k's, if the k's are small, become negligible compared with the other terms for the greater depths. It was therefore thought best to analyze the lower half of the observations first, especially as the assumed very ab-2Proceedings of the Iowa Academy of Science, Vol. 38 [1931], No. 1, Art. 53https://scholarworks.uni.edu/pias/vol38/iss1/531931] ANALYSIS OF COSMIC-RAY OBSERVATIONS 211 sorbable fourth component now disappears altogether, leaving the observations with only seven unknowns instead of nine. Before proceeding with the adjustment, it was necessary to extend the table of the integral, Eq. (2) above, as published in Gold's paper (footnote 3), to larger values of the argument µ H, and to insert values between those given, for greater accuracy in interpolation. This involved many days of labor. The numerical work oi least-square adjustment was done on a calculating ma-chine, and was carefully checked at every stage. The values ob-tained were found to satisfy the normal equations exactly, and to , give smaller residuals, when substituted in the linear observation equations, than Millikan's own estimates.4 It is therefore somewhat disconcerting to have to report that these adjusted results yield an altogether impossible set of absorp-tion coefficients and intensities, some of which even turn out negative. The writer can arrive at only one interpretation of this, namely, that the assumptions upon which the analysis was made are not justified. If, as Millikan and Cameron conclude, the cosmic radia-tion were composed of four distinct principal bands having absorp-tion coefficients and intensities approximately those assigned to them, and if a sufficiently accurate and continuous series of depth-ionization measurements were available, it should be perfectly possible to determine the constants for each component. We have here applied that analysis which, since the time of Gauss, has been accepted as yielding the most probable values of such constants which can be deduced from a set of observations, namely, the method of least squares; yet the resulting adjusted values prove to be physically meaningless and impossible. Millikan and Cameron, using a meter-by-meter, trial-and-error method, have succeeded, it must be admitted, in constructing an empirical formula which represents their results with considerable accuracy. But that these results are incapable of uniquely deter-mining rational constants for the assumed formula, the least square analysis just set forth has amply demonstrated. If this formula were a genuine expression of the absorption law under examina-tion, the small correction to be applied to each assumed constant would have appeared as a matter of routine adjustment. But some of the corrections turn out several times larger than the quantities to be corrected; which indicates some altogether untenable premise. 4 Or more properly stated, the sum of the squares of the residuals is distinctly less for these adjusted values than for Millikan's estimates; as it should be in accordance with the principle of least squares. 3Weld: Progress in the Analysis of Cosmic-Ray Observations (II)Published by UNI ScholarWorks, 1931212 IOWA ACADEMY OF SCIENCE [Voi.. XXXVIII If the influence of the Compton effect is. responsible for the difficulty, the absorption coefficients being in fact variables, this influence must persist at depths of from 20 to 80 meters. Millikan ~nd Cameron remark in their latest article that this phenomenon renders futile a more precise analysis of the curve than that which they have given; a fact which is only too evident if this is indeed the explanation. In that case the obvious course would be to take series of many readings at small, regular depth intervals, not "bunched" as is the case with the published series, and to apply least-square analysis to one section of the curve at a time, so short that the coefficients are sensibly constant throughout the section. In this way the four coefficients, if they exist, could be ascertained to approach true limiting values. It is interesting to note that in a paper shortly to be read before the Physical Society, Mr. Chas. M. Olmsted contends that Millikan and· Cameron's curve can be reproduced just as well on the as-sumption of a continuous ultra-gamma spectrum beginning abrupt-ly at µ = 0.03 and extending on to much less penetrating radiation. Doubtless there are many other ways in which the curve could be reproduced. The present investigation does not undertake to decide between conflicting theories, or to· interpret the nature of the cosmic rays. But whether the uncertainties here manifest arise from insufficient-ly accurate tentative values of the coefficients, from the assump-tion of too few or of too many components, from the distorting effect of Compton scattering, or from an erroneous concept of the physical nature of the whole phenomenon; not to mention the admitted shortcomings of the Klein-Nishina formula; it seems clear that there is every reason to look with reserve upon any such far-reaching conclusions as Millikan and Cameron have deduced from the results of their admirable experimental work. The writer wishes to express his gratitude to the Academy for the grant which has made this analysis possible; also to express his appreciation to his student assistant, Miss Edna Kerchmar, whose painstaking accuracy throughout the long and laborious calculation has supplied the necessary figures. Cm: CoLU:GE, CEDAR RAPIDS, low A. APRIL, 1931. 4Proceedings of the Iowa Academy of Science, Vol. 38 [1931], No. 1, Art. 53https://scholarworks.uni.edu/pias/vol38/iss1/53

Progress in the Analysis of Cosmic-Ray Observations (II)

Proceedings of the Iowa Academy of ScienceVolume 37 | Annual Issue Article 701930Progress in the Analysis of Cosmic-RayObservationsLeRoy D. WeldCoe CollegeCopyright © Copyright 1930 by the Iowa Academy of Science, Inc.Follow this and additional works at: https://scholarworks.uni.edu/piasThis Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion inProceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contactscholarworks@uni.edu.Recommended CitationWeld, LeRoy D. (1930) "Progress in the Analysis of Cosmic-Ray Observations," Proceedings of the Iowa Academy of Science, 37(1),294-296.Available at: https://scholarworks.uni.edu/pias/vol37/iss1/70PROGRESS IN THE ANALYSIS OF COSMIC-RAY OBSERVATIONS LEROY D. w ELD The report herein contained is of a preliminary character, and is intended to exhibit only the first steps of the problem in hand. At the Des Moines meeting of the American Physical Society on Dec. 31 last, the writer presented a paper in which were set forth details of a method of treating the observations of Millikan and Cameron upon the absorption of the cosmic-rays, in order to render them susceptible to adjustment by the method of least squares. In the observation equations, based upon the absorption meas-urements, provision must be made for two unknowns for each component cosmic-ray wave length assumed to be present. These unknowns are the initial intensity and the absorption coefficient of the component. In order that the least-square adjustment may be practicable, the equations must first be reduced to an equivalent linear form, and it was with this process that the Physical Society paper was concerned. The method employed requires that approximate values of the constants be already known. Millikan and Cameron 1 have made estimates of the absorption coefficients of the three principal components. The present report deals with an inquiry, first, as to the magnitude and character of such part of the radia-tion as is not included in these three components, and, second, as to the initial intensities of the three components themselves, ex-pressed in terms of ionizing power. Presumably the residual radiation is of the same type and sub-ject to the same absorption law as the three principal components. It is clear that these three components must include most of the energy responsible for the ionization. There cannot be any very intense radiation of high penetrating power, because of the small ionization obtained at great depths; and if there were much other radiation of low penetrating power, its effect would be observable in the form of the ionization curve. Therefore we may assume that whatever rediation remains when the three main bands are subtracted from the total, is of small intensity and of low mean absorption coefficient. 1 J\Iillikan and Cameron, Phys. Rev. 31, p. 921 (1928). 294 1Weld: Progress in the Analysis of Cosmic-Ray ObservationsPublished by UNI ScholarWorks, 1930COSMIC-RAY OBSERVATIONS 295 As a first approximation, this residual radiation may be con-sidered as a linear function of the depth H, with small slope, over the-range of the observations. Then if it is represented by AH+B, the total ionization at any depth may be expressed by the equation G(0.35H)I1 + G(0.08H)I, + G(0.04H)Is +AH+ B = i. G(µH) is the Gold integral appearing in the absorption equation, and the three values of µ are the absorption coefficients estimated by Millikan and Cameron from a study of their curve. I 1 , I 2 , I 3 are the unknown initial intensities of the three principal compon-ents, making, with A and n, five unknowns in all. We now select five typical observations at intervals along the absorption curve, namely at H=8.45, 17.45, 28.60, 48.60, and 67.45 meters, and substitute their results in the above equation, using the table of the Gold integral to calculate the coefficients of I 1 , I 2 , I 3 • The solution of the five simultaneous equations thus obtained gives, as the preliminary or approximate values sought, I,= 612.9 r. = 23.9 I,= 13.7 A= OJJ06 B = 1.96 It is thus evident that A is probably very small, especially since it turns out positive, whereas it should be negative; which st1g-gests that this value is altogether :fictitious, arising from errors in the three assumed absorption.coefficients, and that its actual value is negligible. Now if A is assumed to be zero and four of the equations are solved for the remaining unknowns, B turns out to be very close to 2.4, which is the value given as the zero of the electroscope, due to leakage. It therefore seems reasonable to as-sume that the three principal components constitute practically all there is of the cosmic radiation, at least all that remains at alti-tudes within the range of the observations; and that the constants for these three components are, approximately: I 1=612.9, ~t 1 =0.35; I2 = 23.9, µ2 = 0.08; 13 = 13.7, µ3 = 0.04. Professor Millikan states, however, that his subsequent results, which he hopes to report within a few weeks, will modify these values somewhat. Therefore this work is held in abeyance for the time being. Meanwhile it may be noted that it has been found necessary to calculate the Gold integral 2Proceedings of the Iowa Academy of Science, Vol. 37 [1930], No. 1, Art. 70https://scholarworks.uni.edu/pias/vol37/iss1/70296 !OW A ACADEMY OF SCIENCE at shorter intervals than those of Gold's published table,2 and to extend it somewhat beyond the limits of the table. For valuable assistance in this task, the writer is indebted to his colleague, Pro-fessor L. M. Coffin. Cm: COLLEGE, CEDAR RAPIDS, low A. 2 Gold, Proc. Ro)'. Soc. A82, p" 62 (1909). 3Weld: Progress in the Analysis of Cosmic-Ray ObservationsPublished by UNI ScholarWorks, 1930

https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=5223&amp;context=pias

Progress in the Analysis of Cosmic-Ray Observations (II)

Abstract

Similar works

Full text

Available Versions

Name not available

University of Northern Iowa

University of Northern Iowa

Name not available