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James Van Allen journal, 1951?-December 1954
Page 82
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This table shows that (P(v/e)) differs from P appreciably beginning at a proton kinetic energy of about 500 Mev. The difference increases rapidly toward lower energies. My whole point is probably confined to energies less than ~500 Mev !! if indeed it amounts to anything. -------------------------------------------------------------- 4 September 1951 (ln _= (log sub e)) Expansion of (a exponent x) (ln (a exponent x)) = ((x) (ln a)) therefore, (a exponent x) = (e exponent ((x)(ln a))) (a exponent x) = ( 1 + ((x) (ln a)) + ((((x) (ln a)) exponent 2)/(2!)) + ((((x)(ln a)) exponent 3)/(3!)) + . . . (see Peirce #760) ( (x exponent 2)<[not infinity? 1? infinity?]) The series, although convergent for ((x exponent 2)< infinity), is of immediate utility in practical approximations only when x is approximately [unity?]. Then we have
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This table shows that (P(v/e)) differs from P appreciably beginning at a proton kinetic energy of about 500 Mev. The difference increases rapidly toward lower energies. My whole point is probably confined to energies less than ~500 Mev !! if indeed it amounts to anything. -------------------------------------------------------------- 4 September 1951 (ln _= (log sub e)) Expansion of (a exponent x) (ln (a exponent x)) = ((x) (ln a)) therefore, (a exponent x) = (e exponent ((x)(ln a))) (a exponent x) = ( 1 + ((x) (ln a)) + ((((x) (ln a)) exponent 2)/(2!)) + ((((x)(ln a)) exponent 3)/(3!)) + . . . (see Peirce #760) ( (x exponent 2)<[not infinity? 1? infinity?]) The series, although convergent for ((x exponent 2)< infinity), is of immediate utility in practical approximations only when x is approximately [unity?]. Then we have
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