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.
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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

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