B~TOL R~SSARCH
A cylinder stands with its axis vertical. FOUNDATION
The problem is to find f(l), the coefficient Co~u~catlon~o. TS. of dl in the expression for the number of cosmic rays which travel distances between l and 1 -k dl in the cylinder. The solution is of importance in connection with the detection of individual secondary cosmic rays by measurement of the ionization which they produce in such a cylinder, and in the interpretation of the results in terms of the ionization per centimeter of path of the rays. In this way it has been used by the writer in connection with experiments to be described in another place. For those whose interest is confined to the solution, and who are not interested in the derivation, it may be stated that the complete results are given in the section "Final Solution" at the end of the paper. They are accompanied by definitions of all the quantities concerned?
Assumptions and Definitions. The problem will be discussed for the cases where the number of rays ~n passing per second through a horizontal element of area ds within a solid angle sin 0 dO d~, whose axis is inclined at the angle 0 to the vertical, is ~n = A sin 0 cos 3 0 dO d~ ds.
Here, in accordance with empirical determinations, the intensity of the radiation is assumed to vary proportionally to cos 2 0 with angle from the vertical. The other cos 0 is, of course, to take account of the angle between the element of solid angle and the normal to ds.
1 In an elaborate paper entitled "H6henstrahlungskoinzidenzen in Z/~hl-r6hren," Berl. Bet., p. 83o ' I93I, Leo Tuwin considers the problem of cosmic ray paths in a cylinder. The paper does not appear, however, to have immediate application to the specific problem here solved. 559 560 W.F.G. SWANN.
[J. F. I.
We make the following definitions:
where l is the variable length for which we seek f(1). ~in,,---contribution to f(l)dl by the rays which enter and leave through the cylindrical surface. 6n,b --contribution to f(1)dl by the rays which enter through the side and leave through the base. 6n,, -contribution to f(l)dl by the rays which enter through the top and ~n,b -contribution to the top and Cases Considered. themselves according to the Case I. 2a < l and l Case 2. 2a <landl Case 3-l < 2a < L, Case 4. 1 <L < 2a, Case 5. L <l < 2a, leave through the side.
f(1)dl by the rays which enter through leave through the base.