Diffraction of Scalar Elastic Waves by a Finite Crack.

arc, with two end-plates energized by a common negative voltage referred to the central arc. Note that these are actually experimental results for a real central uranium arc, operating at about 50 volts, for more than 100 tests, at total arc currents of 1-100 amperes. The floating cylinder was about 4 feet in diameter, and the negatively energized circular end-plates were separated by about 3 feet. The voltage of the discharge to the insulated cylinder was nearly equal to that of the discharge to the end-plates (see Figs. 2 and 3, ref. 2) until that voltage exceeded (e/c28mj)H2r2, mj being the molecular weight of the ion. Then the voltage of the insulated cylinder remained constant at (e/28m4)H2rg as the voltage of the end-plates was raised further. The ion current at the insulated cylinder was equal to the total ion current received by the end-plates. When the cylinder was made up of radial slats, the deposit of ions was found on one side of the slats only, the other side being absolutely clean. This result, that the ion current to the insulated cylinder remains equal to one half the total ion current from the central arc, if the voltage applied to the endplates is high enough, seems quite inexplicable according to the theory advanced by Simon and Rosenbluth.13'8 Looking at Figure 2 of their paper,' we see that they take the radius of the outer wall of their "cyclotron" as infinite, whereas it should have a finite radius. Chapter VII of a recently published book9 gives the results which check my own findings and are thus in sharp disagreement with those of Simon and Rosenbluth. l Simon, Albert, and Marshall N. Rosenbluth, Phys. Fluids, 6, 1566 (1963). 2 Slepian, J., these PROCEEDINGS, 47, 313 (1961). 3 Ibid., 1173 (1961). 4 Ibid., 50, 6 (1963). 6 Slepian, J., Proc. Phys. Soc. (London), 81, 587 (1963). 6 Slepian, J., Phys. Fluids, 3, 490 (1960). 7 Simon, A., Phys. Fluids, 3, 490 (1960). 8 Rosenbluth, M. N., and N. Rostoker, Phys. Fluids, 2, 23 (1959). 9 Ferraro, V. C. A., and C. Plumpton, Magneto-Fluid Mechanics (Oxford Univ. Press, 1961).