It is a simple matter to verify that the second double sum involving d ftPiXlc does not contribute to the stressenergy tensor. The /=m=0 term of the first double sum is excluded, of course, by definition (2). The part of the first sum, with w=0, Z^O, gives the zero-temperature contribution to the stress-energy tensor which we have already considered; the part with 1=0, w^O gives the blackbody contribution which we have just discussed.It is straightforward to show that the sum remaining with neither / nor m vanishing gives the finite-temperature, finite-plate separation correction quoted in Eqs. (17)-(22).
ACKNOWLEDGMENTSWe have enjoyed fruitful conversations on this topic with David Boulware and Robert Puff.Equipment consisting of an ionization spectrometer and spark chambers has been exposed to primary cosmic rays in a balloon flight which allowed a data collection time of 14.3 h at an altitude of 5.7 g/cm 2 . The purpose of this experiment was to study the flux, composition, possible time variations, and nuclear interaction properties of cosmic rays at energies between 44) and 400 GeV. The apparatus has also been exposed to 10-, 20.5-, and 28-GeV/c protons at the Brookhaven AGS in order to study the spectrometer response at three known energies and to be able to extrapolate this response to higher energies. The integral energy spectrum of primary cosmic-ray protons between 40 and 400 GeV was found to be n(>E 0 ) = (0.91.o.2 +0 -8 ) £o _1 -7±01 (E in GeV). The corresponding intensity is a factor of 2 lower than that obtained from the Proton I and II satellite experiments.