Extensive air-shower trajectories and sizes (numbers of charged particles) have been measured using an optical detection system at Volcano Ranch Station near Albuquerque, New Mexico. Light produced by atmospheric scintillation and Cherenkov emission by shower particles was measured at distances of 0.7 to ~ 10 km. The shower sizes determined by the optical measurements are in satisfactory agreement (an average of 10% higher) with measurements by the ground-level scintillation-counter array at Volcano Ranch.

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Dividing both sides of (14) by {o P + o A ) E , it is straight forward to show ( E r l/2 ]We define the unboundedness of the total cross sections as lim {o P J) B = «>.Hence if (o>) and (cr A > are both unbounded the rhs of (15) is zero which is the desired result [Eq.(1)]. Equation (14) shows that the same result holds if only one of the total cross sections is assumed to be unbounded; it then follows that the other cross section must be unbounded, too. From Eq. (1) or (10) it is also clear that there exists a set of points {£*}, ^j-* 00 , on which Aa/ (Op + a A )-~0; in particular, if Aoy^Op + oJ has a limit, this limit is zero.We should like to emphasize that inequality (14) is quite general; it is also valid if we replace (v P ) E and {o^) E by the corresponding elastic cross sections. If one is willing to make a strong assumption that o P , o A are bounded then the coefficient I on the rhs of (12) and (14) should be replaced by unity. In this case one gets a generalization the results of Roy and Singh. 6 For pion-nucleon scattering, if isospin invariance is assumed, a restriction on (Aa) £ in terms of the charge-exchange cross section ir~p -n°n can be similarly obtained. 1 U. Amaldi et al,, to be published; S. R. Amendolia et al., to be published.We report here the results of a measurement of the integral energy distribution of the neutrino-induced muon flux deep underground using the Utah neutrino detector. Five neutrino-induced muon candidates have been obtained from the approximately 10 6 muons which have passed through the detector during 603 days of live operation out of 830 days total elapsed time. By comparing the observed and expected energy distributions we are able to set lower limits on the saturation energy EQ of the total neutrino-nucleon cross section or, equivalently, on the mass M w of the intermediate vector boson if scale invariance of the inelastic structure function vW 2 is assumed. We find at the lcr, 2320, 80, and 29 GeVorM w >10, 5, and 3 GeV, respectively.The observation of a muon flux induced by the interaction of cosmic-ray neutrinos in rock deep underground has been used to investigate the nature of the weak interaction. 1 " 4 Previous experiments have yielded values for the integral muon flux, but none thus far has analyzed the high-energy spectrum of the observed muons. In this communication, we report the results of a measurement of the spectrum of the underground neutrino-induced muon flux made possible by the unique University of Utah neutrino detector. 5 " 8 We compare the observed spectrum with those calculated for different assumptions concerning the high-energy (E v > 10 GeV) behavior of the neutrino-nucleon total cross section. 9 Comments are made on the scale invariance of the structure functions measured in inelastic neutrino-nucleon scattering, and a lower limit is placed on the 66