An approximate theory has been derived describing part of the sound field due to a concave spherical radiator, vibrating with uniform normal velocity; the radius a of the circular boundary is assumed to be large relative to the wave-length and large relative to the depth of the concave surface. The theory describes the distribution of pressure, particle velocity, and intensity along the axis of symmetry and in the vicinity of the focal plane, perpendicular to the axis at the center of curvature. It is shown that the ratio of the intensity at the center of curvature to the average intensity at the radiating surface is nearly equal to (2πh/λ)2 where h is the depth of the concave surface and λ is the wave-length. This ratio can be made very large by suitable choice of dimensions, and the focusing is then very sharp. The point of greatest intensity is not at the center of curvature but approaches it with increasing kh = 2πh/λ, and the greatest intensity is not much greater than the intensity at the center of curvature except when kh is small. In the central part of the focal plane, at angle θ from the axis, the pressure is approximately proportional to (2/ka sinθ)J1(ka sinθ), which is equivalent to the directivity function of a flat circular piston of radius a, for the region at large distance from the piston. The calculations are in reasonable agreement with G. W. Willard's experimental data for a 5-mc concave quartz crystal, when allowance is made for the non-uniform normal velocity of the crystal.

The exact equation of the propagation of plane sound waves in air is not linear and consequently harmonics and combination tones are generated. The pressure of these extraneous frequencies in terms of the fundamental pressure, frequency, and distance from the source has been mathematically determined by Rayleigh, Lamb and others. These equations have been applied to an exponential horn. Measurements of the second harmonic and combination tones have been made at various points within a long tube, and in front of an exponential horn. Measurements, in general, agree with theory, but the absolute values are lower than the calculated values.

Now for energies less than Q 0 (3 Mev in our case) the range energy curve for electrons can be closely approximated by, 14 R(Q) = 0AQ lb 02 in Mev).In view of this relation and that of Eq. (1) one obtains by performing the integrations in Eq. (7) 14 L. E. Glendenin, Nucleonics 2, 12 (1948).

The exact equation of the propagation of plane sound waves in air is not linear and consequently harmonics and combination tones are generated. The pressure of these extraneous frequencies in terms of the fundamental pressure, frequency, and distance from the source has been mathematically determined by Rayleigh, Lamb and others. These equations have been applied to an exponential horn. Measurements of the second harmonic and combination tones have been made at various points within a long tube, and in front of an exponential horn. Measurements, in general, agree with theory, but the absolute values are lower than the calculated values.

We present the optical design of the Background Emission Anisotropy Scanning Telescope (BEAST), an off-axis Gregorian telescope designed to measure the angular distribution of the cosmic microwave background radiation (CMBR) at 30 and 41.5 GHz on angular scales ranging from 20' to 10 degrees. The aperture of the telescope is 1.9 m, and our design meets the strict requirements imposed by the scientific goals of the mission: the beam size is 200 at 41.5 GHz and 260 at 30 GHz, while the illumination at the edge of the mirrors is lower than -30 dB for the central horn. The primary mirror is an off-axis section of a paraboloid, and the secondary an off-axis section of an ellipsoid. A spinning flat mirror located between the sky and the primary provides a two-dimensional chop by rotating the beams around an ellipse on the sky. BEAST uses a receiver array of cryogenic low noise InP High Electron Mobility Transistor (HEMT) amplifiers. The baseline array has seven horns matched to one amplifier each and one horn matched to two amplifiers (two polarizations) for a total of nine amplifiers. Two horns operate around 30 GHz, and six operate around 41.5 GHz. Subsequent campaigns will include 90 GHz and higher frequency channels