The solid angle subtended at a point by any object is determined by the closed contour which outlines the "visible" boundary of the object from the point. By transformation of the double integral 0= f f si.nHd8dtp into a si~gle integral over IJ. or tp 'Yith limits detern:ined by the contour ~nd choice of :ues, the solid angle may be rumply represented m the important cases dlScussed as a contour integral. The mtegration has been carried out on the high-speed digital computer ORACLE at Oak Ridge National Laboratory. Solid angle tables have been prepared for the case of the circular disk and the entire finite right circular cylinder in terms of cylindrical coordinates. Each table contains in excess of 12000 entries to six significant figures.

This paper summarizes the experimental and theoretical status of the optical chronograph developed in the course of ballistic research at the Naval Research Laboratory. The instrument, together with a simple procedure for analysis of data, is capable of yielding the position, velocity, and deceleration of a non-plastically deforming small arms projectile during the armor penetration process, which lasts from 30 to 150 microseconds. Decelerations have been observed up to 5×107 ft./sec.2. The longitudinal vibrations induced in projectiles during impact were observed by a shadow-photography technique which yields time-displacement curves from the motion of the trailing face of a projectile during penetration. The precision of the derived decelerations, about 4 percent, is sufficient to permit the evaluation of strain-rate and inertia effects during high speed indentation by means of conical indenters at strain-rates approaching 2×105/sec.

An improved design for fixed angle quantity type rotors is presented in which the holes are drilled at 10° to the axis of rotation and the Lusteroid tubes containing the centrifugate are individually sealed by means of tapered plugs. The advantages of this design are (a) increased capacity for a given diameter rotor, (b) prevention of tube collapse at all speeds and (c) more efficient concentration of materials in solution. Some charts illustrating differential sedimentation and concentration of proteins are given.

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