126 LOCKHART, PATTERSON, AND SAUNDERS the coefficient matrix of the terms in the system of four simultaneous linear equations. The criteria used were that the filter retentivities or coefficients derived be reasonably close to the filter calibration data and, in addition, permit real solutions to some 40-odd filter collec- tions. A tentative solution has been formulated as follows, where the terms correspond to those of the previous set of equations: A, = 95.00 x, + 30.00 x, + 10.00 x; + 2.00 x, A, = 4.75 x, + 21.00 x, + 9,00 x; + 1.96 x, Az = 0.25 x, + 48.80 x. + 77.80 x3 + 38.00 x, A, = 0.00 x; + 0.20 x, + 3.20 x, + 58.04 x, Particle-size distributions derived for some of the four-filter collections are shown in Table 2. The sizes listed are really particleTable 2— PARTICLE-SIZE DISTRIBUTIONS DETERMINED FROM SOME FOURFILTER-PACK COLLECTIONS OF RADIOACTIVE FISSION PRODUCTS Total Callection dates activity, counts/min 1963 Jan. 18 to 21 Mar. 1 to 4 Apr. 19 to 22 Oct. 18 to 21 Oct. 25 to 28 Nov. 1 to 4 679.9 1423.9 3098.8 380.3 173.7 143 9 1964 Mar. 20 to 23 274,2 Apr. 7 to 10 273.0 Mar. 24 to 27 Apr. 3to7 311.3 456.6 we Activity Activity contribution of maim ci Cc on initial filter, varlous size groups, lip O6p O.3y O.45p 31.3 33.6 27.68 46.0 38.7 34.8 45.3 25,4 21.1 34.8 25.8 17.8 16.0 11.6 2.7 31.9 35,2 49.6 45.4 +0.4 30.1 30,1 33.38 40.3 18.4 + 0.5* 20,2 + 0.1 40.3 + 0.4 + 0.4 42.6 +0.3 39.0+0.2 32.4 24.1 26.2 43.4 38.5 34.2 38,4 67.2 33.1 36.0 29.3 18.0 39,0 30.6 42.3 4.5 4.5 9,0 0.2 3.6 3.2 1.8 2.4 1.9 0.8 Weather eee Cloud cover, % 100 30 40 30 80 30 RO 60 80 60 Rainfall, in. 0.42 0.04 Trace 0.0 Trace 0.71 1.05 0.01 0.76 0.64 *Standard deviation, 0, based on counting statistics. Size distributions of unknown form centered about the indicated particle size. If it can be assumed that the equations adequately define the filter system under the operating conditions given in the table or that the filters and their calibration can be accepted as a standard, measurements made at other times and perhaps under other conditions can be interpreted in terms of the standards. Moreover, simultaneous pack collections, wherein one pack is a duplicate run of the standard that serves to characterize the radioactivity distribution during that particular sampling period, can be employed to define the filtration characteristics of an unknownfilter. The size distributions shown in Table 2, calculated from the four-equation set, again demonstrate that there have been large random changes in size distribution with time, as well as a progressive decrease in size which occurred immediately after cessation of atmo-