The following procedure is recommended for analysis of process 0: (1) Define a region AB on the Dalitz plot where the resonance A may distort the analysis. (2) Check that AB does not include any point corresponding to COSA 23 * = 0 [see Fig. 1(c)].(3) Define a C region large enough to contain the A'B f region. (4) For each event included in C, go to the c.m.s. of particles 2 and 3, interchange their direction, and make thereby a fictitious conjugate event. (5) Ignore the fictitious conjugate events which do not fall into AB.(6) Remove the true events from region AB and repopulate this region with the fictitious conjugate events.One should remember when making the x 2 fits that the sample of fictitious events is highly correlated statistically to the sample of true events from which the former were constructed.The same method can be applied to study the process a provided that AB does not include the points where cosA 12 * = 0 in the A c.m.s.Finally, if one makes an analysis of what is in AB region alone and subtracts from the histograms the contributions of 0 and a, represented by the two kinds of fictitious events in the B c.m.s. andIn this paper we show that an improved (3, 3) isobar model for single pion production in pionnucleon collisions can account for the majority of the observed mass spectra and the ratio of 7T° to 77 + production in ir + -p collisions from 350 MeV to 1 BeV. This is in contrast to earlier analyses using the isobar model. i " 4 The essential new feature of the present analysis is the inclusion of the P-wave decay of the (3, 3) isobar.Although the rough features of the shape of the mass spectra predicted by the isobar model of Lindenbaum and Sternheimer 1 " 3 (called LS model hereafter) have been observed in many experiments, 5 " 8 the LS model fails to describe the IT -TT mass spectra. The main approximations of the LS model are that (a) the interference between the two isobar diagrams (see Fig. 1) can be neglected, (b) the isobar is produced in a S state and (c) the isobar decays isotropically. Bergia, Bonsignori, and Stanghellini 4 (called BBS model hereafter) in the A c.m.s., respectively, one can then study the interference (i.e., process y) by itself. One should remember, however, that in such an operation, one has subtracted the background (process 6) twice.An alternate technique to the one proposed above would be to use a rotation, in the c.m.s. of the resonance being studied, of 180° around the normal n to the plane of production (instead of the spatial parity operation used above). This is equivalent to the product of a spatial parity operation and a reflection with respect to the production plane (a good operation if over-all parity is conserved). With that alternate technique, one should remember that the conjugation inverts the components of the decay particle spins in the plane of production.Two tests to check the uniformity of the background from process 6 are (1) symmetry in eosA 2 3* for those events in band B but not in AB or A'B', (2) symmetry with respect to the quantit...