I.  As to your enquiry about the Cathari, i.e.the followers of Novatian.  cf. Eusebius vi. 43.  cf. De. Sp. Scto. ch. x. p. 17 and note. a statement has already been made, and you have properly reminded me that it is right to follow the custom obtaining in each region, because those, who at the time gave decision on these points, held different opinions concerning their baptism.  But the baptism of the Pepuzeni Or Pepuziani, another name for the Montanists.  “Epiphanius may safely be disregarded, who, treating of the Montanists, in the 48th section of his work on heresies, treats of the Pepuziani, in the 49th, as a kindred, but distinct, sect.”  Dr. Salmon in D.C.B. iv. 303.  The name is derived from Pepuza in Western Phrygia, the Montanist, or Cataphrygian, “Jerusalem.”  (Eus. H.E. v. 18.) seems to me to have no authority; and I am astonished how this can have escaped Dionysius, i.e. of Alexandria.  Jerome (Vir. illust. lxix.) says that he agreed with Cyprian and the African Synod on the rebaptizing of heretics.  The Ben. note says:  “Videtur hac in re major auctoritas Basilio attribuenda quam Hieronymo.  Plus operæ insumpserat Basilius in ea re examinanda.” acquainted as he was with the canons.  The old authorities decided to accept that baptism which in nowise errs from the faith.  Thus they used the names of heresies, of schisms, and of unlawful congregations. παρασυναγωγή.  By heresies they meant men who were altogether broken off and alienated in matters relating to the actual faith; by schisms Archbp. Trench (N.T. Syn. 330) quotes Augustine (Con. Crescon. Don. ii. 7):  “Schisma est recens congregationis ex aliquâ sententiarum diversitate dissensio; hæresis autem schisma inveteratum;” and Jerome (Ep. ad Tit. iii. 10):  “Inter hæresim et schisma hoc esse arbitrantur, quod hæresis perversum dogma habeat; schisma propter episcopalem dissensionem ab ecclesiâ separetur; quod quidem in principio aliquâ ex parte intelligi queat.  Cæterum nullum schisma non sibi aliquam confingit hæresim, ut recte ab ecclesia recessisse videatur.” To these may be added Aug. (Quæst. in Matt. xi. 2):  “Solet autem etiam quæri schismatici quid ab hæreticis distent, et hoc inveniri quod schismaticos non fides diversa faciat sed communionis disrupta societas.  Sed utrum inter zizania numerandi sint dubitari potest, magis autem videntur spicis corruptis esse similiores, vel paleis aristarum fractis, vel scissis et de segete abruptis.” men who had separated for some ecclesiastical reasons and questions capable of mutual solution; by unlawful congregations gatherings held by disorderly presbyters or bishops or by uninstructed laymen.  As, for instance, if a man be convicted of crime, and prohibited from discharging ministerial functions, and then refuses to submit to the canons, but arrogates to himself episcopal and ministerial rights, and persons leave the Catholic Church and join him, this is unlawful assembly.  To disagree with members of the Church about repentance, is schism.  Instances of heresy are those of the Manichæans, of the Valentinians, of the Marcionites, and of these Pepuzenes; for with them there comes in at once their disagreement concerning the actual faith in God.  So it seemed good to the ancient authorities to reject the baptism of heretics altogether, but to admit that of schismatics, τῶν ἀποσχισάντων, ὡς ἔτι ἐκ τῆς ἐκκλησίας ὄντων. The Ben. note is “Quod autem addit Basilius, ut adhuc ex Ecclesia exsistentium, non idcirco addit quod schismaticos in Ecclesiæ membris numeraret.  Illius verba si quis in deteriorem partem rapiat, facilis et expedita responsio, Nam sub finem hujus, canonis de Encratitis ipsis, id est, de hæreticis incarnationem et Dei singularitatem negantibus, ait sibi non jam integrum esse eos qui huic sectæ conjuncti sunt ab Ecclesia separare, quia duos eorum episcopos sine baptismo ac sine nova ordinatione receperat.  Nemo autem suspicabitur Basilium ejusmodi hæreticos ab Ecclesia alienissimos non judicasse.  Quare quidquid schismaticis tribuit, in sola baptismi societate positum est.  Nam cum Cyprianus et Firmilianus schismaticos et hæreticos ita ab Ecclesia distractos crederent, ut nihil prosus ad eos ex fontibus Ecclesiæ perflueret; Basilius huic sententiæ non assentitur, et in schismaticis quia fidem Ecclesiæ retinent, vestigium quoddam agnoscit necessitudinis et societatis cum Ecclesia, ita ut valida sacramentorum administratio ab Ecclesia ad illos permanare possit.  Hinc sibi integrum negat detestandos hæreticos ab Ecclesia separare, quorum baptisma ratum habuerat.  Idem docent duo præstantissimi unitatis defensores.  Optatus et Augustinus.  Quod enim scissum est, inquit Optatus lib. iii. n. 9, ex parte divisum est, non ex toto:  cum constet merito, quia nobis et vobis ecclesiastica una est conversatio, et si hominum litigant mentes, non litigant sacramenta.  Vid. lib. iv. n. 2.  Sic etiam Augustinus lib. i.  De baptismo n. 3:  Itaque isti (hæretici et schismatici) in quibusdam rebus nobiscum sunt:  in quibus autem nobiscum non sunt, ut veniendo accipiant, vel redeundo recipiant, adhortamur.  Vid. lib. iii. n. 26.  Sic ex Basilio hæretici nobiscum sunt quoad baptisma.” on the ground that they still belonged to the Church.