34 REPORT — 1878. 



Page 15, line 23. ' Royal Society's Proceedings,' May 9, 1878. 



P. 15, 1. 33. ' Phil. Trans./ Vol. 169, pp. 55 and 155, and other Papers cata- 

 logued in the ' Appendix to Part II. of the Memoir.' 



Page 16, line 25. See Maxwell ' On Heat,' chap. xxii. 



P. 17, 1. 29. Grunert's ' Archiv,' Vol. vi., p. 337 ; also separate work, Berlin, 

 1862. 



P. 17, 1. 31. ' Linear Associative Algebra,' by Benjamin Peirce, Washington 

 City, 1870. 



P. 18, 1. 10. Sir W. Thomson, ' Cambridge Mathematical Journal,' Vol. iii., p. 

 174. Jevons' ' Principles of Science,' Vol. ii., p. 438. 



But an explanation of the difficulty seems to me to be found in the fact that the 

 problem, as stated, is one of the conduction of heat, and that the " impossibility " 

 which attaches itself to the expression for the " time " merely means that previous 

 to a certain epoch the conditions which gave rise to the phenomena were not those 

 of conduction, but those of some other action of heat. If, therefore, we desire to 

 comprise the phenomena of the earlier as well as of the later period in »ne problem 

 we must find some more general statement, viz., that of physical conditions which 

 at the critical epoch will issue in a case of conduction. I think that Prof. Clifford 

 has somewhere given a similar explanation. 



P. 21 1. 13. S. Newcomb ' On Certain Transformations of Surfaces/ ' American 

 Journal of Mathematics,' Vol. i., p. 1. 



P. 21, 1. 14. Tait ' On Knots,' ' Transactions of the Royal Society of Edinburgh,' 

 Vol. xxviii., p. 145; Klein, ' Mathematische Annalen,' ix., p. 478. 



P. 27, 1. 18. ' Royal Society's Proceedings,' February 3, 1876, and May 9 

 1878. i™™5 



P. 30, 1. 1. For example, in Herbart's ' Psychologies 



P. 30, 1.3. A specimen will be found in the ' Moralia ' of Gregory the Great, 

 Lib. I. c. xiv., of which I quote only the arithmetical part: 



" Quid in septenario numero, nisi sunima perfectionis accipitur ? Ut eniui 

 humanee rationis causas de septenario numero taceamus, quae afferunt, quod idcirco 

 perfectus sit, quia expriino pari constat, et primo,_ impari ; ex primo, qui 

 dividi potest, et primO, qui dividi non potest; certissime scimus, quod sep- 

 tenarium numerum Scriptura Sacra pro perfectione ponere consuevit. _. . 

 A septenario quippe numero in duodenarium surgitur. Nam septenariu3 suis in 

 se partibus niultiplicatus, ad duodenarium tenditur. Sive enim quatuor 

 per tria, sive per quatuor tria ducantur, septem in duodecim vertuutur. . . . 

 Jam superius dictum est quod in quinquagenario numero, qui septem hebdomadibus 

 ac monade addita impletur, requies desiguatur ; deuario autem numero suuinia per- 

 fectionis exprimetur." 



P. 30, 1. 16. Approximate dates B.C. of — 



