1887.] On the Theory of Mathematical Form. 193 



was written I have discovered a method of making fibres with a 

 perfect elasticity, and so have avoided the inconvenience of the 

 shifting zero of the glass fibre, and with a torsion, if required, ten 

 million times less than that of spun glass. This will be described at 

 the next meeting of the Physical Society. 



II. V Note to a Memoir on the Theory of Mathematical Form 

 ('Phil. Trans.' 1886 (vol. 177), p. 1)." By A. B. Kempe, 

 M.A., F.R.S. Received February 26, 1887. 



An interesting letter of criticism from Professor 0. S. Peirce on 

 my recently published Memoir on the Theory of Mathematical Form 

 has led me to reconsider certain paragraphs therein, relating to the 

 definition of what I have termed " aspects," and I am anxious to 

 make the following amendments. 



For Section 5 substitute — 



5. In like manner some pairs of units are distinguished from each 

 other, while others are not. Pairs may in some cases be distinguished 

 even though the units composing them, are not. Thus the angular 

 points of a square are undistinguishable from each other, and a pair 

 of such points lying at the extremities of a side are undistinguished 

 from the three other like pairs, but are distinguished from each of the 

 two pairs arrived at by taking the angular points at the extremities of 

 the diagonals, which pairs again are undistinguishable from each 

 other. Further, though two units a and b are undistinguishable 

 from each other, an absence of symmetry may cause ah to be dis- 

 tinguished from ba. Thus, if we put aside differences arising from 

 their positions on the paper, and the use of reference letters (Sees. 

 41 and 42), the three black spots, a, b, c, shown in fig. 1, are undis- 

 tinguished from each other; but ab is distinguished from ba, for 

 when we take the spots a, b, in the order ab an arrow proceeds from 

 the first spot to the second, but when we take them in the order ba 

 an arrow proceeds to the first spot from the second. 



For Section 7 substitute — 



7. Again, there are distinguished and undistinguished triads, 

 tetrads, .... m-ads, .... w-ads, . . . . ; every m-ad being of 

 course distinguished from every w-ad. Just as we may have ab dis- 

 tinguished from ba, though a is undistinguished from b, so we may 

 have pqrst . . . . uv distinguished from qusvt . . . . rp, though the 

 units p, q, r, s, u, v, are all undistinguished from each other, 



and further, though their pairs are also undistinguished, as likewise 

 their triads, &c. Here pqrst . . . . uv and qusvt . . . . rp will be 

 termed, as in the case of pairs, different aspects of the collection 

 p, q, r, s, t, . . . . u, v. An aspect will be fully defined and con- 



VOL. xlii. p 



