10 



Limonite. Bronzite. 



Fe O per cent 576 



CaO „ 071 8-64 



MgO „ 0-86 32-83 



HaO „ 12-53 



99-28 100-85 



"Note on Envelopes and Singular Solutions," by Sir 

 James Cockle, F.R.S., F.R.A.S., &c, Corresponding Member 

 of the Society. (Continued from Vol. XXI., p. 100.) 



16. Arts. 13 and 15 (misnumbered 14) require a correc- 

 tion. The tac-locus occurs twice (see Mr. J. W. L. Glaisher's 

 Examples, &c., Messenger, N.S., No. 183, May, 1882). And 

 in art. 13 (p. 100, line 1) the reference should be to No. (not 

 vol.) 36, vol. III. 



17. Conceive a system of primitive curves, all constructed 

 according to one law and depending upon a single arbitrary 

 parameter; and each, therefore, marked by the magnitude 

 of its parameter. 



18. When every primitive curve is an envelope, then each 

 touches every other, and the places, or the limits of the 

 places, of intersection of consecutives will be the envelopes. 

 Such places, or limiting places, will be either points or 

 curves. Take them to be primitive curves, finite in number. 

 Then every primitive curve is not an envelope. Take their 

 number as indefinitely large, still they will not (except upon 

 the inadmissible supposition that consecutives entirely 

 coincide, and so are, in fact, identical) comprise every par- 

 ticular primitive curve. Hence, when all the primitive 

 curves are envelopes, the envelopement does not take place 

 along curves. 



19. If all the primitive curves are in mutual contact at a 

 certain point draw their common tangent, and when it does 

 not pass through the origin then on it, let fall a perpen- 

 dicular from the origin. The point of envelopement will lie 



