Sir James Cockle on Criticoids. 201 



perhaps with those of the one or the other of the two fellow hemi- 

 scalenohedrons. The idea of the possibility of internal tensions 

 of this nature does not suggest itself respecting any substance 

 so readily as with regard to silica. If the three tensions are 

 perfectly equivalent, we shall obtain the normal right- or left- 

 rotating effect of quartz ; if all the three tensions are wanting, 

 or when they are balanced reciprocally, there will remain the 

 simple uniaxial effect without rotation, as we have it in many 

 amethysts at some portions. There yet remains the possibility 

 that, according to circumstances, those three tensions are of un- 

 equal intensity or are reduced to two ; and we should then have 

 the biaxial elliptical right- or left-rotating polarization met with 

 in such a marked manner in various quartzes, and as it is ob- 

 served in the built-up piles above described, or in arrangements 

 wherein one of the three systems of plates consists designedly of 

 somewhat thicker or thinner mica. 



With regard to the various phenomena in quartz and amethyst, 

 I beg leave to refer to the copious and well-arranged observations 

 contained in Dove's Farbenlehre (pp. 247-260). 



In conclusion, I must add that an acquaintance with the effects 

 of mica-combinations may possibly be of some value also for the 

 due appreciation of certain phenomena in mica itself. The trans- 

 formations of the system of rings in twins, as well as also the 

 frequent very considerable changes in the angle of the optic axes 

 in the same specimen, are rendered to a certain extent intelligible 

 if we assume the existence of regular penetration and intersection 

 on the part of different individuals. For my acquaintance with 

 these phenomena I am principally indebted to the communica- 

 tions I have received from G. Rose, and to the numerous pre- 

 sents of mica which he has kindly made me, and the possession 

 of which originally gave rise to my formation of the new mica- 

 combinations. 



Tubingen, July 1869. 



XXVI. On Criticoids. By Sir James Cockle, F.R.S., the Chief 

 Justice of Queensland, and President of the Queensland Philo- 

 sophical Society *. 



1. TN continuing to use the term critical function, instead of 

 J- semin variant penin variant or leading coefficient or source 

 of covariant, I do so, not from any predilection, but to avoid 

 words which might lead to the inference that the analogies, here 

 pointed out, between algebra and the differential calculus, are 

 susceptible of a greater extension than I am now prepared to 



* Communicated by the Rev. Robert Harley, F.R.S. 



