20 W. E. Ford — Remarkable Txovas of Ataoamite. 



these faces particularly in the case of the ^ angles. This is a 

 result to be expected from the iisnal rather poor (piality of the 

 prism faces and from the fact that tliey are frequently verti- 

 cally striated. 



It will he noticed that in the case of the one-circle goniom- 

 eter measurements the agreement between the measured and 

 the calculated angles is much closer and in general is very satis- 

 factory. This is as would be expected, since with these small 

 crystals having not the best of faces the adjustment of a crys- 

 tal upon the two-circle goniometer is difficult and can only be 

 approximate at the best, and consequently the angles measured 

 upon it have not as great an authority as those made upon the 

 one-circle instrument where the adjustment is made for each 

 measurement. Considering, however, all the measurements, 

 their agreement with the theoretical angles is sufficiently exact 

 to prove without doubt that the law of twinning has been cor- 

 rectly stated. 



The author does not know of any case of twinning strictly 

 analogous to the one outlined above, and he does not offer any 

 elaborate explanation or theory to account for the peculiarities 

 shown by these twins. An interesting and probably significant 

 fact is that, when in twin position, the faces of individual No. 

 II lie for the most part within a few degrees, at least, of the 

 faces of the normal individual, ISTo. I. This is clearly brought 

 out in the stereographic projection, figure 4, where e' of IS^o. II 

 lies near m of Ko. 1 ; m" of II near 7n"' of I ; m' of II near 

 e' of I ; and h' of II falls near the macrodome zone of I. 

 It would seem here as if we had a case of twinning in which 

 the position of the twin individual was controlled rather by 

 parallelism of a prominent face and by zonal relations between 

 the two individuals than by the presence of a common twin- 

 ning plane or axis. The plane P, which if a possible crystal 

 plane would be considered as the twinning plane, may be 

 regarded as a composition or accommodation plane similar in 

 a way to the rhombic section found in the plagioclase feld- 

 spars when they twin according to the pericline law. 



That all regular intergrowths of crystals do not obey the 

 ordinary laws of twinning has been recognized for some time.* 

 These intergrowths are not accidental in character, but obey 

 laws that can be definitely formulated; they are to be found 

 repeatedly on different specimens and must be included in any 

 complete discussion of twinning. Goldschmidt has recently 

 attempted to include these unusual intergrowths in a new clas- 

 sification of twins and has given various names to the new 

 groups he has formed, such as " Heterozwillinge," " Ein- 

 *See Goldschmidt, Zs. Kr. xxx, 254, 1898; xliii, 347, 1907. 



