352 PROCEEDINGS OF THE AMERICAN ACADEMY. 



in this instance. The pole of (5 •12-17 -8) lies at the intersection of 

 the zones [5164 : 0- ll-TI-4] and [1123 : 1341] both of which are well 

 defined. The form is considerably more probable than the preceding. 



General Conclusions. 



In reviewing the foregoing discussion several facts are brought out 

 with more or less clearness. 



1. — The forms whose poles are marked by three zone intersections 

 are those which a student of the species would recognize as common 

 forms. An apparent exception to this statement is to be found in the 

 negative rhombohedron (0551). The expression "apparent" is used 

 because in the experience of the writer this form is far more common 

 on calcite crystals than is usually conceded. 



2. — It will be noted that the zone of the second order pyramids 

 Z 2 is marked by a fair number of zone intersections and that where 

 the poles of the second order pyramids, particularly those of the (1123), 

 (2243), (4483) etc., series fall in other zones they occur in relatively 

 low normal series. It would be seen that this series of pyramids, which 

 has been regarded as rare up to a comparatively recent date 163 is con- 

 siderably more common than has been hitherto recognized. Thi3 

 again coincides with observation, the pyramid (8 -8 -IB -3) having 

 been the dominant habit in at least four new occurrences of calcite 

 falling under the writer's notice within the last five years. 164 



3. — That portion of the principal zone, Z4, lying between the poles 

 p (1011) and P: (3251) shows a completeness with respect to recorded 

 forms which argues strongly against subsequent additions to this part 

 of the zonal field. Especial care should be exercised by future ob- 

 servers and tentative interpolated forms should be strictly criticized 

 and if possible referred to established indices. 



4. — Although zones Z5, Z$ and Z7 are strongly marked there are 

 several gaps in normal series N 3 some of which will undoubtedly be 

 filled by future observation. The investigator of calcite should keep 

 these well in mind and weigh carefully the data concerning forms whose 

 poles fall sufficiently near them to be within the limits of goniometrical 

 measurement. 



163 See Penfield and Ford, Am. Jour. Sci., 10, 238 (1900). 



164 These occurrences are Kelley's Island, Wisby and two undescribed 

 Canadian localities. 



