WHITLOCK. — CRYSTAL FORMS OF CALCITE. 291 



missing from the developed zone their position is indicated by 

 dots. 3 



It is frequently advisable to divide a zone into fragments, in which 

 case certain points, fixed in the projection by zonal intersections and 

 occupied by the poles of notably frequent and important forms, are 

 taken as the end forms of a series, and are known as " knot points." 



No attempt has been made in the discussion to include forms 

 which have been considered by former monographers as doubtful 

 or vicinal as, in the writer's opinion, such an extension of the discus- 

 sion would not materially add any new light and would unduly cumber 

 the criticism with useless matter. 



In many instances throughout the discussion it will be found that 

 forms of comparatively simple indices and reducible to numbers 

 of low normal series are missing from the hitherto observed forms. 

 Where such an obviously probable form occurs in the series, it will be 

 set aside as a hypothetical form, that is, one which will in all proba- 

 bility be ultimately added to the list of observed forms. It has not 

 been considered wise to develop any portion of a zone further than 

 normal series 4 — X4, although in tabulating the results at the end of 

 each discussion, a column headed " N5 " has been included. 



Knot-points have been assumed at the poles of such obviously 

 common and important forms as <p. (0221), K : (2131), p: (1341) etc. 

 Using the Knot-points of established zones for poles through which 

 to pass zones subsequently to be discussed and numbering the zones 

 approximately in the order in which they are thus established we have 

 the network of zone intersections shown in Plate 1, which is a gno- 

 monic projection of the field covered by about 80° from the pole of 

 (0001). The zones here shown will be designated throughout the 

 discussion by the letter Z followed by an index; thus zone 6 will be 

 designated by Z6. The zones shown on Plate 1 are as follows : 



3 A brief summary of the critical methods here employed will be found in 

 W. F. Hillebrand and W. T. Schaller, Bull. 405, U. S. Geol. Surv., p. 14 

 (1909). 



