J. M. Blake — Plotting Crystal Zones on Paper. 487 



but their presence prevents exact measurement of the perfect 

 crystal, while the want of exactness in determining the perfect 

 crystal likewise interferes with the study of the laws of the 

 vicinal planes. 



A common practice has been to measure two or three of the 

 angles between prominent crystal faces, and to calculate the 

 angles between the remaining faces from these measurements. 

 These angles have sometimes been measured from certain 

 planes which, in a given species, are found to be habitually 

 subject to variation, and in such a case all the calculated angles 

 would be subject to error. 



In carrying out this present method, the zones are plotted 

 from the goniometer measurements, and by this means the sys- 

 tem of equal spacing can be at once developed. We will thus 

 have our work mapped out and the position of the axes indi- 

 cated. The goniometer measurements should furnish a record 

 of the character of the planes in regard to their reflections, and 

 this record will guide us in our selection of the most suitable 

 of the developed spaces from which to estimate the axial ratios. 

 This plan will be found very simple and will require no resort 

 to equations or formulas, while the results in very many 

 instances may be made to exceed in accuracy those obtained by 

 the present commonly used methods. 



Epidote has been selected for the purpose of illustrating the 

 present paper. Decloiseaux has collected data from many 

 sources, and he gives elaborate tables of angles in his Mineral- 

 ogy (1862). He mentions various groups of associated planes 

 on specimens from widely scattered localities. It would seem 

 that the search had been thorough for all possible planes. 

 There remains the possibility that some planes of uncertain 

 standing may have been included, and other errors are possible. 

 The process of clarification and elimination usually adopted in 

 making up crystal descriptions may at times destroy details 

 which would be valuable in making future revisions. 



Plotting an Individual Zone. — This can be done with ease 

 from the complete serial goniometer readings, but more diffi- 

 culty is encountered when we have to work from a published 

 description, as in the case of epidote. In this published descrip- 

 tion, scattering measurements are given, and also the solid 

 angles and not the angles between the normals ; and besides, 

 some of the planes are difficult to locate for the reason that we 

 miss the sequence which complete zone measurements should 

 furnish. Under the conditions as we proceed, we are con- 

 stantly reminded that our method is leading us outside the 

 regular traveled paths. 



The work of Decloiseaux is valuable for its thoroughness. 

 It does not, however, have all the elements we could desire for 



