Blake — Solving Crystal Problems. 659 



planes made on the sphere, the first impression was, 

 that, since the planes were presented from a number of 

 viewpoints, and as a rule all their normal intersections 

 with certain tangent planes fell into equally spaced 

 rows or zones, that from this fact, taken in connection 

 with their several positions on the crystal, there could 

 be gathered data from which it would be possible to 

 make an exact determination of the angular distances 

 between the planes. We would thus be on the verge of 

 solving a most important crystal problem. 



As the development of the projections progresses the 

 conviction grows that there must be a law that could be 

 expressed or made apparent by tangents, and that this 

 law may be more fundamental even than the general 

 laws relating to crystal development, and that the study 

 of this basic tangent law by analytical methods should 

 precede the study of the laws that relate more specifi- 

 cally to crystal growth. 



It would appear that Naumann hoped to solve all 

 crystal problems by analytical geometry, but it may be 

 suggested that the want of success as it would now 

 appear, was due to failure at the start to fully grasp the 

 meaning of a fundamental natural law upon which to 

 base the analytical treatment. The existence of zones 

 of planes was of course understood, but their import- 

 ance as relating. to crystal development was not fully 

 taken into account, and the axial theory was allowed to 

 take the precedence. 



Many attempts have been made since Naumann 's time 

 to coordinate the results of years of work on crystals, 

 and various plans have been tried without effecting a 

 complete and satisfactory solution. If we can once 

 take such a comprehensive view of the situation as will 

 lead to the discovery of a fundamental law which we 

 have reason to believe does exist, we may then expect 

 that a very complicated situation will be resolved and 

 an entirely new point of view be reached. A basic 

 law, like for example the law of gravitation, should 

 admit of successful treatment by analytical methods. 

 The approach of such a desirable result as the complete 

 utilization of such a law, may seem far distant in view 

 of the present complicated conditions and want of coor- 

 dination of all the observed facts, and it is probable that 

 many successive steps will have to be taken before 



