* Introduction. vii 



I have also attempted to supply some rules for 

 studying the forms of crystals, and for what may be 

 termed reading them ; which, although they may not 

 enable the learner to trace at once the relation of the 

 different crystalline forms to each other, they will 

 certainly assist him in his examination of the minerals 

 themselves ; and it is from an attentive study of these 

 that he must at last derive his best information. 



From the very elementary nature of some of the 

 definitions, it is evident that the reader of the earlier 

 part of the volume is supposed to be unacquainted 

 with the first rudiments of geometry. By being thus 

 elementary I have been inclined to hope that crystal- 

 lography may be rendered more familiar, and its prin- 

 ciples be more easily acquired: and that the young- 

 collectors of minerals may be led by these first and 

 easy steps in the path of science, to make their collec- 

 tions subservient to the cultivation of higher sources 

 of amusement. 



The description of the principle and of the method 

 of using the reflective goniometer, has been mi- 

 nutely detailed on account of the importance of the 

 instrument to the practical mineralogist, and with a 

 view to remove the impression of its application to 

 the measurement of crystals being difficult. 



The Abbe Haiiy has used plane trigonometry in 

 his calculations of the laws of decrement. The sub- 

 stitution of spherical for plane trigonometry in this 

 volume, was made at the recommendation of Mr. 

 Levy ; from whom I have also received many other 

 valuable suggestions relative to the methods of cal- 

 culation employed in the section on calculation ; 

 which it will be apparent to the reader, is little more 

 than an outline of a method which must frequently be 

 filled up by the exercise of his own judgment. In 

 this as well as in other respects the mathematical 



