146 Notices respecting New Boohs. 



no longer similar physically. The base will have all the circular 

 bases of the shot in it; the upper plane only the apices. The 

 two types are distinct structures, and the connexion between the 

 parallel faces is only a geometric one. In Prof. Maskelyue's book 

 the cylindrical pile would be regarded as a hemihedral form of that 

 of round shot arising from a loss of the centre of symmetry. With 

 this change of view goes, of course, a somewhat radical change in 

 the technical terms used to denote the type to which the crystal 

 belongs. The technical words used in the book are somewhat 

 complicated, and not always easy to comprehend and remember. 

 They are also rather numerous, and it is questionable whether 

 many of them will live. The phraseology in the new view has, as 

 far as the English student is concerned, yet to be created. 



The early portion, to which we have already alluded, is taken up 

 with the general relations which exist between the faces possible 

 on a crystal, subject, that is, to the law of rational indices. The 

 mathematical treatment is elegant, though in some cases it is 

 capable of considerable simplification ; as is the case, for instance, 

 in M. Cesaro's beautiful proof of the rationality of the anharmonic 

 ratio of four tautozonal planes. Prof. Maskelyne's treatment is a 

 great advance on anything which has emanated from the active 

 pens of our German friends. Of course a good deal of it follows 

 closely that of the late Prof. Miller, as, e. g., the elegant way of 

 obtaining formulae for the transformation of the axes of reference. 

 But Prof. Maskelyne has not been so anxious as his predecessor 

 to abbreviate his discussion, and his proofs are therefore more 

 easily followed and less artificial. 



A marked and excellent feature of the book is the amount of 

 space given to the discussion of those remarkable crystalline aggre- 

 gates known as twins. A good deal of the preparation for the 

 matter in this portion is probably due to Prof. Maskelyne's friends 

 at the Natural History Museum. The discussion of the more 

 conspicuous instances in each system is fairly complete. The 

 fictitious nature of the twin- axis is carefully pointed out, but one 

 regrets that the confusing term " twin-plane " has been retained. 

 As a term for a plane perpendicular to the axis it is not wanted, 

 and I fear its use in this sense is too well established for it to be 

 employed in a more rational way. All mineralogists will appre- 

 ciate the excellence of the treatment of the troublesome and 

 confused twins of the anorthic felspars. The views of the many 

 distinguished crystallographers who have written on them are 

 clearly stated and most carefully illustrated by well-drawn dia- 

 grams. The error made in one instance by the late Prof, vora 

 Bath in the calculation of the so-called rhombic section is detected. 

 Attention has already been called to it many years ago, but like 

 other errors it has great vitality, as is shown by its remaining un- 

 corrected in that monument of learning and conscientious work, 

 Mr. E. S. Dana's recent edition of his father's 'Mineralogy.' 

 Doubts are justly thrown on this rhombic section, but research 



