296 Analysis of Scientific Books, 



pullet's egg, at the same time serving as a defence to protect it, 

 and allow of the blood being aerated. 



The black matter, says Sir Everard, lining the vesicle can only 

 answer some secondary purpose, since it is not met with in the 

 aquatic salamander, whose mode of breeding very closely re- 

 sembles that of the frog. Upon reflecting that the frog's spawn 

 is exposed to the scorching effect of the sun, and in places where 

 there is no shelter, this nigrum pigmentum may be given to the 

 eggs as a defence for the young during its growth, which cannot 

 be required in those of the aquatic salamander, since they are 

 separately enclosed within the twisted leaves of water-plants, and 

 screened from the full force of the sun's rays. The plant 

 whose leaves the aquatic salamander most generally selects to lay 

 its eggs upon is the polygonum persicaria. 



This paper is illustrated by three very curious and instructive 

 plates. 



iv. A general Method of calculating the Angles made hy any Planes 

 of Crystals^ and the Laws according to which they are formed. By 

 /AeRev. W. Whewell, F.R.S., Fel. Trin. Col. Camb. 



The author, after stating the inconveniencies, inelegancies, and 

 imperfections of the received notation for expressing the planes of 

 a crystal, and the laws of decrement by which they arise, and of 

 the usual methods of calculating their angles, explains the object 

 of the present paper, which is, to propose a system exempt from 

 these inconveniencies, and adapted to reduce the mathematical por- 

 tion of crystallography, to a small number of simple formulae of 

 universal application. According to the method here followed 

 each plane of a crystal is represented by a symbol indicative of 

 the laws from which it results, which, by varying only its indices, 

 may be made to represent any law whatever ; and by means of 

 these indices, and of the primary angles of the substance, we may 

 derive a general formula, expressing the dihedral angle contained 

 between any one plane resulting from crystalline laws, and any 

 other. In the same manner we can find the angle contained be- 

 tween any two edges of the derived crystal. Conversely having 

 given the plane, or dihedral angles, of any crystal and its primary 

 form, we can, by a direct and general process, deduce the laws of 

 decrement according to which it is constituted. 



The purely mathematical part of this paper depends on two for- 

 mulae demonstrated by the author elsewhere, and here assumed as 

 known, by means of one of which the dihedral angle included be- 

 tween any two planes can be calculated when the equations of 

 both planes are given, and by the other the plane angle included 

 between any two given right lines can, in like manner, be ex- 

 pressed by assigned functions of the coefficients of their equations 

 supposed given. These formulae being taken for granted, nothing 



