1825.] PJiilosophical Transactions for 1825, Part 1, 463 



mediary decrements, is quite devoid both of simplicity and of 

 uniformity, and indeed, it may be added, of precision. The 

 object of the present paper is to propose a system which seems 

 exempt from these inconveniences, and adapted to reduce the 

 mathematical portion of crystallography to a small number of 

 simple formulae of universal application. According to the 

 method here explained, each plane of a crystal is represented by 

 a symbol indicative of the laws from which it results ; the sym- 

 bol, by varying the indices only, may be made to represent any 

 law whatever : and by means of these indices, and of the primary 

 angles of the substance, we obtain 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 between any two edges of the 

 derived crystal. Conversely, knowing 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 same formulae are capable of being 

 applied to the investigation of a great variety of properties of 

 crystals of various kinds, as will be shown in the sequel. We 

 shall begin with the consideration of the rhomboid, and the 

 figures deduced from it; and we shall afterwards proceed to 

 other primary forms.'' 



We cannot transfer to our pages the formulae, occupying ten 

 sections, in which the author proceeds to develope his method ; 

 and must, therefore, refer the student in crystallography to the 

 Transactions for them. 



Article V. is Dr. Roget's Explanation of an Optical Deception, 

 already given in the Annals for August last. 



VI. On a new Photometer y with its Application to determine 

 the relative Intensities of Artijicial Light, S^x. By William 

 Ritchie, AM. Rector of the Academy at Tain : communicated 

 by the President. 



The accuracy of Mr. Ritchie's photometer is founded, he 

 states, " on the axiom, that equal volumes of air are equally 

 expanded by equal quantities of light, converted into heat by 

 absorption by black surfaces : and also on the well established 

 principle that the quantity of light diminishes as the square of 

 the distance of the luminous source from the object on which it 

 is received. * 



" The instrument [of which a plate is given] consists of two 

 cylinders of planished tin plate from 2 to 10 or 12 inches in 

 diameter, and from a quarter of an inch to an inch deep. One 

 end of each cylinder is inclosed by a circular plate of the same 

 metal soldered completely air tight, the other ends being shut 

 lip by circular plates of the finest and thickest plate glass, made 

 perfectly air tight. Half way between the plates of glass and 

 the ends of t!ie cylinders, there is a circular piece of black 



