138 SCIENCE PROGRESS. 



lengths of the sides of the elementary parallelepiped of the 

 crystal (the unit cell described in a previous article), and V 

 be its volume, and if a b c be the crystallographic axes ; then 

 supposing- (merely for illustration) this elementary cell to be 

 rectangular and the axes to coincide in direction with its 



sides ; V = A r B I C t = - , where/ is the molecular weight, 



and s is the specific gravity of the salt. A x B x C : therefore 

 represent the molecular intervals along the edges of the 

 cell — and these edges may be taken for crystallographic 

 axes. 



_ A, B, Q 



1 hen — = —r = — = ai 

 abc 



V = abc /u 3 and /n + \f ___ . 



abc 



From this it follows that 



A, = V^; B,= ^:i V ;C, = ^ 2 V 

 be ca ab 



Similar formulae involving- one or more measured ano-les 

 can be easily obtained when the cell is not rectangular, 

 or where its sides do not coincide in direction with the 

 crystallographic axes. 



A, B, C, are called the topic axes of the crystal. 



So far the topic axes present no advantage over the 

 ordinary crystallographic axes, since they are merely num- 

 bers expressed in terms of an unknown unit. But the next 

 step is to calculate the topic axes for a number of sub- 

 stances belonging to a strictly isomorphous series ; Muth- 

 mann did this for the acid phosphates and arsenates of 

 potassium and ammonium, and for certain alkaline perman- 

 ganates ; Tutton for the sulphates of potassium, rubidium 

 and caesium. 



Let A r B x C I5 A 2 B 2 C 2 , etc., be the topic axes for such 

 a series. We may reasonably assume that the molecular 

 arrangements of isomorphous crystals are similar, and, there- 

 fore, that they have the same elementary parallelepiped, 

 which only varies slightly in its dimensions for the various 

 members of the series. If this be so we are enabled to 

 compare (for the first time) crystals of different substances. 



