832 Professor William J. Pope [April 15, 



minerals. The comparison may, however, be made more accurately 

 by including the changes in both relative dimensions, ajh and c/&, in 

 the calculation in the following manner. The " equivalence para- 

 meters " are the rectangular dimensions, x^ y and z, of a rectangular 

 block having the volume W, and are in the ratio of the axial ratios, 

 a :b :c. The parameters x and y preserve almost constant values 

 throughout the series, and addition of the increment, Mg^SiO^, leads 

 to a practically constant increase of about 2*86 in the dimension 0, 

 on passing from one mineral to the next in the series. The mineral 

 forsterite also gives nearly the same x and y values as before, and its 

 z value, 2*87, is equal to the differences between consecutive pairs of 

 z values in the main series ; these differences vary between 2 -85 and 

 2*88. The axial ratios and equivalence parameters of forsterite can 

 indeed be calculated with considerable accuracy from the data avail- 

 able for the series of four minerals. 



The relations here displayed may be rendered more obvious by 

 a series of models (Fig. 5). Rectangular blocks having as the 

 horizontal dimensions the x and y values, and as vertical dimen- 

 sion the z value, for forsterite, when superposed upon a similar 

 set of blocks having the corresponding dimensions for prolectite, 

 form a stack exhibiting the equivalence parameters of chondrodite ; 

 superposing on this a second set of forsterite blocks leads to a stack 

 showing the equivalence parameters of humite, and on again repeating 

 the operation, a stack with the dimensions of clinohumite results. 

 From the numerical data and the models exhibited it must be 

 regarded as definitely proved that, in this series, the volumes appro- 



