QUANTITATIVE STUDY OF THE PURKINJE CELLS 239 



faces of similar solids vary, we know, as the squares of the cube 

 roots of their volumes. A priori we should perhaps not be safe 

 in assuming that large and small cerebella are exactly similar 

 solids, it being possible that small cerebella might be more 

 convoluted than large ones so that the disparity in surfaces 

 might to some extent at least be removed. 



Careful examination, however, of large and small cerebella — 

 where the latter are from cases at least one month old — does not 

 justify this a priori assumption. Individual differences do exist, 

 but size has not been found to alter materially the convolution 

 pattern after birth (Berliner, '05). Furthermore, our results 

 based on the assumption that large and small cerebella are 

 similar solids will be found to agree with theoretical expectations. 

 In order, then, to compare areas which represent the same 

 fraction of the total number of Purkinje cells in different cere- 

 bella, it is necessary to take areas which vary as the squares of 

 the cube roots of their volumes. As a convenient indication of 

 volume we have used the weight in grams of the fixed cerebellum, 

 this having been corrected, if necessary, for change in specific 

 gravity. A constant fractional part of each cerebellum, an 

 equivalent unit area (EUA), has been secured by taking a line of 

 Purkinje cells as many millmieters long as the numerical value 

 obtained, by taking the square of the cube root of the cerebellar 

 weight in grams — this being from a section cut 25^ thick and 

 corrected for shrinkage as already explained. 

 If, then, we let 



N = the number of cells per EUA 



L = the length of the line of cells as projected in millimeters 



M = the magnification 



C = the total number of cells counted 



Si = the sum in mm. of the length and breadth of the block 

 as first measured 



S2 = the sum in nun. of the length and breadth of the section 

 on the slide 



W = the weight of the cerebellum in grams after fixation then 



^ = (^4)x(l^^^* 



