Hatai, Spinal Ganglion Cells of Rat. 477 



in various planes. In some cases the knife makes a right angle 

 with the longest axis {dc^ Fig. 3) of the cell-body and some cases 

 with the shortest axis {ab). In the remaining cases the angles 

 will always be less than 90°. It must be remembered that the 

 1 108 cells counted are those which contain both nucleus and nu- 

 cleolus, and therefore it is assumed that the knife always passed 

 through the approximate center of the cell-body. The chance 

 that the knife will make a right angle with shortest axis^ must 

 however be very small compared with a failure. Whichever 

 plane we cut, as long as the knife passes through the center, the 

 diameter {ab) is constant and therefore the product of the diame- 

 ters varies directly with the changes in the longer. But {cd) is the 

 maximum diameter and its length diminishes as the axis moves 

 from the original position toward the axis {ab). As soon as it 

 reaches {ab) it becomes minimum. As was stated already, there 

 are more chances for the knife to pass through somewhere between 

 the two points {a) and {c) than to cut through {c) itself. If there- 

 fore we determine the two diameters of the cell from the cut surface 

 and the square root of their product is taken as the mean or "cal- 

 culated diameter" of the given cell, the final value thus obtained 

 will often be less than it should really be, because ^'^ ab X ^c is always 

 > V ab X xy, where [xy) is any arbitrary line between {a) and 

 (c). But as was stated already, the sections of the smaller cells 

 are more nearly circular in outline. Therefore the mean diame- 

 ters thus obtained may represent nearly the true value in the case of 

 the smaller cells but less nearly, in the case of the larger cells which 

 have become ovoid. From this it will be clearly seen that the 

 frequency curve of the diameters of the ganglion cells based on 

 the square roots of the product of the observed diameters can not 

 represent the true frequency. 



As to the range of the diameters, the maximum "calculated 

 diameters" found may be considered to be the true value since 

 there is at least one chance that the knife could pass through the 

 longest axis while on the other hand the observed minimum 

 diameter may be somewhat less than the true minimum diameter 

 since there is a tendency for the diameter of those cells which are in 

 any degree ovoid to be made smaller. Consequently if the values 



^ The maximum size of the cell is obtained only when the knife makes 90° with the axis {ah), pro- 

 vided it also passes through the center of the cell. 



