292 C. M. CHILD 



give the number of pieces in each case. The pieces are numbered 

 1, 2, 3, 4, etc., from the anterior and posteriorly. The designa- 

 tions of the different groups are those of section 2 above. 



A glance at the table is sufficient to show the character of the 

 results. It is evident at once that the frequency of normal 

 wholes, of teratopthalmic wholes and of headless tails is a func- 

 tion, both of the size of the piece and of the region of the body 

 from which it was taken. Even with the relatively small num- 

 ber of pieces, i. e., ten in each class, the irregularities are slight, 

 and my notes show that in most cases they were connected with 

 irregularities in the size of pieces, which cannot be wholly avoided, 

 even with the greatest care in isolating the pieces. 



This table affords a basis for the graphic representation of the 

 frequency of the various groups or of any particular result of 

 regulation recorded. In fig. 40 the data of table 1 are presented 

 in graphic form so as to show the frequency of head formation 

 in pieces of different size and from different regions. In the figure 

 the ordinate represents percentages, each division being equal 

 to 10 per cent. The abscissa represents the size of the pieces 

 and the region of the body from which they are taken : it is divided 

 above into sixteenths and below into twelfths. Below it the 

 longitudinal axis of the planarian body is drawn to the same 

 scale with the approximate position of the pharynx and the fission 

 plane indicated in dotted lines. Each curve represents the fre- 

 quency of headformation, including both normal and teratop- 

 thalmic heads, at different levels of the body for pieces of a given 

 size. Thus the curve ab for the quarter pieces is plotted from 

 four points and is a straight line since all four pieces form heads 

 in 100 per cent of the cases. The curve ac, drawn with long 

 dashes shows the frequency for the sixth pieces, the curve ad, in 

 dashes of medium length that for the eighth pieces, ae in short 

 dashes that for the twelfth pieces and af in alternate long and 

 short dashes that for the sixteenth pieces. 



The curves show^ in the clearest manner that in all except 

 the quarter pieces the frequency of head formation decreases 

 rapidly with increasing distance of the level of section from the 



