130 



P. B. SIVICKIS. 



section is the chief factor in determining these early deaths in 

 short pieces. In the experiments presented here the pieces dying 

 in this manner are included in the totals in calculating percentages 

 and in graphing, but in certain lines of future investigation it will 

 probably be desirable to exclude these early deaths in determining 

 total head frequencies. 



The head-frequency data are tabulated in percentages, the full- 

 grown animals in Table I., the young animals in Table II. From 



Table II. 



Head Frequencies of Young P. lata (4-6 mm.) in Relation to Length of 

 Piece and Level of Body. 



the tabulated data graphs are plotted by the method of assigning 

 numerical values to the different head forms as follows : Normal 

 heads, 5 ; teratophthalmic, 4 ; teratomorphic, 3 ; anophthalmic, 2 ; 

 acephalic, 1 ; dead, o. To obtain a head-frequency value for a 

 given lot of pieces, the number of pieces or the percentage of each 

 head form is multiplied by the numerical value of that form and 

 the sum of these products for the particular lot is divided by the 

 number of pieces in the lot, or, if the data are in percentages, by 

 one hundred. The results are the same whether actual number of 

 pieces or percentages are used. These values plotted as ordinates 

 against the successive levels of section, A, B, C, etc., from the 

 heads of the original animals posteriorly as abscissae, give curves 

 which permit direct comparison of the head frequencies of pieces 

 of different lengths and from different levels. 



