76 



DISCOVERY REPORTS 



growth of the various parts of the body relative to the total length satisfy the equation 

 y = bx^ where x equals the total length, y equals the length of the part, and b is the 

 fractional coefficient (the value oiy when x equals i). The tangent of the angle which the 

 line makes with the x axis equals k, the growth coefficient. The value of k thus obtained 

 is given for each measurement in Table XXIII. Values of k over unity indicate an 

 increasing rate of relative growth and those less than unity the converse. That is to say, 

 in the case of a value over unity, the greater the total length, the greater the rate of re- 

 Table XXIII. Humpback whale. Growth coefficient of the body 

 measurements to satisfy the equation y = bx'' 



Measurement 



3. Tip of snout to blow-hole 



4. Tip of snout to angle of gape 



5. Tip of snout to centre of eye 



7. Centre of eye to centre of ear 



8. Notch of flukes to posterior emargination of dorsal fin 



9. Width of flukes at insertion 



ID. Notch of flukes to centre of anus 



11. Notch of flukes to umbilicus 



12. Notch of flukes to end of system of ventral grooves 



13. Centre of anus to centre of reproductive aperture: 



Male 

 Female 



14. Vertical height of dorsal fin 



15. Length of base of dorsal fin 



16. Axilla to tip of flipper 



17. Anterior end of lower border to tip of flipper 



19. Greatest width of flipper 



20. Length of severed head from condyle to tip 



21. Greatest width of skull 



Growth 

 coeflicient 



1-38 

 1-23 

 1-19 

 I -08 

 0-92 



0-93 

 0-8 1 

 0-84 

 079 



0-56 

 -o-6o 



1-37 

 1-32 

 1-05 

 1-03 



0-73 

 1-50 



o-8o 



lative growth, and vice versa. The values of k greater than unity are those of measure- 

 ments nos. 3, 4, 5, 7 and 20 relating to the head region, nos. 14 and 15 relating to the 

 dorsal fin and nos. 16 and 17 relating to the flipper. Those less than unity are nos. 8, 

 10, II and 12 relating to the tail region, nos. 9 and 21 relating to width of body, no. 16 

 the width of the flipper, and no. 13 the genito-anal distance. 



The indications of different growth rates for different parts of the body discussed in 

 an earlier section are here shown much more precisely, and it is of interest to note that, 

 with the exception of measurement no. 20, the more anterior the measurement the 

 greater is the value of the growth coefficient. This increase in value is doubtless corre- 

 lated with the development of the anterior part of the skull to accommodate the baleen 

 apparatus. Corresponding with the increasing relative growth rate of the anterior part 

 of the body there is a decreasing rate for the posterior part, so that the whole growth of 

 the whale may be said to be directed largely towards developing the feeding mechanism. 



The height, and length of base, of the dorsal fin both have an increasing rate with in- 



