148 DISCOVERY REPORTS 



signs of ankylosis, so it may be concluded that physical maturity is not reached until an 

 age well above this, probably 6-8 years at least. Ankylosis of the vertebral epiphyses, 

 therefore, seems in the Sperm whale to be a sign of old age and to occur at an age of 

 about 8 or 10 years in both sexes. 



Table XIV also shows that in the Sperm whale, as in other species, the scars on the 

 skin become so confused that the number of different ages of scars gives no indication 

 of the age of the whale. 



The data in Tables IV and V, which show the average values of the measurements of 

 different parts of the body according to the length of the whale (in roman type), are 

 plotted on a double logarithmic scale in Figs. 47-63, where the points derived from males 

 are separated from those derived from females. With Humpback whales similar 

 plotting of the corresponding data gave straight-line curves, or very close approxima- 

 tions to them, and a similar result was expected when the Sperm whale data were thus 

 treated. But this was found to be so only for certain measurements, Nos. 6, 10, 11 

 and 20 (Figs. 47-50). Of the remaining measurements some, Nos. 4, 5, 7, 8, 9, 13, 

 17, 19 and 25 (Figs. 51-59), show a much less close approach to a straight line or 

 form a straight line in only part of the curve; and others, Nos. 2, 14, 15 and 16 

 (Figs. 60-63), are very irregular. The very irregular diagrams are of measurements re- 

 ferring to the dorsal fin, the flipper, and the projection of the snout beyond the tip of 

 the jaw — measurements the limits of which are vague and difficult to determine accur- 

 ately, as explained above. Their irregularity is thus probably due to inaccurate 

 measuring. 



The four measurements which show a fairly good approximation to a straight line 

 when plotted on a double logarithmic scale may be taken to show that the rates of 

 growth of the appropriate parts of the body relative to the total length satisfy the equa- 

 tion y = hx^, where x is the total length, y the length of the part, h the fractional 

 coefficient (the value oi y when x equals i), and k is the growth coefficient. The values 

 of k for these four measurements are shown in Table XV. Values of k over unity indicate 

 an increasing rate of relative growth and those less than unity, the converse. Values of 

 k for measurements Nos. 10 and 11, relating to the posterior part of the body, are below 

 unity, and those for measurements Nos. 6 and 20, relating to the anterior part, are over 

 unity. From this we may conclude that with increasing total length the relative growth 

 rates of the anterior and posterior regions of the body increase and decrease respectively, 

 and lead to the enormous relative size of the head in the adult bull Sperm whale. 



The remaining graphs. Figs. 51-59, show that some parts of the body follow a re- 

 lative growth rate that satisfies this simple equation only during part of their growth, 

 and that, for the rest the relative growth rates appear to be very irregular, so that no 

 simple relationship can be traced. It is difficult to suggest any reason for this irregu- 

 larity in relative growth rates when compared with the striking regularity found in the 

 Humpback whale. 



