300 
bulletin of the bureau of fisheries. 
and k denotes a constant, according to Lataste, the relation of these quantities would 
be expressed by the following equation : 
N^kP; 
N 
Whence k = -^. 
P 
He has drawn up a table (based on table 15 of 149), from the data of which he 
deduces the cubes of lengths, the ratios of the average number of eggs to cubes of length 
(k), and the means of these ratios. 
In the lobster the reproductive powers are manifested suddenly at a certain age, 
after which they increase steadily, reach a maximum, and then presumably slowly 
decline. Accordingly during the first period only does the fertility increase proportion- 
ately to the increasing volume of the body, as expressed in the equation given above. 
We have no definite information upon the duration of life, or decline of rate of 
growth in these animals. It is certain, however, that the renewal of the shell is 
quite as necessary for the continuance of life as of growth, since in the course of time 
death would result were not the injured and abraded shell restored. In higher animals 
the skin and at least some of the tissue cells are being continually renewed throughout 
life, while size limit of the body is early attained, and it is not likely that a dense and 
heavy shell like that of the lobster could be sloughed without increase in the size or 
volume of the body. The decline in sexual vigor may therefore result from the tax 
which molting continues to levy upon the capital stock of energy at every period of 
life. According to Lataste: k=f {t), k being a function of age which has no real value, 
except as it is confined within certain limits. 
In conclusion, we wish to observe that upon the principle of correlation of parts 
the ratio of the number of eggs to body length should correspond in a general way to 
the ratio of the volume of eggs to the total volume of the body were the latter a con- 
stant quantity, but owing to the frequent loss of the great claws this is not accurately 
represented by the cube of the length. All that we can say is that in the long run 
there is a tendeney to produce in such a ratio, but the physiological condition of the 
animal is an inconstant and indeterminable factor. The high birth rate of the lobster 
teaches us to expect a correspondingly high death rate, a subject which will be later 
considered. 
BREEDING HABITS AND BEHAVIOR IN CRAYFISH. 
The breeding habits of lobsters, so far as they were then known, were described 
in 1895. Since that time a number of important facts have been ascertained, but 
our knowledge of the subject is still defective at many points. The behavior of the 
American lobster at the time of pairing and extrusion of the eggs has probably never 
been witnessed in a state of nature, and certainl)'- but seldom in any of the higher Crus- 
tacea. We have had more or less circumstantial accounts from Chantran, Ishikawa, 
and Cano, regarding the time and proeess of egg laying in the crayfish, shrimp, and 
crab. The pairing habits and process of laying the eggs in the European lobster have 
been described by Anderton and Scott, as will be noticed later, while a remarkably 
