224 DE. G. H. FOWLEE— BISCATAN PLANKTON : 



successive moult (or at least eacli growth-moult). Fortunately, the shell-contour in 

 Halocypridge does not alter so much as the principal organs : it does alter somewhat 

 in most of the species studied below, but more gradually and to a less extent than do 

 the cephalic appendages adopted by Dr. Mtiller for diagnosis. 



Something more, however, than a general resemblance of shell-contour is necessary 

 in order to link up securely older and younger stages of a species. The clue, which for 

 some time I sought in vain, is to be found in an observation of W. K. Brooks *. He 

 noticed, in four specimens of Stomatopod larvae captured at St. Vincent, a curious 

 mathematical relation : that if the length of the shortest larva, 4'16 mm., be multiplied 

 by f , and the product by |, and so on, the following numbers are arrived at : — 5-20, 6'50, 

 8-13, and 1016 mm. ; and his other three larvse were actually 529, 6-49, and 10-21 mm., 

 the 8"13 stage not having been captured. 



I have developed this relation for Halocypridge in the following pages, and propose 

 that it should be termed " Brooks's law," in honour of one of the most ingenious of recent 

 naturalists. If it prove to be true in other Ciustacea (as I expect, having tested it in a 

 Macruran and a Brachyuran), it could be phrased as follows : — " During early growth, 

 each stage increases at each moult by a fixed percentage of its length, which is approxi- 

 mately constant for the species and sex." In Halocypridge this percentage differs in 

 males and females, as the egg is presumably of the same size in both sexes, but the 

 males are ultimately shorter than the females of the same stage in nearly every species 

 and group. 



I am well aware that a great many more instances must be recorded before this 

 proposed "law" can be accepted, even with probable modifications, but I have over- 

 emphasized it in order to call the attention of students to the necessity for testing it 

 wherever possible. If it proves to be general, it will be of great value to the plank- 

 tologist, as helping him to connect the swarms of larvse in a neritic haul with each other 

 and with their adults. 



It will carry more conviction, if one takes for the first illustration a species with a 

 quite unmistakable shell-contour such as Couchcecia imbricata (figs. 110-121, PI. 20). 

 Of this species only a few specimens were captured, but by selecting imbricata, though 

 the mathematical completeness is less, the zoological certainty is greater; and it will 

 serve as well as any other species to demonstrate the simple mathematical methods 

 employed. 



When all available specimens of imbricata had been measured and sexed, they formed 

 the following series : the number of specimens in each sex at each length being placed 

 opposite to that length. 



* Eeport H.M.S. 'Challenger' : Zoology, xvi. The Stomatopoda, p. 105. 



