1918] 



Michael: Behavior of Salpa clemocratica 



249 



made in July, while ten hauls consuming five hours were made in 

 December, neither the haul nor the time frequencj^ of the July hauls 

 would be comparable with that of the December hauls. For the 

 probability of capture by the ten hauls consuming ten hours, would 

 exceed that by the ten hauls consuming five hours. Therefore, it is 

 necessary to determine what the frequency would have been had the 

 ten December hauls consumed ten instead of five hours ; otherwise both 

 haul and time frequency might be misleading. 



Since haul frequency, by definition, is unrelated to the time con- 

 sumed in hauling, it can not be standardized with respect to time. 

 Time frequency, however, is amenable to such correction ; and as 

 the method of standardization employed was developed by Dr. G. F. 

 McEwen of the Scripps Institution, I have asked him to give, in his 

 own language, the derivation of the formula : 



Let F = time frequency, 



f =^ standardized frequency, 



a = average time per haul, 



b = standard time per haul, 



a 

 m = ^, 



f n = frequency corresponding to n units of time of duration aj, 

 p, z= probability of catching no animals in a haul of duration a^, 



Then from the principle of compound probabilities of independent events: 

 f 

 -^ = 1— Pi time = a„ 



f 



~- = 1— pr time = 2a, 



-^— = 1— p\ time = 3a„ 



-jQ^ = 1— Pi" time = nai. 



Let 



b = kai 

 then 



a = mkai 

 Therefore 



w = >-■>'"•■ <^> 



and 



w = ^ - "■"■ ■ ''' 



From (1) and (2) 



v- "■ = '-m <'' 



p"' = <> - iS ' " (^> 



Therefore, equating the logarithms of the second members of (3) and (4) 



f b F 

 log (1 )= — log (1 — jYin^ Standardization formula. 



