1892.] Correlated Variations in Crangon vulgaris. 



7 



Table II. — Mean Value of Total Carapace Length (c) for every 

 observed Length, of Post-spinous Portion (ps) in Plymouth. 

 (1000 individuals.) 



Length of 



Mean 

 associated 



Hps 



c — M c 



Length of c 

 when 



Difference 

 observed, 



ps. 



length of c. 



r = 0-81. 



c. 



Over 186 



262*11 



+ 3-43 



+ 2-74 



262 -27 



-0-16 



186 



258 -25 



+ 2-41 



+ 1-89 



258-51 



-0-26 



185 



256-15 



+ 2-13 



+ 1-43 



257 *48 



-1-33 



184 



256 -84 



+ 1-85 



+ 1-59 



256 -45 



+ 0-39 



183 



254 -88 



+ 1-56 



+ 1-15 



255-38 



-0-50 



182 



254-18 



+ 1-28 



+ 1-00 



254 -36 



-0-18 



181 



253-28 



+ 0-99 



+ 0-80 



253 -25 



+ 0-03 



180 



251 -73 



+ 0-71 



+ 0*46 



252 -25 



-0-52 



179 



251 -34 



+ 0-42 



+ 0*38 



251-18 



+ 0-16 



178 



249 -78 



+ 0-13 



+ 0*03 



250-77 



-0-99 



177 



249-10 



-0-15 



-0-12 



249 -08 



+ 0-02 



176 



248 -53 



— 0-44 



—0-24 



248-01 



+ 0-52 



175 



246 -79 



-0-72 



-0-62 



246 -97 



-0-18 



174 



245-73 



-1-01 



-0-86 



245 -90 



-0-L7 



173 



245 -02 



-1-30 



-1-01 



244 -83 



+ 0-19 



172 



243 -89 



-1-58 



-1-26 



243 -80 



+ 0-09 



171 



243 -67 



-1-87 



-1-31 



242 -73 



+ 0-94 



170 



241 -28 



-2-16 



-1-84 



241 -76 



-0-48 



169 



241 -06 



-2-44 



-1-91 



240 -63 



+ 0-43 



Under 169 



239 -88 



-3-22 



-2-14 



237 '75 



+ 2-13 



the position of one point in fig. 4. Those points whose position is 

 determined from Table I, taking the carapace length as fixed, are 

 indicated by crosses : those obtained from Table II, taking the post- 

 spinous portion as fixed, are shown by dots surrounded by circles ©. 

 The straight line drawn across the diagram indicates the ratio! x = 

 0'%ly; and every point, determined from either table, should there- 

 fore lie upon it. It will be seen that the points do, in fact, lie fairly 

 closely round the line, though few lie actually upon it. 



The accuracy of the assigned value of r may be tested in another 

 way. When the value of r is known, it is evidently possible to cal- 

 culate, from a known deviation of one organ, the mean associated 

 deviation of the other ; and in the fifth columns of Tables I and. II the 

 mean length of each dependent organ which should be associated with 

 every observed value of the independent organ has been calculated 

 on the assumption that r = 0-81. The length calculated in this way 

 is found to agree very fairly well with the observed length, which is 

 recorded in the second column of each table. The difference between 

 the observed and calculated length of each dependent organ is shown 

 in the sixth column. 



A third way of checking the value of r is given by the ratio of the 

 probable error of distribution of one organ to that of the other. If 



