468 Variation in " Ophioroma Nigra" 



thc dividers was placud at an angle of the puntagon and the othcr at the niiddle 

 of the opposite side, whereas in circular discs thc nicasureinent was made along 

 a dianietcr. I next nieasured tlie leiigth of the rays, which in a perfect specimen 

 taper gradnally to a very fine thread. This measurement was made with the 

 vontral surfaco upwards, for whcn a brittlc-star is vicwed dorsyilly cach ray scems 

 to conie froni a side of tho disc whereas when viewed ventrally it is seen that the 

 rays begin innrer the mouth. Accordingly, the length of tlie ray was nietisured 

 froin the very tip of the ray tu tlie iiiiierniost edge of the arni-plate nearest 

 the niouth. 



Forbos says* that "the rays taper gradnally, and vary in thiir prujKjrtions as 

 coMipared with the dise, biit are generally from three to three and a half tinies 



as long as thi' disc is broad The disc of this species generally nieasures half or 



three-fourths of an ineh aeross. It somctinies grows ninch larger. Mr Ball has 

 a specimen six inchcs in diameter; the disc half an ineh broad: and I have one 

 before nie at ])resent which nieasures eight inches aeross the rays." On the other 

 band, Jetirey Bell says-f that this species of ophiuroid is " nioderately sized," and 

 that the arms are " seven or eight times the radius of the disc," instancing 

 five specimcns whose discs varied from 4'5 to 11 millimetres and rays from 

 40 to 95 millimetres, thc ray being therefore on the average about seven and 

 a half times as long as the disc is broad. 



Table III. givcs the calculalions on this convlation, the figures given being 

 those only for the second thoiisand specimens examined. This table shows 

 not only the various disc-breadths and arm-lengths, but each Square gives the 

 number of animals having a certain disc-breadth associated with a certain arm- 

 length. From this table, by the methods and formul» now familiär to readers of 

 Biometriku, there have been deduced the following re.sults: 



Meau of disc-breadth = ^fx = lO'lOG mm. 



Standard deviation of disc-breadth = o-^ = 2"14+9 nun. 

 Mean of arm-length = My = ö0'656 mm. 



Standard deviation of arm-length = tr,, =ir279G nun. 

 Coefficient of uorrelation = ;• = O'l'.Sll. 



Knowing these results, we are now ablc to find the lines of regre.ssion. The 

 line givjng mean arm-length for known disc-breadth is found from the formula 



y = — - cc and is 7/ = 489G2.r. From thc formula a;= ^y we find the line giving 



O'x O'ii 



mean disc-breadth for known arm-length is .;• = Ol770-'5y. The equation to the 

 line of mean values of arui-lengths referred to the axes, arm-length = 0, disc- 

 breadth = 0, is 



Cx 



which is y = 4-8962,r-t- 11747. 



* Op. cit. Forbes, pp. 51, 52. t Op. cit. Jeffrey Bell, p. 129. 



