534 THE AMERICAN NATURALIST [Vol. XLIX 



Comparing the proportionate abundance of asymmet- 

 rical genera at different depths with the frequency of all 

 the genera expressed as percentages of the total, we find 

 that the former decreases while the latter increases to 

 50-100 fathoms; from this point the two run roughly 

 parallel to 300-350 fathoms, after which the former in- 

 creases with progressively greater rapidity, while the 

 latter decreases steadily and gradually to 3,000 fathoms ; 

 the two cross each other between 600 and 700 fathoms. 



The- proportion of the families including asymmetrical 

 species to those composed entirely of symmetrical species 

 increases from one third at 0-50 fathoms to three times 

 as many at 1,600 fathoms and twice as many at 1,900 

 fathoms and over. The increase, though irregular — 

 largely as a result of the small numbers involved at the 

 greater depths — is constant. 



The number of families at different depths, expressed 

 as percentages of the total number, increases from 0-50 

 to 50-100 fathoms, and then decreases to 1,800 fathoms 

 and beyond. Except for a minimum between 350 and 

 500 fathoms the decrease is fairly regular. 



The two lines cross between 200 and 300 fathoms. 



The reversal of the direction of the line representing 

 the frequency of the families im-hiding asymmetrical spe- 

 cies as a percentage of the number of the families not in- 

 cluding asymmetrical species at different depths, as com- 

 pared with the line representing the frequency of the 

 families at different depths expressed as percentages of 

 the total number, indicates that the less favorable the 

 environment for crinoids as a whole the greater becomes 

 the proportion of asymmetrical forms. 



In the proportion of genera including asymmetrical 

 species to those composed entirely of symmetrical species 

 we find a minimum between 100 and 650 fathoms or, con- 

 sidering only the most markedly asymmetrical types, be- 

 tween 50 and 400 fathoms, the numbers above 100 (or 50) 

 fathoms and below 650 (or 400) fathoms being greater. 



Considering families in the same light we appear tc 



