REPORT ON THE ECHINOIDEA. 6 



on comparing, unitatis mutandis, the following table, which shows the same agreement 

 pointed out by Lovdn whichever ambulacrum we start with. These formulae are all made 

 from Lovdn's own figures. 



I. Loven's formula — 



I La, II. a, III. 6, IV.a, \.h, large plates, 

 ( 1.6, 11.6, III. a, IV. 6, V.a, small plates. 



II. Taking the ambulacrum he has called II. as I., we get both for the Spatangoids 

 and Echinids — 



f La, ll.h, Ill.a, IV.6, V.a, large plates, 

 I Lh, ll.a, III.6, IV.a, V.6, small plates. 

 If we take III. as I. the formula is — 



( 1.6, Il.a, III.6, IV.a, V.a, large plates, 

 1 La, 11.6, IIT.a, IV.6, V.6, small plates. 



If we take IV. as I. — 



( La, II.6, Ill.a, IV.o, V.6, large plates, 

 ( 1.6, Il.a, III.6, IV.6, V.a, small plates. 



If we take V. as I. — 



( 1.6, Il.a, Ill.a, IV.6. V.a, large plates, 

 I La, II.6, III.6, IV.a, V.6, small plates. 



Showing most conclusively that any one of the ambulacra taken as I. will give a corre- 

 sponding formula for all the Echinids, and that the I. chosen by Loven with reference to 

 the madreporic body has not the taxonomie value he has suggested, as far as an 

 antero-posterior axis is concerned, any one of the other ambulacra giving precisely the 

 same relation. I do not wish by this to deny the importance of the relations between 

 the ambulacral plates established by Loven. I only wish to show their general character, 

 and deprive them of the geometric value he has assigned to them. The formulae for the 

 interambulacral plates are similarly universal. 



Taking 1 as adopted by Lovdn — 



Lovdn's formula for large plates is 16, 26, 3a, 46, 56, 

 „ „ small „ la, 2a, 36, 4a, 5a. 



Taking 2 as 1 we get — 



for large plates, 16, 2a, 36, 46, 56, 

 „ small „ la, 26, 3a, 4a, 5a. 



And so on, the corresponding formulae finding their universal application to all the inter- 

 ambulacra taken in turn, and that in addition no one has any pre-eminence above any 



