52 THE VOYAGE OF H.M.S. CHALLENGER. 



series, and only two of three joints. But, excepting in rare cases like this, the 



predominant characters of the individual may be safely taken as those of the type, and 



the formula constructed accordingly. 



Bell's method of writing a formula for every slight variation, as he has done in the 



case of Actinometra variabilis, would result in the following list of formulae for 



Actinometra parvicirra. 



(2) (2) (">) 



a. (3) ; a.^; a.3.(2); a.3.7^ ; x a.3(3) ; a.2.7^ ; a.2.(3), and so on. 



Such a collection of formula? would be worse than useless from its confusion, and 

 very far from being the shorthand system which Bell rightly wishes to see employed. It 

 would be much easier to refer to the specific diagnosis at once than to try and make out 

 the predominant characters of the arm-divisions from a supposed shorthand of this kind. 



Two points must therefore be noted in determining the formula of a species. 

 1. What are the characters of the majority of the arm-divisions in a given individual, or 

 better still, in a number of individuals ? 2. Whether examples ever present themselves 

 in which a given character, such as the occurrence of distichal, palmar, or post-palmar 

 divisions, is sometimes entirely absent 1 In this case, but only in this, the corresponding 

 symbol should be put between brackets in the formula, e.g. — 



Antedon lusitanica, A.(2). 

 Actinometra parvicirra, a.3.[3.(3)]. 

 Actinometra multiradiata, a.3.2{p.(p f )br}. 

 But the fact that all the ten distichals or twenty palmars do not always occur in every 

 individual of a species is no reason for placing the corresponding symbol in brackets. 

 Were this done, I have no hesitation in saying that both symbols would have to be 

 enclosed in brackets in the formula of every species with less than forty-one arms and 

 no post-palmar divisions. This of course would be absurd, and render the use of 

 formulae altogether futile. 



The principles of classification which have been explained above 2 enable us to divide 

 the numerous species of Antedon and Actinometra respectively into groups of very 

 variable size. These are arranged in the following lists, which contain the names of 

 all the species described by myself and my predecessors, Eetzius, Lamarck, Muller, 



1 This is s imil ar to the expression given by Bell for Antedon elegans, in which there are generally two palmars, but 

 sometimes three. His figured specimen presents one case of the latter to four of the former ; and it is therefore clear 

 that the formula should be written A.3.2. 



2 I may just remark here that I cannot at all agree with the dictum of Walther that " Wer sich je mit Crinoiden 

 besehaftigt hat, der wird wissen, wie wenig specifischen Werth die Gabelungen der Arme besitzen" (Palreontographica, 

 1886, Bd. xxxii. p. 182). Walther's experience seems to have been limited to a comparatively small number of fossil 

 Crinoids, not always in the best state of preservation. But so far as concerns the recent Crinoids, both stalked and free, 

 the number and characters of the arm-divisions afford points of much importance in the discrimination of species. I am 

 convinced that the same may be said of the fossil Neocrinoids, if not of the Palaeocrinoids too, provided that a sufficient 

 range of specimens is brought under consideration. 



