270 MERISTIC VARIATION. [part i. 



of the diastema on the other, it seems more likely that the one 

 tooth balances or corresponds to the two of the other side, which 

 may be supposed to have arisen by division of a single germ. On 

 the other hand since the two anterior premolars found in such 

 cases are not always identical in form and size, either the anterior 

 or the posterior being commonly larger than the other, there is no 

 strict criterion of duplicity, and it is clearly impossible to draw 

 any sharp distinction between cases of duplicity of the first pre- 

 molar and cases in which the two small premolars are related to 

 each other as first and second. These two conditions must surely 

 pass insensibly into each other. If the case of the teeth is com- 

 pared with that of any other Linear series in which the number of 

 members is indefinite, as for example that of buds on a stem, the 

 impossibility of such a distinction will appear. A good illustration 

 of this fact may often be seen in the arrangement of the thorns on 

 the stems of briars. For large periods of the stem both the angular 

 and linear succession of the thorns of several sizes may be exceed- 

 ingly regular ; but it also frequently happens that a thorn occurs 

 with two points, and on searching, every condition may sometimes 

 be found between such a double thorn and two thorns occurring 

 in series, having between them the normal distinctions of form or 

 size. Very similar phenomena may be seen in the case of the 

 strong dermal spines of such an animal as the Spiny Shark (Echi- 

 norhinus spinosus). These structures are of course from an anato- 

 mical standpoint closely comparable with teeth. In them, spines 

 obviously double, triple or quadruple, are generally to be seen 

 scattered among the normal single spines, but between the double 

 condition and the single condition, it is impossible to make a real 

 distinction. 



The remarks made as to the first premolars apply almost 

 equally to the last molar. See Phoca vitulina No. 336, Mycetes 

 niger No. 206, Man, Magitot, Anom. syst. dent, PI. v. figs. 4, 5 

 and 6, Canis cancrivorus Nos. 251 and 252, Crossarchus zebra 

 No. 302. 



(6) The least size of 'particular Teeth. 



What is the least size in which a given tooth can be present in 

 a species which sometimes has it and sometimes is without it ? In 

 other words, what is the least possible condition, the lower limit of 

 the existence of a given tooth ? This is a question which must 

 suggest itself in an attempt to measure the magnitude or Dis- 

 continuity of numerical Variation in teeth. 



The evidence collected does not actually answer this question 

 completely for any tooth, but it shews some of the elements upon 

 which the answer depends. 



In the first place it is seen at once that the least size of a 

 tooth is different for different teeth and for different animals. 



