THE MEASUREMENT OF VARIATION. 15 



knowledge is derived chiefly from the work of Ludwig, 

 De Vries, and Vb'chting. The majority of variations 

 hitherto examined have not been found to be at all ac- 

 curately in accordance with the law of frequency of 

 error, for reasons which will be referred to later. 

 However, in the case of one or two local races of Torilis 

 anthriscus (hedge parsley) examined by Ludwig*, the 

 distribution of the frequencies of the numbers of 

 branches in the main umbels more or less conforms, 

 and the same is true for the numbers of ray florets in a 

 pure race of Chrysanthemum segetum (corn marigold) 

 examined by De Vries. f Again H. VochtingJ has 

 recently examined the anomalies occurring in 61,736 

 flowers of Linaria spuria (toadflax), obtained in differ- 

 ent years and from different sources. He determined 

 the proportions of the various forms of peloric flowers 

 and anomalous zygomorphic forms, of flowers of vary- 

 ing structure and with various numbers of spurs, and 

 came to the conclusion that their distribution followed 

 the law of error. For instance, the numbers of flowers 

 in each inflorescence showed the following variations : 



Number of flowers, 234 5 678 



Frequency, 1 6 283 61,060 221 9 1 



Percent., .0016 .0097 .459 99.153 .358 .014 .0016 



Here we see that though more than 99 per cent, of the 

 flowers exhibited the normal pentamerous form, yet 

 the variations from this normal are very evenly 

 distributed on either side of it. The distribution of 

 the numbers in all the peloric flowers (i. e., regular 



*Bot. Centralb., vol. Ixiv. p. 40. 



f Arch. f. Entwickelungsmechanik, ii. p. 52, 1896. 



\ Jahrb. f. wiss. Bot., Bd. xxxi. p. 391, 1898. 



