1919] Frost: Mutation in Matthiola 145 



The fluctuations in habit, leaf form, etc., within the type are such 

 that the determination of familiar types is often a matter of some 

 uncertainty, as is shown by data that have been presented. It may 

 well be that among the doubtful types are included several definite but 

 comparative rare mutant forms, which occurred too infrequently to 

 afford adequate material for positive classification. 



8. SOME PEOBABILITES OF EANDOM SAMPLING 



For compactness of presentation and convenience of comparison 

 the material in tables 39 and 40, to which some incidental references 

 have already been made, is collected here rather than scattered through 

 the discussions of the various types concerned. Some statements as 

 to methods are also necessary in connection with each of the topics 

 here treated. 



First, it should be noted that the percentages previously given 

 have regularly been accompanied by the probable errors of simple 

 sampling. These probable errors have been calculated by the formula 



£'pgr cent = -6744898 yi!l . where p is the percentage of the mutant 



n 

 type ("successes"), g is 1 — p, and n is the size of the sample (the 



number of plants concerned). 



In the heredity tables for each type, p has uniformly been taken 

 as the percentage of the total of the lots compared, or p^. 



For the "mutation coefficient" the percentage of the grand total 

 of unselected house-sown lots has regularly been used. Evidently the 

 few selected progeny included in tables 1, 28. and 37 should be omitted. 

 All the percentages here are so low that the probable errors deserve 

 little confidence, even though n is usually fairly large. The rather 

 close agreement of the percentages of all apparent mutants in the 

 three distinct lots of unselected house-sown cultures suggests that 

 they represent fairly well the population value for the potentialities 

 of the seeds ; and even if the mean percentage of the total of the lots 

 for the main comparisons is actually nearer, it is safer to u.se the 

 larger probable errors resulting from the method here employed. 

 Furthermore strict use of p„ would sometimes require several slightly 

 different probable errors for the same percentage, for use in different 

 comparisons in the same table. , 



