C. A. BARBER 163 



in passing, that other characters have been studied in the same twenty canes, 

 e.g., length of leafy shoot, \\idth of leaf, thickness of cane 'u\ various parts, and 

 the canes here too are arranged in the same order.) 



The problem immediately before us is to construct an. ideal cane as far as 

 length of organs is concerned, representative of the twenty measured, and, 

 for the purpose of illustration, I have selected the length measurements of the 

 leaf sheaths in twenty Khari canes, given in the table at the end of this section. 

 It will be seen from this table that, while there are 41 sheaths in one cane, 

 there are only 26 in another, and that there are all gradations between these 

 two extremes. The average number of sheaths in. the twenty canes is 32. and, 

 consequently, only this number of averages is rec^uired in the ideal cane. We 

 obtain it in the following way. The last eight measurements are regarded as 

 those of more or less immature organs, and, forming the close of the series, are 

 retained intact. These are placed at the end of each line, blank columns 

 being left for the inclusion of the whole 41 of the longest cane (No. 19). The 

 last eight columns are thus presen.t in all the can.es, but the n.irith from the end 

 is only present in one cane, the longest. Working backwards, the next column 

 is found in two canes, the 13th in four canes, and so on, until, at the 24th from 

 the end, we again get all the canes represented. These two points, the 24th 

 and 8th from the top of the cane, or the 18th and 34th from the base, are marked 

 by arrows pointing towards one another. The averages of the columns between 

 these two arrows are not truly represen.tative, in. that the shor-ter canes are 

 left out, and, in those that have organs, these are at varying distances from 

 the top, and they become less an.d less representative the further we proceed 

 from base to apex. To bring the total number of measurements to 32, nine 

 columns have to be left out, and the nine selected are those immediatelv 

 preceding the last eight, as these measurements are taken from the smallest 

 number of canes and are only representative of the longer ones. These nine 

 columns are placed in brackets, and are no longer taken into consideration, and 

 we are merely concerned in striking averages of the first 24 an.d last 8 columns. 

 It will now be found that there may be a sudden break in the series from the 

 24th to the 25th column, namely, where the omissions have taken place. It 

 is necessary to smooth out this break and make the fall to the last eight gradual. 

 This is the first alteration which it is found necessary to make in the curve. 

 But there is another point to be considered. In each series the lowest members 

 are short, these are succeeded by longer and longer ones until a maxinuim is 

 reached, after which a dechne follows, until, in the terminal immature mem- 

 bers, there is a rapid fall. As these maxima are reached at different points in 



