C. A. BARBER 175 



VI. Periodicity in the length of the joints. 



An inspection of the general curve of length of joints given above (Plate III), 

 shows that it is fairly uniform in its course. There are few ups and downs. 

 After a comparatively high start it rapidly ascends to a maxinnm), it then 

 descends gradually for some distance, while, in the last eight joints, the descent 

 is rapid. As a matter of fact, the curve connnences at 3*6", which is the 

 average length of the first joint above ground ; the succeeding joints are longer 

 and longer until they reach 4"5" at the fifth joint ; then the joints gradually 

 decrease in length until, at the fifteenth, they are only 2"6" long ; the descent 

 in the last eight is quick until the ultimate joint measured is 0"1" long. These 

 last eight are more or less immature joints at the top, for all canes are measured 

 from ground-level to that joint at the growing tip which first falls to merely 

 one-tenth of an inch in length ; further measurements are not well possible 

 in the field, and the foot-rule used is one divided into tenths of an inch. The 

 curve is smooth throughout its length and there are few irregularities. It is 

 made up of 89 unit observations of 20 canes each and is thus the resultant of 

 over 50,000 separate measurements. It is different with the unit curves, some 

 of which have been reproduced in the diagrams (Plates IV and V), these being 

 the averages of only 20 canes growing at one time and place. The inequalities 

 are greatly increased, and there are a series of ups and downs throughout the 

 length of the curves. But, when we turn to the curves prepared for individuals 

 of these 20 canes, these differences assume larger proportions, and it is not 

 unusual for two consecutive joints to differ by as much as two or three inches 

 in length (Plate VI). The greater the number of canes used in making up a 

 curve, the more uniform is the curve obtained. The general summation curve 

 js in this respect unlike any curve of the whole series, and neither it nor the 

 ordinary varietal curves are to be regarded as average joint curves in the usual 

 sense. They are representations of the usual course of events rather than a 

 picture of the average cane of the plot. Such curves have been called else- 

 where " ideal," as contrasted with average ones. 



There are great difficulties in obtaining such a curve. One of these will 

 readily occur, when it is remembered that the canes of any clump vary greatly 

 in the number of joints, and it is therefore impossible to take an average of 

 them in succession. Again, each cane varies a good deal in the length of its 

 successive joints ; some are long and some are short, and in averaging these it 

 will often happen that the long joint in one cane will fall opposite to the short 

 in the next. Any system of averaging will therefore have the tendency to 

 smooth out the differences in different parts, and, the greater the number of 

 canes dealt with, the smoother the resulting curve will be, as is seen in the 



