358 MESSES. CTEIL WEST AND H. TAKEDA ON 



Therefore, if tlie number of series on a flank of either of the stelar lobes be 

 determined *, then the approximate total number of roots produced by that plant may 

 1)6 calculated from the following formula, where 



X = approximate total number of roots produced by tbe plant, 



y = number of stelar lobes f, 



z = number of series on the flank of a stelar lobe. 



.-. X — yz (2+1). 



Text-fig. 18 



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Isoete^ lacustris. Diagram showing tlieoretical arrangement of the roots on one half of a lobe of the caudex. The 



consecutive numbers denote the succession of roots on one flank of a stelar lobe, whereas the numbers 1, 5, 9, 

 la, etc., which correspond to those of text-figs. 15, 16, and 17, denote the succession of roots on the plant. 



Arrangement oe the Leaves- 



As stated above, many leaves are produced every year. A. Eraun (3, p. 34), referring 

 Isoetes setacea^ another tri-lobed species, says that even in a young specimen the leaves 

 e arranged on the caudex in a spiral of complicated phyllotaxis. In young plants of 



* n^ 



number 



with the plane of a main furrow. 



t Two in bi-lobed species and three in tri-lobed species, since the number of stelar arras is always equal to the 

 number of lobes of the caudex- 



