290 THE BIOLOGY OF HYDRA : 1961 



to two types of tubes: secondary stolons and uprights. Secondary 

 stolons leave their parent stolons at right angles along the sub- 

 stratum, while uprights leave at right angles away from the sub- 

 stratum. Uprights, in contrast to stolons, are hydranth-bearing 

 tubes, and give rise to one additional hydranth-bearing tube, the 

 side branch. Side branches leave upright tubes at about 45 degree 

 angles away from the substratum. Thus one can classify three types 

 of tubes: stolon, upright, and side branch. 



Other differences further distinguish these tubes. Hydranth- 

 bearing tubes develop only directly behind growing tips; they never 

 develop in any other part of the colony. They are spaced at regular 

 intervals along their tube of origin; upright tubes in particular 

 occur at about three mm. distances along the stolon. In contrast, 

 stolon tubes never develop at growing tips, but always come out of 

 some old part of the colony, as at the base of a well-developed up- 

 right. Further, stolon tubes are not spaced regularly; rather secon- 

 dary stolons develop erratically with respect to any other part of the 

 colony. 



How do these tubes grow? Since they are of uniform diameter, 

 one can detemiine the growth rate of individual tubes by measuring 

 increase in length with time. This has been done by photographing 

 a colony over the course of a few days or a week in a growth cham- 

 ber in front of a time-lapse camera. The movie is then used to plot 

 the extension of the tube as a function of time. Such plots, for both 

 stolons and uprights (side branch growth has not been measured), 

 demonstrate that these tubes increase in length linearly with 

 time. Stolons grow at a rate of about 0.1 mm. per hour, and uprights 

 at a rate of 0.05 mm. per hour. 



You will recall that a colony as a whole grows exponentially in 

 terms of hydranth number. The colony also grows exponentially in 

 temis of dry weight, so that hydranth number is a measure of the 

 mass of a colony. The observation of linear growth of tubes poses 

 a dilemma : if the tubes which comprise a colony grow at a constant 

 rate how does the colony as a whole grow exponentially? This ques- 

 tion was first examined by model-building. One can diagram a col- 

 ony in the form of a geometric progression, such that linear growth 

 of tubes with regular branching at constant inten'als gives rise to 

 exponential growth of the whole. Such a model does not look 



