408 W. E. RITTER AND M. E. JOHNSON 
Some variation in the graphs of wheels of different sizes was 
noted, and to make sure of its general trend, the data for all the 
wheels were considered. The wheels were first grouped accord- 
ing to size, Group A included wheels whose zooids averaged 5-10 
mm. in length; Group B, 10-15 mm.; and so on. In Group A 
were ten wheels. Not only does the number of zooids in a wheel 
vary, but the number in one-half of a wheel is not always the same 
as in the other half. For this reason the ten wheels were re- 
garded as twenty half wheels. 
Among these twenty half wheels of Group A were three contain- 
ing four zooids; one with five zooids; nine with six zooids; and seven 
with seven zooids. The corresponding values of the three four- 
zooid half wheels were averaged, the three first zooids together, 
the three second zooids, the three third, and the three last zooids. 
The result was a typical curve for a four- zooid half-wheel whose 
zooids have an average length of 6-10 mm. The five, six, and 
seven-zooid half-wheels were averaged in the same way. Similar 
computations were made for the other four groups. and the results 
plotted. The graphs were smoothed and those for each size were 
averaged in order to get the typical curve for that size. These 
curves (fig. 3) show that the size differences between the zooids 
of a half-wheel greatly increase as the zooids grow and that the typical 
form already noted becomes increasingly evident. 
Passing now to the unbroken portion of the chain, we find that 
the zooids increase in length very slowly at first and more rapidly 
later; also that though the curve is fairly smooth at first, it be- 
comes quite irregular toward the end. Upon closer examination 
of fig. 2 and the graphs of other chains, we surmise that these 
irregularities are the forerunners of the groups making up the 
wheels; in other words that the periodicity shown so plainly in 
the wheel part of the chain extends back into the unbroken part. 
Were this found to be true, the fact could hardly be ignored in 
considering the problem of the break-up of the chain and the pro- 
duction of wheels. 
In order to test the conjecture more critically we submitted 
the measurements to Mr. George F. McEwen, the mathematical 
expert of the Marine Biological Station of San Diego for examina- 
