PECULIARITIES OF DAPHNIA AND ITS ALLIES. 401 



the direction of the stroke of the large. antennse be taken together, 

 it will be seen that certain results may be predicted, upon 

 elementary mechanical principles, which should, if the facts are 

 really as reported, be found to actually occur. Thus in considering 

 the case of a Daphnia (-Fig. 2), we know that the action of gravity 

 is to pull the animal downwards with the long axis of the body 

 in a vertical position. We also know that the direction of the 

 stroke is oblique to the long axis, being approximately as shown 

 by the line m s, and that the forward motion from this cause 

 alone would be in the direction s m. The real path will therefore 

 be represented by the resultant of these two forces. Taking 

 gravity at about one-half of the pull exerted by the antennae (it 

 is probably much less as a rule, but it cannot be much more, or 

 the animals would scarcely be able to raise themselves in the 

 water), the actual direction of progression will be represented by 

 the line m\ Owing to the tendency, however, of the long axis to 

 arrange itself parallel to the line of movement, the body of the 

 animal will come to assume the position shown in Fig. 3, where 

 the long axis I a is parallel to m^ of Fig. 2. Now the position 

 shown in Fig. 3 is actually about the normal position assumed by 

 a Daphnia when swimming at a medium speed. It is true that 

 all Daphnias are not precisely alike in this respect, but it is also 

 true that all approximate more or less closely to the position 

 shown in Fig. 3 when they are swimming normally in the water. 

 So far, therefore, as the normal position of a swimming Daphnia 

 is concerned, the facts already given, as to the action of the 

 antennae and gravity, seem to offer a sufficient explanation. 



Looking into the subject a little deeper, it will be seen, however, 

 that if we only take the two factors of the net result of gravity 

 and the direction of the stroke into consideration, the animal 

 ought not to remain in the position indicated in Fig. 3, but, in 

 accordance with the reasoning already used, should tend to take 

 up a position with its long axis parallel to the resultant of the 

 two forces at work — i.e. parallel to the line m\ As this process 

 would necessarily be repeated again and again, the conclusion 

 seems to follow that the real path of the animal ought to be a 

 circle, or, to speak more correctly, a series of loops, each of 

 which approaches more closely to a circular form, the greater the 

 power of the antennae compared with the action of gravity. But 

 this is not supported by observation, for although I have 



