BIOLOGICAL LECTURES. 



sphere had been the form chosen, the anticlines would have 

 been meridional planes and the periclines equatorial, the typi- 

 cal cleavage of a hololecithal animal ovum by two meridional 

 planes followed by an equatorial, being in perfect harmony with 

 Sachs' law. 



Let us now leave for a time further consideration of this law 

 and consider briefly another one also .formulated by a botanist, 

 Berthold, 1 and known as the law of minimal contact surfaces. 

 If air be driven through water to which a considerable amount 

 of albumen has been added, a froth is produced, the globules 

 composing it flattening against one another so as to give an 

 appearance resembling closely that presented by the paren- 

 chymatous tissues of plants. The forces which determine this 

 pseudocellular formation, as it has been termed, have been 

 investigated principally by the physicist Plateau, who discov- 

 ered the law of minimal contact surfaces, which Berthold has 

 applied to cases of true cell-formation. This law is to the 

 effect that the lamellae which separate the various air particles 

 arrange themselves so that the sum of the surface-areas which 

 they form, shall, under the given conditions, be a minimum. 

 The force to which this result is due is that known as surface 

 tension. 



Berthold examined the arrangement of the division-planes in 

 certain plant tissues with reference to this law, and found that 

 it held good, and also pointed out that the movements or re- 

 arrangement of cells, which frequently take place after division 

 is completed, especially in animal ova in which definite and 

 firm cell-walls are wanting, is explicable under the same law. 

 The division of any two cells takes place in a plane which is 

 determined by the law acting on these particular cells, but this 

 plane need not be that which is called for when the entire mass 

 of cells is taken into account, and therefore a rearrangement is 

 necessary. There seems to be little room for doubt but that 

 this law of minimal contact surfaces acts in the determination 

 of the arrangement of cleavage-planes, and we have thus two 

 factors which enter into the question, or rather four, since 

 Sachs' law involves three distinct factors. 



1 G. Berthold: Studien liber Protoplasmamechanik. Leipzig, 1886. 



