APPENDIX Y. 



THE CALCULATION OF THE COEFFICIENTS OF THE 

 QUANTITATIVE PLANKTON NETS. 



This is an extremely difficult and laborious operation and I can 

 only barely indicate the manner in which the calculations are made. 

 If we were to attach only the ring which forms the mouth of the 

 quantitative net to a rope and haul it up from a depth of (say) twenty 

 metres to the surface, then a column of water of twenty metres in 

 height, and of a sectional area equal to that of the opening of the ring, 

 would pass through the latter. But if, again, we were to attach a bag 

 made of some impermeable material to the ring and then haul it up 

 through the water none of the latter would pass through the fabric, 

 and instead we should have a pressure on the walls of the latter. 



This pressure would be determined by the rapidity with which the 

 apparatus was hauled. It can be ascertained by the application of 

 the well-known Torricellian Theorem and is 



where V is the velocity with which the apparatus is hauled, and g is 

 the acceleration of gravity. 



But whenever we attach the permeable silk net to the ring the 

 case becomes quite different. The pressure D obtained as above no 

 longer exists. It is as if a water main had been tapped or was 

 leaking : then the pressure within it falls off. The net is not 

 impermeable and water issues from each of its pores. If we wish to 

 find how much water passes through the net fabric at a known 

 velocity of hauling then we must determine what is the mean 

 pressure on it per unit of filtering area. This pressure varies from 

 part to part of the net : it is greatest near the mouth (near the 



