496 DISCOVERY REPORTS 



In Fig. 25 let us combine Figs. 22-24. The sea ABODE is really stationary, the tunnel 

 moving from right to left, and XY in relation to the sea follows the path through X' Y' 

 to X"Y". A, B, C, D and E are at half-mile intervals. The water sieved by the section 

 XY as it crosses the tunnel will be taken from the consecutive half-miles of sea in 

 proportions corresponding to the areas covered by the parallelogram Y"X' Y'X. The 

 triangle BB'X is one-eighth or 12J per cent of the area of the parallelogram; so is the 

 triangle Y"D'D. Thus of the water filtered by the section XY 75 per cent will come 

 from the mile of sea BD and 12! per cent from the preceding half-mile AB and i2| per 

 cent from the following half-mile DE. 



Fig. 26 shows diagrammatically this relation of the sections on the gauze to the units 

 of distance travelled if a point on the gauze crosses the water tunnel for every unit of 

 distance that passes the machine. If the units of distance are 

 miles, the proportions of the water filtered from each mile may 

 be represented by the parallelograms a, b, c,d,e,f,..., which lie 

 across the rectangles 1, 2, 3, 4, 5, ..., which in turn represent the 

 sections on the gauze. As seen in Fig. 25, 75 per cent of the water 

 filtered by section 1 comes from mile b and 12! per cent from 

 the second half of the mile a and i2i per cent from the first half 

 of the mile c. Now if we examine only the plankton deposited 

 along the dotted lines crossing the middle of the sections 2 and 

 3 at x and z, that on each line will be a sample representative 

 of the miles c and d unadulterated by proportions of the plankton 

 from the miles b and d, and c and e respectively. If the organisms 

 we are estimating are small and numerous a single-line examina- 

 tion traverse may suffice to give an estimate of the number per 

 mile. If we examine an area on the section 2 lying between the 

 dotted lines zv and y which lie at the quarters of the section, then 

 the plankton will have come from water of which 87-5 per cent belongs to the mile c and 

 only 6-25 per cent to the last quarter of the preceding mile b and 6-25 per cent to the 

 first quarter of the following mile d. Similarly if we examine one-quarter of the section, 

 with the line x down its middle, the plankton will have come from water of which 9375 

 per cent belongs to the mile c and only 3-125 per cent to the last eighth of the preceding 

 mile b and 3-125 per cent to the first eighth of the following mile d. Usually the plankton 

 sample deposited on each section is rich enough to render a traverse examination of a 

 quarter of the section or less sufficient to form the basis for an estimate of the whole ; 

 thus we may say that, for all practical purposes, the plankton estimated on each section 

 does represent the plankton belonging to the mile (or whatever distance it is) which is 

 known to have passed the machine during the time that a point upon the gauze has 

 crossed the tunnel, i.e. the distance found by dividing the length of the run by the 

 number of divisions exposed. It will of course be realized that Fig. 26 shows a 

 geometrical representation of the proportion of the water filtered by each section ; it does 

 not mean, for example, that in section 2 the top right-hand corner only will filter water 



Fig. 26. 



