MEMORANDA. * 107 



water, and as we cannot expect all of each sort to be present 

 in a gathering, the above number (200) is an ample allow- 

 ance, and I myself have never seen so many in a slide. 



Assuming this to be the probable number^ each species 

 ought to occupy a space equivalent to the ^^oth part of the 

 area allowed for diatoms, or portion protected by the cover. 

 As the specimens should not be crowded, I hope that I 

 make a liberal allowance for a vacancy, when I ask only 

 the y^oth part of the whole area to be devoted to any one 

 species, in order that it may have as much space allotted to 

 it as to the others ; when, therefore, it occupies the 3-^ X)th 

 part, it ought to be called neither " common " nor " rare." 

 To this line there may be allowed a margin, so I propose 

 that when a species occupies from the 200^^1 to the tooo^^^^ 

 part, it may be denominated as above ; and this may be con- 

 veniently divided into those which occupy from the ^oo^^ ^^ 

 the 5Jjoth, and from the j^^th to the lo^jo^^ part; the former 

 receiAang the name of "not common," the latter of "not 

 rare." In the same way from 4V th to guo^^ may be 

 called " common," and from ^^^ ^th to 3 oVtr^b " rare ;" beyond 

 these extremes, on either side, we have " very common," 

 and " very rare." 



To apply this : If the cover be about half an inch = "5 in 

 diameter, the area of diatoms is "5 x '5 x '7854 = -2 nearly; 

 in which case, if a species does not occupy -^'^^^ — '00004, 

 it is " very rare ; " from that to "0002 " rare ; " from that 

 to "0004 " not rare," from that to "001 " not common," 

 from which to '005 " common," and if more copious, " very 

 common." In measuring any diatom, it is sufficient to multi- 

 ply together the length and greatest breadth, allowing the 

 vacancy caused by its not having a rectilinear figure to be 

 added to the vacancy already mentioned. If we now take 

 Campylodiscus costatus, its length and breadth in the un- 

 twisted state is about "003, and its surface, got in the 

 way just alluded to, '00001 nearly; hence dividing by this 

 number, we get less than 4 frustules when " very rare " 

 (^'.r.), in a slide, from 4 to 20 when "rare" (r.), from 20 

 to 50 when " not rare " (w.r.), 50 to 100 when " not 

 common" (w.c), and from 100 to 500 when "common" 

 (c.) In Eunotia tc4raoclon, the average length is about 

 '002, and breadth '001, and surface '000002 ; hence, when 

 there are not oVo'oVa — ^^ under a cover half an inch in 

 diameter, it is "very rare," from 20 to 100 "rare," and 

 so on. In Navicula cryptocephala, the average surface is 

 •0011 X -00035 = 0000004 nearly; so when there are 



VOL. V. K 



