Dr. Schumann s Formula for Diatom-lines. Bij W. J. Hickie. 11 
pleura pellueida, Denticula, Nitzschia amphioxys (with less distinct 
longitudinal lines), almost all species of Cocconeis, perhaps all 
species AchnantJdditm- and Achnanthes; Bhoicosphenia curvata, 
marina, frada and haltica; Cymhella, Cocconema, Encyonema, 
Amphora, all species of Ceratoneis known to me, Gomphonema, 
almost all species of Navicula (and amongst them perhaps N.firma), 
Amphigomphus dilatata, Scoliopleura Jennerii (with irregular 
longitudinal lines), Scol. convexa, almost all species of Siauroneis, as 
Staur. punctata, truncata, Eichhornii, Phoenicenteron and am])hi- 
cephala ; Pleurostaurum acutum, FrustuUa Saxonica, Doryphora 
B'dchii, those species of Pleurosigma treated of by Smith and 
Eahenhorst as Section 2, several cylindrical forms, on their front 
sides, as Melosira distans, nivalis, salina. 
The formula c = V + is excellently well adapted for deter- 
mining the amount of error of estimate. 
For example, I found in one specimen of Pleurosigma 
attenuatum, 
a = 30, b = 22, c = 36. 
If the proportionably easy estimates of a and h be assumed to 
be exactly correct, then must c = V 900 + 484 = 37 * 2 ; conse- 
quently the relative error of the last estimate^ 
1-2 _ 1 
37^ ~ 31 ' 
Again, three specimens of Pleurosigrii)3^!^^gUlst,^^^n English 
slide gave me, 
(1) a = 25, 6 = 35, c = 44, instead of 43. 
(2) a = 26, h = 36|, c = 46, „ 45. 
(3) a = 26i, 6 = 38, c = 47^, „ 46i. 
Smith's estimate is, if we turn his figures into our measurement, 
a = 32, 6 = 35J, 
and therefore the number of the transverse striae perceptibly 
greater. To be sure, I measured the width of the lines in all three 
instances close to the central knot, and this may possibly have given 
rise to the divergence. 
In Pleurosigma fasciola I found a = 54, ?) = 50. The oblique 
striae in this case I was unable to see.* 
* And no wonder ; for there are no oblique strise on it. In resolution, to know 
beforehand what to look for is half the battle; therefore drawings of the Dia- 
tomacesB without the striae are almost worthless. 
