1 88 metcaIvF: notes on north dakota plants 



The principle of this method of plotting on radiating lines 

 instead of parallel ordinates becomes clear when it is realized 

 that all parallel lines in a projection meet at a point at infinity. 

 If we consider the projection plane to be one of the faces of a 

 cube in which a sphere of unit radius is inscribed, and each point 

 in the projection to be the intersection of a line from the center 

 of the sphere with the projection plane (gnomonic projection); 

 then an ordinate {CP) in the projection plane normal to the Z- 

 axis (front face of the cube, figure 2) represents a plane which 

 contains the F-axis, and hence becomes a radiating line {OD) 

 in the projection plane normal to the F-axis (top face of the cube, 

 figure 2). 



If the coordinates of the projections normal to the Z-X-Y- 

 axes be designated x,y, x' ,y' , and x" ,y" , respectively (Fig. 2), 

 the coordinates of a point P{x,y) become y^= x' /y' = i/x" and 

 X = i/y' = y" /x" in the other projections, respectively. A 

 straight line y = ax -\- b (such as GH, Fig. 2) becomes by' = 

 x' - a and ay" = -bx" -^ 1 (as line HE, Fig. 2), in the other 

 projections. 



BOTANY.— Notes on North Dakota Plants. F. P. Metcai^P, 

 Biological Survey. 



During the summer of 191 7 the writer and D. C. Mabbott 

 were engaged in conducting an extensive survey of the marsh 

 and aquatic plants of North Dakota for the Biological Survey, 

 U. S. Department of Agriculture. This was an exceedingly 

 valuable opportunity to study intensively the marsh and aquatic 

 flora throughout the state. The results of this work were so 

 interesting from the standpoint of plant distribution that it 

 was thought advisable to make known the most salient features 

 in a preliminary paper. 



Before this work could be completed the writer was called to 

 the military service and for nineteen months had no time to 

 think of North Dakota and its plants. This was fortunate for 

 one reason, at least, in that in September, 191 8, Bergman's 

 Flora of North Dakota^ was published. This made additional 



1 Bergman, H. F. Flora of North Dakota. Sixth Biennial Report, North Dakota 

 Soil and Geological Survey, 1911-12. Published September, 1918. 



