y8 MAINE AGRICULTURAL EjXPERIMENT STATION. I914. 



in the work of Ten Eyck ** and that of Rotmistrov.t The 

 former states that the roots of oat plants growing in drills eight 

 inches apart interlace within two inches of the surface. Rot- 

 mistrov found the roots of oat plants Oif one variety exitending 

 laterally 94 cm. or 3.08 ft., of another variety 54 cms. or 1.8 ft. 

 Assuming all the plants in this marginal area to be better devel- 

 oped because of the greater space allotted each plant it may be 

 of interest to plant breeders to point out the relation of this 

 marginal area to the total area of plots of different rectangular 

 shapes and sizes. 



The periphery oi a unit area in the shape of a square and in 

 rectangular plots having the length 2, 4, 8 or 16 times the width, 

 is considered in Table 2. 



Table 2. 



The Periphery of a Unit Area in Terms of x, x being the Side 



of a Square of Unit Area. 









Rectangle 



Rectangle 



Rectangle 







Rectangle 



with length 



with length 



with length 





Square. 



with length 



4 times 



8 times 



16 times 







twice vvddth. 



width. 



width. 



width. 



Area 



a:2 



a;2 



x" 



a;2 



a;2 



Width (in feet) 



X 



.7071 * 



.5000a; 



. 3536a;* 



.2o00.T 



Length (in feet) 



X 



2(.7071x) 



4(.5000x) 



8(.3o36a;) 



16(. 2500a;) 



Periphery (in feet). . . 



4a; 



4.2426a; 



5.0000a; 



6.3640a; 



8 . 5000a; 



Per cent, increase i n 













length of periphery 













on basis of peri- 













phery of the same 













unit area in the 













form of a square. . . 



- 



6.0650% 



25.0000% 



59.1200% 



112.5000% 



An area 6 inches wide 













within the borders 













in terms of x will be 













(in sq. ft.) 



2a;- 1 



2.1213a;-l 



2 . 5000a-l 



3 . lS24a--l 



4. 2500a;- 1 



Note: It should be borne in mind that x always refers to the side of a square. Hence, 

 in the use of x the periphery of any oblong plot may be compared directly with that of a 

 square of equal area. 



* These factors to six places of decimals are .707107 and .353553. They are derived 

 algebraically as follows: 



In a plot with a length two times its width let x represent the width and 1 the area. 

 Then 2a;2=l 

 x-= 5 

 a:='. 707107 

 In a plot with a length eight times its width, let x represent the width and 1 the area. 

 8x2=1 

 x2=.125 

 x= .353553 



**Ten Eyck, A. M. The Roots of Plants. Bulletin 127, June 1904- 

 Kansas Expt. Sta. 



t Rotmistrov, V. [Distribution of the Roots of Some Annual Culti- 

 vated Plants.] Zhur. Opuitn (Russ. Jour. Expt. Landw) 8 (1907), No. 

 6, pp. 667-705; 9 (1908), No. I, pp. 1-24. 



