The expected number of particle intersections (E) was calculated from 

 30° 



- sin ede 



■(0° - 30°) poj 



„ =0' r^^ sin ede 



(30° - 60°) 3o°j 



90° 



^60° - 90°) = o;^o/ / 



where 0' equals total number of observed particle intersections in all six 30°-wide 

 sectors. 



These calculations are appropriate because the probability of a randomly positioned 

 plane intersecting a particle is proportional to the sine of the angle between particle 

 and plane (Kendall and Moran 1963). Consequently, the number of particles intersected 

 at any angle is also proportional to the sine of the angle of intersection. 



RESULTS AND DISCUSSION 

 Surface-to-Volume Ratios 



Two observations of o on each of 13 ponderosa pine needles of average thickness 

 averaged 57.57 square centimeters per cubic centimeter with a standard deviation of 

 6.81 square centimeters per cubic centimeter. 



Average o for the entire cheatgrass plant was 144.03 square centimeters per cubic 

 centimeter. This average, as well as average density, was weighted according to volume 

 of each particle found on all plots. Table 1 summarizes average values of o for the 

 six cheatgrass particles. 



Table 1. -- Averages and measures of variation of surface area-to- 

 volume ratios for six particles comprising cheatgrass 



Kind 



Average surface- 

 to-volume ratio 



Number of 

 observations 



Standard 

 deviation 



Coefficient 

 of variation 





2 



Cm. /cc. 





Cm.^/cc. 



Percent 



Stalks 



75.8 



880 



5.8 



7.6 



Leaves 



167.4 



50 



17.7 



- 1,0.6 



Peduncles 



277.3 



100 



14.1 





Spikelets 



321.5 



5 





(^) 



Awns 



331.7 



20 



75.4 



22.7 



Glumes 



709.1 



9 



130.3 



18.4 



■^Not calculated. 



8 >■ 



