THE SPORABOLA 187 



Let us assume that the vertical velocity at any time is within 

 1 per cent, of the terminal velocity, and that y is the distance 

 the spore has fallen before attaining this velocity, then putting 

 log,, = 2-3 log 10 and | = 0-99, we get 



2/ = X 2 j - log 10 (0-01) 2-3 - 0-99 J 



For Amanitopsis vaginata, since V = 05 cm. per second, we find 



that 



y=0*0009cm. = 9/z. 



The diameter of a spore is approximately 10 //,. Hence we can 

 state that the distance fallen by a spore of A. vaginata before 

 reaching its terminal velocity (within 1 per cent.) is less than its 

 diameter. 



The length of time required for any spore after being set free 

 to attain its terminal vertical velocity within 1 per cent., can be 

 shown to be equal to 0-0047 x V, where V is the terminal velocity. 

 For Amanitopsis vaginata the terminal velocity may be taken as 0-5 

 cm. per second. It can be calculated, therefore, that a spore would 

 attain its terminal vertical velocity in approximately T1 Lj second. 

 The terminal velocities of fall of the spores of other species are of 

 the same order as that of Amanitopsis vaginata. We are therefore 

 justified in drawing the general conclusion that the spores of 

 Hymenomycetes attain a uniform velocity of fall practically at the 

 instant of their liberation. 



We can also calculate the length of time required for a spore to 

 arrive within 1 per cent, of the total horizontal distance to which 

 it is projected. At the end of the time in question, the position of 

 the spore on the sporabola will be x cms. from the vertical axis 

 and y cms. below the highest point. According to our assump- 

 tion - = 0-99. By substitution in the equation for a sporabola we 



find that 



y = 0-0009 cm. = 9 m- 



It has been shown, however, that a spore falls through this 

 distance in approximately j^- second. We may conclude, therefore, 

 that the spore will have travelled for only T i Tr second before arriving 



