338 RESEARCHES ON FUNGI 



projectile, (2) the time taken in the night of the projectile, and (3) the 

 time taken in the discharge of the gun, i.e. in everting the inner 

 peridial membrane ; and this will lead to (4) a discussion of the 

 function of the air-spaces between the sinuses of the outer and inner 

 peridial teeth. We shall then calculate mathematically : (5) the 

 momentum of the projectile at the moment of leaving the gun, 

 (6) the kinetic energy of the projectile at the moment of leaving the 

 gun, (7) the average force of the propelling peridium while this acts 

 upon the projectile, and (8) the rate of developing energy in the 

 gun. In concluding this Section, (9) the results of the calculations 

 will be summarised. 



(1) Initial velocity of the projectile. From the equation : 



v 2 = 2 gs 

 where v = the initial velocity, g the acceleration due to gravity, 

 and s the vertical height to which a projectile is discharged when 

 shot vertically upwards, neglecting the resistance of the air it can be 

 calculated that a Sphaerobolus projectile, if shot vertically upwards 

 to the maximum observed height of 14-5 feet, has an initial velocity 

 of about 30- 4 feet per second. 



A similar calculation to that just made shows that, if a 

 Sphaerobolus projectile is shot vertically upwards to a height of 

 only 7 feet instead of 14-5 feet, the initial velocity of the projectile 

 would be about 21 feet per second instead of about 30 feet per 

 second. 



A Sphaerobolus projectile is only about 1-25 mm. in diameter, 

 and therefore its surface area relatively to its mass is large. The 

 resistance offered to its flight through the air must be considerable. 

 It seems clear, therefore, that a projectile which has been shot 

 vertically upwards to a height of 14-5 feet must have had an 

 initial velocity which exceeded 30 feet per second, and that a 

 projectile which has been shot vertically upwards to a height of 

 7 feet must have had an initial velocity which exceeded 21 feet 

 per second. 



(2) Time taken for the flight of the projectile. Employing the 

 equation : 



s = | gt* 

 where s = the vertical distance of rise or fall, g the acceleration due 



