November 3, 1905.] 



SCIENCE. 



571 



The adaption of thistle-down to floating in 

 the air is seen at once to be quite remarkable. 



The down acts as a parachute to carry the 

 seed, and a calculation will set forth how 

 great this force may be. It will be considered 

 that the lamina referred to is placed horizon- 

 tally and the achene attached. The rate at 

 which the achene (with the down attached) 

 will fall in still air is as explained in the 

 solution given below: 



In the formula P =-- .0047^S'r P stands for 

 the pressure in pounds per square foot, V the 

 velocity in miles per hour, and S the number 

 of square feet. 



The downs and the achenes in a head weigh 

 .108 + .0561 = .1641- gram, 



and the surface area of one side of the lamina 

 is 326.713 square centimeters; but one gram 

 = .0022046 pound, and one sq. cm. = .155 

 sq. in., therefore, 



326.713X155 



.0022046 X • 1641 = 004 V^ X 



144 

 .35 miles per hr. (approx. ) 



From this it may be seen that a thistle-down 

 starting from an elevation of 20 feet, would 

 take 20/1848 hours to fall; and if we suppose 

 the wind to be blowing at 20 miles per hour, 

 the achene would be carried a distance of .21 

 mile, i. e., about one fifth of a mile. In this 

 calculation, all cross currents and changes of 

 air are neglected. 



In this parachute calculation, the lamina is 

 supposed to be horizontal. This condition 

 would necessarily give the maximum of the 

 parachute effect. Now, if this be represented 

 by E, the minimum effort could not be less 

 than 1/V2 E, because of the configuration of 

 the parts of the thistle-down. 



Another illustration might possibly bring 

 out more prominently the parachute effect : 

 If a weight of 150 pounds be attached to the 

 down in such a way that they will act with 

 the maximum effect; and it be required to 

 ascertain how many would be required to 

 ' parachute ' that weight so that it would fall 



^ Kent's ' Mechanical Engineering,' pocket edi- 

 tion, p. 492. This is the value given by Smea- 

 ton, 1759, but others have given it as low as 

 P = .0029T'\Sf. 



at the rate of five miles per hour, the equation 

 would be 



150 = .004 X 5 X 5 X -S, 

 therefore, 



/S^ 1,500 square feet; 



but the down-lamina is, for a whole head of 



108 achenes, 326.713 sq. cm., or .3624 sq. ft., 



therefore it would require 



1,500X108 ,,^^,nj 

 ' „/^,, — = 447,019 downs. 

 . 36244 



In all these calculations, neither the vis- 

 cosity of the air nor its capillary (surface) 

 attraction is taken into account, though the 



\y.: 





Fig. 4. The plane abdc is at an angle of 45°. 

 The horizontal cross-section of the mass of air 

 displaced in the descent of the plane, in this posi- 

 tion, would be the area of abdc divided by the 

 square root of 2. From the configuration of the 

 parts of the down, this would give the minimum 

 efifect. (See Fig. 1.) 



latter is very considerable, as may be seen 

 from the fact that small (microscopic) par- 

 ticles of sand, iron and the like, float, and 



