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79.

[[underline]] Appendix F [[/underline]].

[[underline each individual word]] Proof that the Retardation Between 500,000 ft. and 1,000,000 ft. is Negligible [[/end individual word underline]].

The falling-off of velocity, [[underline]] w [[/underline]], due to air resistance, is given by 

P S/So sh = 1/2 M [[subscript]] o [[/subscript]] w [[superscript]] 2 [[/superscript]] 1
where P = the mean air resistance in poundals per square inch between the altitudes 500,000 and 1,000,000 feet from the previously mentioned velocity curves; the pressure being considered as atmospheric, 
  = the mean density over this distance, 
s = the mean area of cross-section of the apparatus throughout the distance, taken as 24 square inches in view of the average mass, [[underline]] M [[/underline]] [[superscript]] o [[/superscript], throughout the interval and 
h = the distance traversed; 500,000 feet.

It is thus found that the loss of velocity [[underline]] w [[/underline]] is less than 10 ft/sec., (for a = 150 ft/sec. even when S/So is taken as constant throughout the distance and equal to that at 500,000 ft. (i.e., 2.73 x 10 [[superscript]] -9 [[/superscript]]).