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59. 

are calculated [[underlined]] for the condition under which air resistance is a minimum [[/underlined]]. 

The above simple case is not realizable in practice because of the large mass of propellant for each shot compared with the total mass; i.e., provision is not made for the mass of the chamber. The result will be the same, however, if smaller charges are fired in rapid succession; as will be evident from a calculation similar to the above, which is carried out in Appendix E, p.77, under the assumption of smaller charges for successive shots.

[[underlined]] RECOVERY OF APPARATUS ON RETURN [[/underlined]]. 

A point of considerable practical importance is the question of finding the apparatus on its return, and of following it during flight; both of which depend in a large measure upon the time of flight. 

Concerning the times of ascent, Table VII shows that those are remarkably short. For example a height of over 230  miles is reached in less than [[strikethrough]] 2 [[/strikethrough]] ^[[6]] 1/2 minutes (s[[subscript]] 8 [[/subscript]]; a = 50). The reason is, of course, that the rocket under present discussion possesses the advantage of the bullet in attaining a high velocity, with the added advantage of starting from rest. In fact, the motion fulfills closely the ideal conditions for extremely rapid transit; namely, starting from rest with the maximum acceleration possible, and reversing this acceleration, in direction, at the middle of the journey. 

The short time of ascent and descent is, of course, highly advantageous as regards following the apparatus during ascent, and recovering it on landing. The path can be followed, by day, by the ejection of smoke at intervals; and at night by flashes. Any distinctive feature, as for example, a long black streamer, could