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56.

These large numbers, to be sure, agree with one's first impression as to the probable initial mass of a rocket designed to reach extreme altitudes; but the comparatively small initial masses, possible with high efficiency, are not intuitively evident until one realizes what an enormous reduction is involved in extracting anything as large as the twenty-seventh root of a number.

It should be observed that the apparatus is taken as weighing one pound. Strictly speaking, if the recording instruments have a mass of one pound, the entire final mass of the apparatus must be at least three or four pounds. The mass for the recording instruments may be considered as being very small, yet many valuable researches could, of course, be performed with an apparatus weighing no more than this. The entire final apparatus should if possible be designed to weigh not over 3 or 4 lbs. at most, unless the efficiency of the apparatus is so high that the "effective velocity", c(1-k), is at least in the neighborhood of 7^[[,]]000 ft/sec. An examination of Table VII makes very evident the [[underline]] necessity of securing maximum effectiveness of the apparatus before a rocket for such a purpose as meteorological work, for example, is constructed; in order to make the method as inexpensive as possible [[/underline]]. It should be remarked, however, that the "total initial mass" [[underline]] will really not be increased in as large a proportion as the final mass [[/underline]] if the latter is made greater than one pound by virtue of equation (2).

Before pr[[overwritten with "o"]]e[[/overwritten with "o"]]^[[e]]ceding further it will be well to consider carefully the question of air resistance as dependent upon the cross-section of the rocket during flight. It has already been assumed that the cross-section, in the calculation of the minimum [[underline]] M [[/underline]] for each interval, was one square inch. If we make the apparatus as long,