68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 7I 



assumption that hydrogen and oxygen are used (in the liquid or solid state, to 

 avoid weight of the container), giving the same efficiency as that for which 

 " Infallible " smokeless powder produces respective velocities of, for example, 

 5,500 ft./sec. and 7,500 ft./sec, the velocities (deducting 218.47 calories per 

 gram as the latent heat plus specific heat, from boiling point to ordinary tem- 

 perature) would be 9,400 ft./sec. and 11,900 ft./sec; and the total initial masses 

 for a start from 15,000 feet, respectively, 119 pounds and 43.5 pounds. 



Incidentally, except for difficulties of application, the use of hydrogen and 

 oxygen would have several other evident advantages. 



""This calculation is made under the assumption of stationary centers for 

 the earth and moon. 



^ The time of transit for the case under discussion would, of course, be 

 comparatively large. If, however, the final velocity were to exceed by 1,000 or 

 2,000 ft./sec. the velocity calculated, the time would be reduced to a day or two. 



The time can be calculated from the solution, by Plana (Memoire della Reale 

 Accademia della Scienze di Torino, Ser. 2, vol. 20, 1863, pp. 1-S6), of the 

 analogous problem of the determination of the initial velocity and time of 

 transit of a body, such as a volcanic rock, projected from the moon toward 

 the earth. 



^^ At the time of signing of the armistice, the net result of the development 

 of a reloading mechanism had been the demonstration of an operative appa- 

 ratus that was simple and travelled straight, with the essential parts suffi- 

 ciently strong and light, using a few cartridges of simple form. 



The work remaining, upon which progress has since been made, has been 

 the adaption of the device for a large proportionate weight of propellant. 



^^ The probable number of collisions here calculated is the sum of the 

 probable numbers obtained by taking the velocity of the spherical body, and of 

 the meteors, separately equal to zero. 



Let V = velocity of the spherical body, 

 V = velocity of the meteors, 



n = the number of meteors per unit volume, which number is, of 

 course, a fraction (mutual collisions between meteors being 

 neglected), and 

 S = the area of cross-section of the spherical body. 



For V ^ o, the meteors, if any, which strike the sphere during the time 

 t to t-f- dt will have come from a spherical shell of radii Vt and V(t-1- dt), 

 neglecting the diameter of the spherical body in comparison with that of the 

 spherical shell. Further, the probable number in any small volume, in this 

 shell, which are so directed as to strike the body, is 



S . 

 47rV=t- ' 



being the ratio of the solid angle subtended at the element, by the spherical 

 body, to the whole solid angle, 47r. Hence the probable number of collisions, 

 N, from all directions, between the time ti and tz is, evidently, 



N = nSV(t2 — ti). 



For V=:o, an expression of the same form is obtained for the probable 

 number of meteors within the space swept out by the spherical body. 



