Tlie Construction oj a Parabolic Trajectory. 157 



and E„ which constitute then the partial atom-structural 

 formula. Thus e. g. the four isotopes of element with 

 atomic number 88 are as follows : 



AcX=w . He 4 E 8+2 with an atomic weight of «-i-4He = 222*4 



ThX.= *.He 4 E 8+2 „ „ „ *4-4He = 224'2 



Ra=«« . He 5 E 10+2 „ „ „ «+5He = 226-4 



M3th=i . He 5 E 10+2 „ „ „ *+5He=228-2 



As 'has been pointed out previously * this partial atom- 

 structural formula indicates 



(a) the series to which the isotope belongs by u resp. t ; 



(b) the atomic weight, by the addition of the number 



of He (4-00) to u resp. t ; 



(c) the valency, by the number of valency electrons (E„) 



written at the end ; 



(d) the number of metastasic electrons lE m ), by simply 



adding the inner and valency electrons together. 



The relationship of this system of radioactive elements to 

 the periodic system is established by attaching figure 1 to 

 the lower part of the new periodic table t« Whether or not 

 it is possible to extend this scheme of isotopes to the non- 

 radioactive elements is a problem of the future. 



Berkeley, Cal., 



July 26th, 1919. 



XI V . Note on the Construction of a Parabolic Trajectory and 

 a Property of the Parabola used by Archimedes. By 

 W. B. Morton and T. 0. TobinJ. 



IF a particle is projected, in a given direction, from a 

 given point A with such a velocity that it hits a second 

 given point B, then any number of points on the path may 

 be obtained by the simple construction shown in fig. 1. 

 AH is drawn to any point on tho vertical through B, HI is 

 parallel to the direction of projection, then the vertical 

 IP meets AH in a point of the path. This construction 

 involves a simple property of the parabola which does not 

 appear in the ordinary text-books. If chords are drawn 



* Phys. Rev. he. cit. 



t Loc. cit. 



X Communicated by the Authors. 



