Constitution and Stability of Atom Nuclei. 329 



range the atomic weights of the isotopes may be expected to 

 include the multiples of two adjacent to the mean atomic 

 weight, and in general it seems that at least four such 

 isotopes should be expected. The isotopes of even atomic 

 number with odd atomic weight cannot be predicted so 

 definitely, but they may be expected to be fewer in number 

 than those of even atomic weight, and also to extend to a 

 lesser distance from the mean value. 



According to the above principles silver should consist 

 either wholly or mainly of isotopes of atomic weights 107 

 and 109, rubidium of atomic weights 85 and 87, copper 63 

 and 65, and ruthenium of a single species mostly of weight 

 103, provided the chemical atomic weights are as precise as 

 they are supposed to be. The general predictions are easily 

 applied to the elements of even atomic number. 



Representation of the Isotopic Number by a 

 Straight Line Plot. 



Thus far five variables, P, N, M, n, and N/P, have been 

 used in describing the composition of atom nuclei. It is 

 evident that from these ten different two-dimensional plots 

 may be constructed, and that any two of the five may be 

 taken as independent, when the other three become dependent 

 variables. When P and N/P are chosen as independent, as 

 in fig. 1 (PI. XII. }, constant values of the isotopic number n 

 are represented by hyperbolas. By choosing n and M as 

 the independent variables it is obviously possible to repre- 

 sent constant values of n by straight lines. The remarkable 

 feature of the plot thus obtained, fig. 5 (PI. XII.), is that 

 constant values of all of the five variables are represented by 

 straight lines, and that for four out of the five, ?i, M, P, 

 and N, constant values are represented by a series of parallel 

 straight lines, while various constant values of the ratio 

 N/P are indicated by straight lines radiating from the 

 origin, n = 0, M = 0. 



The equations for the five sets of straight lines are : — 



P = const. n = 2(gf-M), . . . . (1) 



N = const. n = q-M, (2) 



n = const. ?< = (/, (3) 



M = const. M = 0, (-1) 



N/P = const. n=kM. (5) 



In these equations q is any positive whole number, and k 

 is a constant which may have any positive value, but is for 

 real cases always a proper fraction with values between 



