460 



Mr. E. Wilson. 



would mean that the volume to be ascribed to potassium in that 

 particular molecule is found by dividing the number 90 by 3, and 

 then multiplying the quotient by the number of atoms of potassium 

 in the molecule. Let us take an illustration from Table (IX) . The 

 molecular weight of potassium sulphate is expressed by K 2 S0 4 ; the 

 expression for its molecular volume is K'gS'gO^, which means that the 

 number K' ( = 90) has to be divided by 6 and the quotient multiplied 

 by 2 ; the number S' ( = 96) has to be divided by 6 ; the number 

 O'( = 20) has to be divided by 4, and the quotient multiplied by 4, 

 and that the sum of the resulting numbers (30 + 16 + 20 = 66) 

 is the molecular volume of potassium sulphate. The specific gravity 

 is then obtained by dividing the molecular weight by the molecular 

 volume : thus the specific gravity of potassium sulphate= 1 gy- = 2*636, 

 which agrees very well with its observed value = 2*640. 



Another method of notation might have been adopted which has 

 the advantage of getting rid of the accent and exhibiting both the 

 molecular weight and volume in one and the same formula. Thus 

 both the molecular weight and volume of potassium sulphate might 

 be expressed by K|S|.0|, if the numerators of the fractions are under- 

 stood to represent the number of atoms and the denominators the sub- 

 multiples of the atomic volumes. 



It is now necessary to explain more in detail, how the fundamental 

 numbers of column IV, Table I, have been obtained. In the first place 

 it may be observed that these numbers are always some multiple of 

 the atomic weight of the element divided by its specific gravity ; but 

 that it requires an examination of \the compounds of the element to 

 determine what this multiple ought to be. Let us take one or two 

 illustrations. The atomic weight of sodium divided by its specific 

 gravity is 24, and an examination of the compounds of sodium dis- 

 closes the fact that this element assumes in its compounds most fre- 

 quently the volumes 8 and 12, and occasionally 24 : the number 2, 

 therefore, is the proper multiple in this case, and the fundamental 

 number to be assigned to sodium is 48. Again, the atomic 

 weight of iodine divided by its specific gravity is 25*6, but the most 

 frequent volume of iodine in its compounds is 32 and, less fre- 

 quently 21-^ : the number 5 therefore is its proper multiple, and 

 the fundamental number to be assigned to iodine is 128. For 

 25*6 x 5 = 128, whilst 32 and 21^ are respectively one-fourth and one- 

 sixth of the same number. One more instance, perhaps, will suffice. 

 The atomic weight of boron divided by its specific gravity is about 

 = 4, whilst its compound volumes are 7 and 14 : whence 7 is the proper 

 multiple and 28 its fundamental number. 



Ammonium (NH 4 ) and cyanogen (CIST) may be treated as simple 

 elements, having as fundamental numbers the sum of the fundamental 

 numbers of their constituents, viz., N' + 4H' = 24 + 32=56 and 



