412 Dr. G. J. Stoney on the 



we make the deviations slightly different according as we use- 

 the logarithmic or the elliptic curve for our central curve. 



In the last two paragraphs a representation of the laws by 

 a diagram referred to rectangular coordinates has been kept 

 in view. It is the most convenient diagram for the stud}- of 

 deviations. But a spiral referred to polar cordinates, which 

 is equally legitimate, makes the chemical grouping of the 

 elements more conspicuous ; and is that which was used in 

 the original from which Plate IV. is copied. Equidistant 

 radii are here what represent the steps of the Mendeleeff' 

 progression. The spiral as engraved is the central curve 

 which is furnished by a logarithmic equation : if it had been 

 plotted down from the corresponding elliptic equation, the 

 part of the spiral represented in the diagram would have 

 been nearly the same in all but its innermost coil, which would 

 have been steeper. 



Using either of these curves, the deviations from it follow 

 one law for the artiads and another for the perissads, and 

 these laws can be partly worked out. It will not be possible 

 to work them out fully until atomic weights shall have been 

 determined with greater accuracy and more certainty. How- 

 ever, some terms of the equations representing these laws were 

 obtained ; and the remarkable fact emerged that they both 

 depend on a period of 18 places on the diagram of PL IV., 

 whereas most chemical and physical properties of the elements 

 are associated with the period of lb' places, which is repre- 

 sented on the diagram by each revolution of the spiral. 



It is the existence in nature of these deviations that renders 

 possible an apparent reversal of the Mendeleeff order of suc- 

 cession, such as almost certainly prevails between tellurium 

 and iodine, where the element to which we must assign the 

 greater atomic weight comes first in the ascending Mendeleeff' 

 series. That there are not several cases of this kind is only 

 because the range of the deviations is everywhere small, iu 

 other words, the two sinuous curves nowhere recede far 

 from their common central curve. 



Another fact that came to light was that in order that it 

 may be possible to represent the atomic weights of the 

 elements by definite laws such as are above described, it is 

 essential that we add to the Mendeleeff' series, as it was 

 known in 1888, the places indicated on sesqui-radius 16 of 

 the accompanying diagram. The necessity for this addition 

 made it certain that these places have a real existence in 

 nature, although at the time no elements were known that 

 occupied them. The anticipation that this was so has been 

 in the most satisfactory way justified by the discovery in 

 recent years of argon by Lord Ravleigh and Sir "William 



