It was pointed out by Mendeléeff that, with the exception of series 1 and 2 at the top of the table, the alternate members of the groups show particularly close relationships. These subordinate groups, marked A and B, in most cases show remarkable analogies and gradations in their properties, for example, in the alkali-metals from lithium to cæsium, and in the halogens from fluorine to iodine. The two divisions of a group do not usually show very close relations to each other, except in their valency, and they even display, in several instances, opposite gradations in chemical activity in the order of their atomic weights. For instance, cæsium stands at the electro-positive end, while gold stands at the electro-negative end of its subordinate group. The difference between the two divisions is very great in Groups VI and VII, but it is extreme in Group VIII, where heavy metals are on one side and inactive gases on the other. Many authorities separate these gases into a “Group O” by themselves at the left-hand side of the table, but this does not change their relative positions, and the plan may be objected to on the ground that many vacant places are thus left in the groups VIII and O. The periodic law has been useful in rectifying certain atomic weights. At the outset Mendeléeff was obliged to change beryllium from 14·5 (assuming Be_{2}O_{3}) to 9 (assuming BeO), and later the atomic weights of indium and uranium were changed to make them fit the system. All of these changes have been confirmed by physical means. Mendeléeff found a number of vacant places in his table, and was thus able to render further service to chemical science by predicting the properties of undiscovered elements, and his predictions were very closely confirmed by the later discovery of scandium, gallium, and germanium. The table indicates that there are still two undiscovered elements below manganese and probably two more among the rare-earth metals. The interesting observation has just recently been made by Soddy that the products of radioactive disintegration appear to pass in a symmetrical way through positions in the periodic system, giving off a helium molecule at alternate transformations until the place of lead is reached. It appears, therefore, that the five vacant places in the table above bismuth are probably occupied by these evanescent elements, and it is to be noticed that all of the elements that have been placed in this region of high atomic weights are radioactive.