The best way to start with the table is to go to the Legend at top center. It shows that there are many small colored symbols for natural occurrences of ions. Then go to the left side of the table, to the block labeled Hard or Type A Cations. In this block, you should see that those symbols fall in blue-and-green, red-and-brown, and blue-and-green swaths. You're seeing the main strength of this new table: natural occurrences of ions fall in predictable patterns across this table, whereas the conventional table doesn't make much sense of natural occurrences.

As you look at this left-hand block of “Hard or Type A Cations”, you'll notice one of the table's two major differences from previous tables: the ions are rowed by charge and so go, for example, from Na¹⁺ to Mg²⁺ to Al³⁺ to Si⁴⁺ to P⁵⁺ to S⁶⁺. That new arrangement is what lets the swaths of color emerge.

If you now go to the right, to “intermediate cations” and onward over to the anions, you'll see the table's second and even more fundamental change from conventional tables: some elements appear multiple times. That's because they take on multiple charges in nature, and behave very differently in those different conditions. For example, sulfur appears as S⁶⁺ (sulfate), S⁴⁺ (sulfite), S⁰ (elemental sulfur), and S^2- (sulfide). Sulfur exists in all those forms in nature, generally from earth-surface oxidizing conditions on the left (as S⁶⁺ in sulfate) to deeper reducing conditions on the right (as S^2- in sulfide).

If you now look at the entire table, or at least the left and middle (the blocks hard and intermediate cations), you'll see the colored symbols fall in swaths across the table. Those swaths follow some colored curving lines. Those curving lines are contours, just like the contours on a topographic map, but these contours are of ionic potential z/r, or of ionic charge divided by ionic radius. For example, Ca²⁺ in the hard cations has a charge of +2 and a radius of 1.0 angstroms, so its z/r is 2. That's why the blue line for z/r = 2 goes through the center of the box for Ca²⁺.

The reason for pointing out these lines is that they coincide with the swaths of symbols very well, suggest­ing that the ratio of charge to radius, or z/r, is an important parameter in chemical behavior. z/r is essentially a measure of how highly focused charge is in an ion – the larger the ratio, the more intense the charge. If z/r is small, a cation has weakly focused charge and so only weakly bonds to O^2-, our most abundant anion. Such a cation is easily dissolved from minerals and goes into solution – hence all the blue symbols for dissolved substances at the left of the hard cations. Higher ionic potential allows more effective bonding with oxygen to allow formation of oxide minerals and retention in soils and solids – hence the red and brown symbols down the middle of the hard cations. Very high ionic potential, however, means that cations begin to repel each other in solids (despite bonding very strongly to O^2-), so that such ions are more soluble – hence the blue symbols at the right of the hard cations. Inset 7 at the bottom of the table shows all this schematically.

The other insets at the bottom of the table contain some graphs to show that various mineral properties follow that same patterns as the overall trends in the main part of the table. There's a lot more to see in the new table, but hopefully this helps get you started.