Why does the anomalous Zeeman effect not show up on some atoms?

[carllacan]

Why does the "anomalous" Zeeman effect not show up on some atoms?

I read this:

While the Zeeman effect in some atoms (e.g hydrogen) showed the expected equally-spaced triplet, in other atoms the magnetic field split the lines into four, six, or even more lines and some triplets showed wider spacings than expected. These deviations were labeled the "anomalous Zeeman effect" and were very puzzling to early researchers. The explanation of these different patterns of splitting gave additional insight into the effects of electron spin.

I don't see why the electron spin affected the number of lines to go up in some atoms and not in others. The electron(s) on the H atom also have spin.

Thank you.

 

[DrClaude]

I guess that that's a quote from HyperPhysics. I must say that I don't get it either: the normal Zeeman effect is seen in states with $S=0$ (such as in helium), which is not the case for hydrogen ($S=1/2$).