Transitions in hydrogen
When Bohr started from scratch with his own calculations, he arrived at a formula which reproduced the same information as Rydberg's for the Balmer series of lines--and the other series which fall outside the visible range. But essentially all Bohr was saying is:
ΔE = hν

So he had arrived at a model of the atom based on the emission spectrum which appeared to describe how the electrons were arranged around the nucleus. Except....

There were two problems with Bohr's theory and description of the atom. First, although he recognized that the electrons do not "run out of gas", he did not have a complete explanation of how they performed this seemingly impossible feat. Second, his calculations only worked for hydrogen and other one-electron species such as He+.