Complex sentence: The result was a great demand for specie, which many banks did not have enough of to exchange for their notes, causing the Panic of 1837, which threw the national economy into a deep depression.
Split into simpler sentences: The result was a great demand for specie, which many banks did not have enough of to exchange for their notes. This was a direct cause of the Panic of 1837, which threw the national economy into a deep depression.