There was a connection at the time in question, in that note circulation was restricted to the amount of the paid up capital. One needs to remember that the notes were not all in circulation at the same time. The 1906 issue, for instance, was in use for a decade. They were not printed all at once either, but in batches that were ordered as needed. They were put into circulation only as needed by the economy. With daily settling of balances between banks, any notes not immediately required for business soon found their way back to the issuing bank. New notes were issued as old ones were worn out and withdrawn for destruction. In our own time, you will find only a small percentage of all Journey $5s ever issued, for example, in circulation at any given time.
There were stiff fines for exceeding circulation limits, and banks kept close control to avoid the fines. Notes in the banks own vaults and tills did not count towards their circulation liability.
Things got a bit more complicated just before WWI when bank circulations were empowered to exceed their capital by a small percentage as needed for "moving the crops", subject to a small tax on the overissue.
