Here's a relative example: Isaac Newton, 1642 - 1726. He was the second Lucasian Professor of Mathmatics at the University of Cambridge, which was one part of his research funding. He spent a lot of time and money in his office at Cambridge using the space to mostly study alchemy actually. As far as money transferring goes, theres probably a very old ledger that would show Isaac Newton being payed to teach and do whatever other scientific research he could while he was a professor at Cambridge. About half of the research was funded by Isaac Newton, although the university would have payed for materials and expenses as well. The other half came from the monarchy at the time. The Royal Society functioned like it does today, dispersing money to researchers after a hearing. Back in the 17th century the Royal Society would hear about any new ideas presented, and would debate whether these new ideas were correct. Isaac Newton had problems with this, as he didn't like criticism. It was really just an early scientific community in Great Britain at the time.

Isaac Newtons case was by no means standard however. In most cases researchers were privately funded, like James Watt, because they were inventors as well. Patents would supply income to pay off the debts, as they would often be made in favor of the inventor, like with Thomas Savery who recieved a patent that was continously extended so that he recieved royalties for "anything that moved using steam as a power source".

Edit: date fix

Here's an excerpt from the book 48 laws of power describing how Galileo used to get funded for his research:

Galileo Galilei a great mind with a pathetic pocket. His whole life he was troubled by financial shortcomings and instead of getting peanuts from working for multiple monkies, he decided to dance on one wedding exclusively. He managed to put his chosen master in the spotlight and make him appear greater than he was.

In 1610, he discovered the “Galilean Moons,” Jupiter’s 4 biggest moons. He dedicated this discovery to the Medici family whose symbol was the Jupiter, and after the discovery, the Galilean Moons were said to represent the 4 sons of the Medici family, revolving around their patriarch.

Usually, the Galilei’s procedure was to dedicate one small part of the discovery to one patron and receive gifts in return, rarely monetary support, but this time, he chose a different path and dedicated all of his discovery to one family. The Medici family enjoyed standing in the spotlight and being praised, leading them to become Galilei’s biggest supporter and rewarding him with a steady job and constant financial support.