'But that' means 'except that'. It means that he makes no doubt except one - that there are many potential Newtons. It's quite a formal, even archaic, way to express the idea. It is from the 18th century after all 🙂 These days, writers would just use 'that'.

The style is old-fashioned, and the word ‘but’ superfluous i e unnecessary. ‘I make no doubt that . .’ means ‘I have no doubt that . .’ He is saying that people are generally more naturally capable than we realise, because they need a supportive environment [education, culture, soil cultivated] and the right circumstances [situation, occasions, season favourable] to demonstrate their ability. We will never know how many great people are farming the land [‘at the ploughtail’] or working in shops and workshops [‘behind counters’].

It is a mistake. The sentence means the opposite of what the author intends. The way it is written, it means that the author does doubt that there are many potential exceptional people. But he is trying to make the point that he does NOT doubt that. The sentence can be fixed by striking out the word "but". Alternatively, the sentence could be written like this: "I am certain of nothing if not that there are ...."