But Tom, from the book itself:
Let the method of simple inquiry--the "Zetetic" process be exclusively adopted--experiments tried and facts collected--not such only as corroborate an already existing state of mind, but of every kind and form bearing on the subject, before a conclusion is drawn, or a conviction affirmed.
Experiments to "corroborate an already existing state of mind". That sounds awfully like "see for yourself."
Please reread ENAG.
Perhaps you missed the word "not" before your chosen quote. He is saying that experiments should
not be conducted to corroborate an already existing state of mind (a specific hypothesis), but of every kind and form bearing on the subject (explore all possibilities), before any conclusion may be drawn.
Rowbotham is deriding the Scientific Method. In the Scientific Method the scientist must ask a question, create a hypothesis, test that hypothesis, and if the hypothesis is true, publish your results. You are testing a specific hypothesis rather than competing possibilities.
The flaw in the Scientific Method is that there might be half truths or lesser truths. If you are framing experiments around a single hypothesis you are only testing that specific idea, rather than all ideas.
There are a lot of Zetetic sciences which operate without hypothesis, where experimentation is conducted without working towards a pre-conceived conclusion. Medical chemists certainly use the Zetetic Method for creating drugs. See the Folding at Home project. The project goes through a rapid series of different configurations to see what works and what does not. When chemists want to know how different chemicals will react to red blood cells, for example, they create rooms and rooms of vials which test each and every result for the desired cause.
Experiment first, conclude after. That's how the truth is found.
When you hypothesize first and create an experiment around that hypothesis your experiment is fallacious because you are deliberately framing your experiment around whatever you are trying to prove. You might find a half-truth or misdirection. Finding the truth of the matter has nothing to do with the Scientific Method. With the Scientific Method you are attempting to prove your idea (hypothesis) true. In the Scientific Method you're also told to stop experimenting as soon as you get a successful result.
Experimenting without hypothesis = Zetetic Method
Experimenting around a specific hypothesis = Scientific Method
Zeteticism (Empericism) blows the Scientific Method out of the water. While it might not always be the most practical option to test all possibilities before coming to a conclusion, it is certainly the method which will bring the experimenter the closest to truth. The Scientific Method fails because it is based on creating and testing a hypothesis, rather than testing all competing possibilities. Multiple hypothesis' might very well be correct in a particular subject, but the experimenter wouldn't know that, as he was taught in school to publish his result and declare victory as soon as his hypothesis achieves a positive result.
This is what Zeteticism is. It is not "you have to see it to believe it," or any other such nonsense. The text does not say that at all. I am appalled at the poor reading comprehension on this forum.