ALTHOUGH I am confident that the foundation on which I have been building is firm, and will never fail, I also feel that there are probably errors in raising the superstructure. "Truthful deductions must ultimately harmonise; like light, they will shine by their own effulgence." "If, however, we determine that we will not receive any truth against which objections can be raised, we shall remain in a state of universal scepticism, for against truths of every description objections have been and may be suggested." Appearances are often contrary to facts— "the straight stick looks crooked in the tide." And the question has always to be decided, whether the objections neutralise the positive evidences in favour of the truth of any assertion.
It seems desirable that I should briefly state my entire ignorance of natural science, and that what I do know has been gained without technical knowledge, with the determination that imagination should not interfere with strict investigation.
I had for a long time studied the development of the harmonics of colour, and believed that I had gained them correctly; but I saw no way of proving this. The thought occurred—Why not test the laws in musical harmonies? I wrote down the development of the seven major keys of the white notes in keyed instruments. I was perplexed by the movement as of "to and fro," but the development of numbers explained this point, and I found that the method of development in colours, tones, and numbers agreed. I remembered the keys with sharps, but had forgotten that B♭ belonged to the key of F, and here I thought that the laws failed. But I found by reference that all were correct, the eighth being the first of a higher series, the laws having enabled me to distinguish between flats and sharps,