I enter upon the subject with the deepest sense of my own inability to do justice in any measure to the grandeur of the topic; but I trust that my remarks may prove suggestive to others of far higher truths. They are the result of the leisure hours of nearly fifty years, during which the conviction has ever deepened, that "philosophy of the natural kind does but push man's ignorance farther back," and that, in the concluding words of Sir John Lubbock's inaugural address to the British Association at York in 1881, "the great lesson which Science teaches is, how little we yet know, and how much we have still to learn."
If health is still granted to me, and if an interest is created on the subject of these pages, I shall endeavour to explain by what means I gained the laws here described, and to enter upon the development of numbers as showing the stream of time ever falling into infinity, and gliding onwards; also the sevens in creation, with several other branches of the subject which are here untouched, or but briefly alluded to. It is my earnest desire that all may be closely examined. Indifference will grieve me, but even severe criticism will afford me pleasure, as proving that the subject is considered worthy of investigation.
The publication of this work has been unavoidably delayed for a year, and I now quote briefly from an address of Dr. C. W. Siemens, during the late meeting of the British Association at Southampton, as reported in the Times. I have strictly endeavoured to make my investigations according to his views of combining scientific knowledge with practical utility.
"The time was when Science was cultivated only by the few, who looked upon its application to the arts and manufactures as almost beneath their consideration: this they were content to leave in the hands of others, who, with only commercial aims in view, did not aspire to further the objects of Science for its own sake, but thought only of benefiting by its teachings. Progress could not be rapid under this condition of things, because the man of pure science rarely pursued his inquiry beyond the mere enunciation of a physical or chemical principle, while the simple practitioner was at a loss how to harmonise the new knowledge with the stock of information which formed his mental capital in trade. The advancement of the last fifty years has, I venture to submit, rendered theory and practice so interdependent, that an intimate union between them is a matter of absolute necessity for our future progress." "It is to the man of science, who also gives attention to practical questions, and to the practitioner, who devotes part of his time to the prosecution of strictly scientific investigation, that we owe the rapid progress of the present day, both merging more and more into one class, that of pioneers in the domain of Nature." "These considerations may serve to show that, although we see the men of both abstract and applied science group themselves