Mr. Johnson's health had been always extremely bad since I first knew him, and his over-anxious care to retain without blemish the perfect sanity of his mind contributed much to disturb it. He had studied medicine diligently in all its branches, but had given particular attention to the diseases of the imagination, which he watched in himself with a solicitude destructive of his own peace, and intolerable to those he trusted. Dr. Lawrence told him one day that if he would come and beat him once a week he would bear it, but to hear his complaints was more than _man_ could support. 'Twas therefore that he tried, I suppose, and in eighteen years contrived to weary the patience of a _woman_. When Mr. Johnson felt his fancy, or fancied he felt it, disordered, his constant recurrence was to the study of arithmetic, and one day that he was totally confined to his chamber, and I inquired what he had been doing to divert himself, he showed me a calculation which I could scarce be made to understand, so vast was the plan of it, and so very intricate were the figures: no other, indeed, than that the national debt, computing it at one hundred and eighty millions sterling, would, if converted into silver, serve to make a meridian of that metal, I forgot how broad, for the globe of the whole earth, the real _globe_. On a similar occasion I asked him, knowing what subject he would like best to talk upon, how his opinion stood towards the question between Paschal and Soame Jennings about number and numeration? as the French philosopher observes that infinity, though on all sides astonishing, appears most so when the idea is connected with the idea of number; for the notion of infinite number--and infinite number we know there is--stretches one's capacity still more than the idea of infinite space. "Such a notion, indeed," adds he, "can scarcely find room in the human mind." Our English author, on the other hand, exclaims, let no man give himself leave to talk about infinite number, for infinite number is a contradiction in terms; whatever is once numbered, we all see, cannot be infinite. "I think," said Mr. Johnson, after a pause, "we must settle the matter thus: numeration is certainly infinite, for eternity might be employed in adding unit to unit; but every number is in itself finite, as the possibility of doubling it easily proves; besides, stop at what point you will, you find yourself as far from infinitude as ever." These passages I wrote down as soon as I had heard them, and repent that I did not take the same method with a dissertation he made one other day that he was very ill, concerning the peculiar properties of the number sixteen, which I afterwards tried, but in vain, to make him repeat.