Harsh as it may seem, an idea in any branch of knowledge has never attained a sure basis until it is expressible in terms of mathematics. There was a time when physics and chemistry were divorced from mathematics to a large extent. Now even the phenomena of electricity and the reactions one upon another of chemical bodies are expressed in algebraical formulae. This is the result of the increased precision of our knowledge. Following in the footsteps of physics and chemistry the biological sciences are becoming every day more mathematical. We have formulas to express the manner of the arrangement of leaves upon a stem, the manner of arrangement of the parts of a flower. One of these days every structural and functional fact in regard to every living thing will be related to some formula of mathematics more or less general. We shall not all become martinets or dryasdusts. There is a beauty in exactness. I sometimes think that the difference between the loveliness of our thinking and of our dreaming on natural phsenomena, as compared with that which the older thinkers and dreamers enjoyed, will be as the difference between the joy of a game of chess between skilled players or between those that know not even the moves. The child pushes the kings and queens and rooks and knights and bishops and pawns about at random, and laughs gaily. But the master' of the game, moving them according to definite rules, obtains a far higher enjoyment, and produces a combination that has its poetry.