Though for my part I am unable to adopt this view, it is certainly very remarkable that neither the "Rigveda," which consists almost entirely of hymns to heaven, nor the "Zendavesta," the Bible of the Parsees or fire-worshipers, nor the Old Testament, nor the Homeric poems, ever allude to the sky as blue. On the other hand, from the dawn of poetry, the splendors of the morning and evening skies have excited the admiration of mankind. But as the sun sinks toward the horizon the atmospheric distance increases, and consequently the number of the scattering particles. They weaken in succession the violet, the indigo, the blue, and even disturb the proportions of green. The transmitted light under such circumstances must pass from yellow through orange to red, and thus, while we at noon are admiring the deep blue of the sky, the same rays, robbed of their blue, are elsewhere lighting up the evening sky with all the glories of sunset. Another remarkable triumph of the last half-century has been the discovery of photography. But, owing to the properties of light itself, the fringes due to interference begin to produce confusion at distances of 1 74000 , and in the brightest part of the spectrum at little more than 1 90000 they would make the obscurity more or less complete. If, indeed, we could use the blue rays by themselves, their waves being much shorter, the limit of possible visibility might be extended to 1 120000 ; and as Helmholtz has suggested, this perhaps accounts for Stinde having actually been able to obtain a photographic image of lines only 1 100000 of an inch apart. Passing from geometry proper to the other great branch of mathematical machinery, viz., algebra, it is not too much to say that within the period now in review there has grown up a modern algebra, which to our founders would have appeared like a confused dream, and whose very language and terminology would be as an unknown tongue. Into this subject I do not propose to lead you far. But, as the progress which has been made in this direction is certainly not less than that made in geometry, I will ask your attention to one or two points which stand notably prominent. It would be a long and perhaps invidious task to enumerate the many workers in this fertile field of research, especially in the schools of Germany and of Italy; but it is perhaps the less necessary to do so, because Sylvester, aided by a young and vigorous staff at Baltimore, is welding many of these results into a homogeneous mass in the classical memoirs which are appearing from time to time in the "American Journal of Mathematics."   ​ In order to remove any impression that these extensions of algebra are merely barren speculations of ingenious intellects, I may add that many of these derivative forms, at least in their elementary stages, have already found their way into the text-books of mathematics; and one class in particular, known by the name of determinants, is now introduced as a recognized method of algebra, greatly to the convenience of all those who become masters of its use. That which at first seems to have been due to a single mind proves to have been the result of the successive action of many minds. Attempts more or less successful in the same direction are frequently traced out; and even unsuccessful efforts may not have been without influence on minds turned toward the same object. Lastly, also, germs of thought, originally not fully understood, sometimes prove in the end to have been the first stages of growth toward ultimate fruit. The history of the law of the conservation of energy forms no exception to this order of events. It is, however, the less necessary to refer in detail to these views, seeing that in the now prevailing theory of atomicity we possess a generalization which, while greatly extending the scope of chemical science in its power of classifying known and predicting unknown facts, includes all that was valuable in the generalizations which preceded it. Indeed, the extent to which hitherto undiscovered substances can be predicated is doubtless the greatest triumph achieved by chemists during the past fifty years. As yet, however, only the statical side of chemistry has been developed. While the physicist has been engaged in tracing, for the gaseous condition at least, the paths of the molecules and calculating their velocities, the chemist, whose business is with the atoms within the molecule, can point to no such scientific conquests. By the aid of this system it has been possible to predict the properties and atomic weights of undiscovered elements, and in the case of known elements to determine The saving in dead weight, by this improvement alone, is from ten to sixteen per cent. The speed has been increased from nine knots to fifteen, or even more. Lastly, the steam-pressure has been increased from less than five pounds to seventy pounds per square inch, while the consumption of coal has been brought down from five or six pounds per horse-power to less than two. It is a remarkable fact that not only is our British shipping rapidly on the increase, but it is increasing relatively to that of the rest of the world. I can not but feel confident hope that fifty years hence, when perhaps the city of York may renew its hospitable invitation, my successor in this chair—more competent, I trust, that I have been to do justice to so grand a theme—will have to record a series of discoveries even more unexpected and more brilliant than those which I have, I fear so imperfectly, attempted to bring before you this evening. For one great lesson which science teaches is, how little we yet know, and how much we have still to learn.     ↑ Presidential address before the York Meeting of the British Association for the Advancement of Science.