tain to be made, independently of the existence of any particular investigator. Such a truth is apt to put the scientist in that humble mood characteristic of the true man of science, and to show him how unimportant in the scheme of nature is any particular individual, but it need not leave him in the state described in the hymn, "Great God, how infinite art Thou, what worthless worms are we!" Examples of this conclusion are numerous. The discovery of Neptune simultaneously by Adams and Leverrier has already been mentioned. Singularly enough the planet was seen first by Galle, at Berlin, on September 23, 1846, and then independently by Professor Challis, at Cambridge, on September 29, he being ignorant of Galle's discovery. The statement of the Second Law of Thermodynamics in 1850 by Clausius and Lord Kelvin, and the discovery that the specific heat of saturated vapor is negative by Clausius and Rankine and others. The published work of Sir Oliver Lodge on electric waves shows that it admits of no doubt that had not Hertz published his researches when he did Lodge would have obtained many of his results. The work of Helmholtz and Lord Kelvin is full of interesting parallelisms, while the important application by Helmholtz of thermodynamics to chemical phenomena was anticipated by our own Willard Gibbs. Coming down to the present time, it is no disparagement to Wilbur and Orville Wright to say that had they not succeeded in the conquest of the air the same result would shortly have been achieved by Blériot, Voisin and others. I have no doubt that, had not Columbus discovered America in 1492, some other intrepid navigator would have done so in ten years. Had not Peary discovered the pole—but I pause, as fiction is sometimes stranger than truth.
I will now, with your permission, undertake to make a rough classification of the sciences, and make some remarks on the differences in their methods. Sitting serene at the head as queen of all is mathematics. Ready she is to serve all, and what a servant she can be is witnessed by those other sciences that have most need of her. Mathematics is probably the most misunderstood of all the sciences. Huxley called it "that science which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." To this a sufficient answer might be that she does not need to, but a better one is that it is not true. Intuition and induction have a great part in all mathematical discoveries, as all of the great mathematicians agree. Mathematics has no subject matter, but may be applied to anything that has exact relations. To sing the beauties of mathematics to those ignorant of that subject is as futile as to praise music to the tone-deaf, or painting to the color-blind. I have a friend who describes a symphony as a horrid noise. The president of a great eastern university has said that the manipulation of mathematical symbols is a mark
