SCIENTIFIC FAITH AND WORKS 117 



tain to be made, independently of the existence of any particular in- 

 vestigator. 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 simulta- 

 neously by Adams and Leverrier has already been mentioned. Singu- 

 larly 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 state- 

 ment 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 Eankine 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 Helm- 

 holtz 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 Bleriot, 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 classi- 

 fication of the sciences, and make some remarks on the differences in 

 their methods. Sitting serene at the head as queen of all is mathe- 

 matics. Eeady she is to serve all, and what a servant she can be is 

 witnessed by those other sciences that have most need of her. Mathe- 

 matics 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 univer- 

 sity has said that the manipulation of mathematical symbols is a mark 



