PROFESSOR LOVERING'S ADDRESS. 199 



the laws of Kepler ? With such an indorser, I may venture to quote 

 these words of a consummate mathematician without fear of their be- 

 ing cast aside by the naturalists as one of Bacon's Idols of the Tribe : 

 " An intelligence which at any given instant should know all the forces 

 by which Nature is urged, and the respective situations of the beings 

 of which Nature is composed, if, moreover, it were sufficiently com- 

 prehensive to subject these data to calculation, would include in the 

 same formula the movements of the largest bodies of the universe and 

 those of the slightest atom. Nothing would be uncertain to such an 

 intelligence, and the future, no less than the past, would be present to 

 its eyes." The time has already come when a knowledge of physical 

 laws and familiarity with the instruments of physical research are in- 

 dispensable to the naturalist. I would not recommend that dissipa- 

 tion of intellectual energy which will make a man superficial in all 

 the sciences but profound in none. But Helmholtz has established, 

 by his own example, the possibility of being an eminent physiologist, 

 and, at the same time, standing in the front rank of physicists and 

 mathematicians. The restlessness of human inquiry will never be 

 satisfied with knowing what things are, until it has also discovered 

 how and why they are, and all the relations of space, time, matter, and 

 force, in all the kingdoms of Nature, have been worked out with math- 

 ematical precision. 



It is a happy circumstance in the history of science, that this vast 

 mechanical problem did not rush upon the mind at once in all its 

 crushing generality. The solar system, with a despotic sun at the 

 centre, competent to overrule all insubordination among planets and 

 comets, and check all eccentricities and jealousies, and so far isolated 

 from neighboring systems as to fear nothing from foreign interfer- 

 ences and entangling alliances, presented a comparatively simple 

 problem ; and yet the skill and labor of many generations of mathe- 

 maticians have not yet closed up the argument upon this first case. 

 On the orbits of this domestic system they have been sharpening their 

 tools for higher and more delicate work. The motions of binary stars 

 have also been brought under dynamical laws, and partially subjected 

 to the rule of gravitation, so far as the astronomer can judge from the 

 best observations which he can make upon those remote objects. But 

 when he launches out, with his instruments and his formulas, into clus- 

 ters of stars, even those of greatest symmetry, he is wholly at sea, with- 

 out chart or compass or light-house, and with no other illumination than 

 that which comes from a prophetic demonstration in Newton's "Prin- 

 cipia." The mathematician has here to treat, not with an unlimited 

 monarchy, as in the solar system, but with a republic of equal stars, 

 and the dynamical condition of the clusters is involved in all the ob- 

 scurity of molecular mechanics ; for it matters not whether the indi- 

 vidual members of a system are atoms or worlds, if the intervening 

 spaces have corresponding magnitudes. Even in astronomy, the in- 



