The peopled sea Hath coral castles through whose lurid aisles Patined with gold and crusted o'er with gems- Yet, shall we say the rich, ripe fruit of Time Fell from the womb of Chance? The dreams, freshdrawn From lustral fountains by a naiad troop, And borne like dew in lily chalices To my lone couch, are witnesses that still The universe proclaims there is a God! He bids the planets sing-aye, and he feeds His whirlwinds filch what his beneficence Lo, now, what festering horrors feed our grief: Beauty decays, Nobility is slain, Sin sheds his larve, and curst Hypocrisy Tiptoe, the twilight muses on the hill;- Being banished, all the elder gods again Sorrow and Sin and Shame begone from earth. Man must approach to God by purity, E'en as the highest mountains, undefiled By human footfall, where the virgin snow Let us, too, be brave! Canst thou bribe thunderstorms with honeyed words, Or curb with sandhills the choleric sea? Where Sorrow strikes, let honorable scars Remain, the blazon of our fortitude. Be not of such slight, puny courage as Than in the trodden heart's tear-wine of hope? Of her allurement, or the sword of Sin Transmute one earthy atom of this race Yea, there is One that walks in human hearts, She stoops to kiss the humblest flowering thing; And Peace, sweet child of life's lorn Enna, sleeps Have ye heard her name; Knelt in her temples; walked among her groves? Love that doth kiss the lids of Death ajar, Mother of men and genetrix of time At once the Law, the King, the Throne; at once Breath of the gods that fills the lungs of space, GEORGE SEIBEL. PITTSBURGH, PA. CRITICISMS AND DISCUSSIONS. TIME AND SPACE.1 The conceptions of time and space which I wish to develop here have arisen on the basis of experimental physics. Therein lies their strength. Their tendency is radical. From now on spacein-itself and time-in-itself are destined to be reduced to shadows, and only a sort of union of the two will retain an independent existence. I. I wish first to show how from the mechanics now generally accepted we might arrive by purely mathematical considerations at a change in our ideas of space and time. The equations of Newton's mechanics show a double invariance. Their form is maintained, first, if we subject our system of original coordinates in space to any change of position; second, if we change its state of motion, that is to say, impart to it any uniform translation; neither does the zero-point of time play any part. We are accustomed to considering the axioms of geometry as settled before we approach the axioms of mechanics, and therefore these two invariances are seldom mentioned together. Each of them represents a certain group of transformations, which transform the differential equations of mechanics back into themselves. The existence of the first group is regarded as a fundamental property of space. It is usually preferred to treat the second group with contempt in order to 1 Lecture delivered at the eightieth Congress of Naturalists at Cologne, September 21, 1908. Published in Physikalische Zeitschrift, X (1909, pp. 104111, and Jahresbericht der deutschen Mathematiker-Vereinigung, Vol. XVIII, pp. 75-88; Gesammelte Abhandlungen, edited by D. Hilbert, pp. 431-444; also separately, Leipsic, B. G. Teubner, 1909. Translated from the German by Edward H. Carus who herewith expresses his gratitude to Prof. W. B. Smith of Tulane University for many suggestive criticisms. |