TJie Infinities Around Us Richard A. Proctor. 



THE INFINITIES AROUND US FAREWELL 

 LECTURE. 



EVIDENCE OF THE INFINITE IN SPACK THE INFI- 

 NITY OF MATTER EVIDENCES WHICH POINT TO 

 AN INFINITE GOD THE LIMITS OP OUR SENSES 

 THE VARIETY OF THE UNIVERSE RESOLUTIONS 

 OF THANKS ADDRESSES FROM PROFS. HITCH- 

 COCK AND NEWI3ERRY PARTING WORDS OF MR. 



PROCTOR. 



The 101st and. farewell lecture in this country of 

 Prof. Richard A. Proctor, the eminent English, as- 

 tronomer, who was to leave for his home across tlio 

 water in the Cuba, April 8, was made the occasion of 

 avery pleasant gathering. The usual crowded audi- 

 ence was present to hoar the Professor's views on the 

 subject of "The Infinities Around Us," and many 

 warm admirers lingered after the lecture to shake 

 bands with the scienlist and wish him Godspeed on 

 his voyage. The use of the stereopticon was dispensed 

 with, no pictures being exhibited. A pleasant pro- 

 gramme to follow the lecture having been arranged 

 previously, the stage was tilled with prominent gen- 

 tlemen, among them the Rev. Dr. S. Ireuzeus Prime, 

 the Rev. James Waters, W. H. Fogg, W. Oliver 

 Stone, Seabury Brewster, the Rev. Dr. Vincent, the 

 Rev. Dr. Chessire, H. B. Sands, M. D. ; R. W. Weir. 

 M. D. ; the Rev. Thomas Armitage, D. D. ; A. F. 

 Hastings, Theo. Roosevelt, Robert L. Stuart, Noruiau 

 White, James B. Colgate, Samuel B. Schiefl'elin, 

 J. W. Pirsson, S. A. Bunco, John Taylor Johnston, 

 S. S. Constant, Nathan Bishop, the Rev. Dr. Sey- 

 mour, the Rev. Dr. Roswell D. Hitchcock, Prof. 

 Newberry, Prof. Peaslee, the Rev. Dr. Sawyer, the 

 Rev. Dr. Holme, and John R. Ludlatn. 



LADIES AND GENTLEMEN : I have to-night to 



speak on a subject not astronomical in itself, but one of 

 those to which the study of astronomy naturally leads 

 us. I suppose that there is no thought more common or 

 which has been more ordinarily entertained than this 

 Shat space must necessarily be infinite. Utterly incon- 

 ceivable, though, the idea of infinity is. Ev- 

 .try one must have had the thought that 

 if you take a line, as it were, a line through, space, 

 \n any direction, there is no boundary ; the line may be 

 carried onward and onward, forever and ever, and 

 whether it meets a solid substance, -whether it arrives 

 at a void space, still it may be carried onwara aud 

 onward, aud c.o forever; but that this space 

 in that direction, rim^t bo influite. To a student 

 of astronomy this idea is, perhaps, more naturally 

 presented than to any other, because he is in the habit of 

 considering telescopic power, which carries the mind's 

 eye, as it were, further aud further into the depths of 

 space, still without any limit. Thus the idea of the iu- 

 fluit.v of space is the one with which the student of 

 astronomy naturally has to deal. 



We begin, then, with this subject of the Infinity of 

 space first of all, because it is the one we are best able 

 to deal with, the one about which we feel the most cer- 

 tain. We mar entertain doubts as to infinity of tituv, in 

 past or iu future; although, as I shall presently show, 

 infinity of time as an idea LAS not near as 

 much force upon us as that of infinity of space. 

 In infinity of space wo recognize a view that we must 

 bold. We have, the.u, som.'thirig th it is inconceivable, 

 and that yet must be admitted. And I want, this eveu- 



ing, to bring before you the Idea that that which u in- 

 conceivable may necessarily bo that whirli 

 is true. So, inconceivable is this idea of 

 infinity of space, tho id-'a that all 

 around us there are immensities of space, not in rdv a.s 

 Sir John Ilerschel has sai.!, practical infinity, but real 

 infinity, absolute infinity, going on forever and furever. 



OTHER DIMENSIONS TH VN LENGTH, UHKADTir, AND 

 THICKNESS. 



Tho Idea seemed so inconceivable that men in out 

 time, great mathematicians, of most powerful uiimi.s, 

 have endeavored to escape- from it, by 

 this strange conception, that our idea of epaco 

 may be limited by certain imperfections. They be- 

 gin by conceiving: the possibility that there niigut be a 

 kind of creature having only length, living always as 1C 

 were, having for itsbody an Influite straight line without 

 any breadth, only length. Aud then they p.iss tmni 

 that idea to tho idea of a creature living 

 always in space of two dimensions in 

 thickness and breadth and show how to creatures of 

 that kiud the idea of space of three dimensions would 

 he inconceivable ; and they say, therefore, that we may 

 be limited by some such want of concept ion in our 

 powers, aud that there may be space of four dimensions; 

 in otner words, souiethiug else than length, breadth aud 

 thickness may be a uossibihty. Now, if you consider 

 you will find that you can thus get over the diffi- 

 culty, although the explanation is not a whic 

 more conceivable than the difficulty it is intended to 

 meet. For instance, if there were creatures living 

 in space, of one dimension, having only length, then in- 

 stead of living on a straight line, as the first siippusit iou 

 was, it might have for its body, or raiher its con- 

 ceptions might be liniice.l to, a perfect circular 

 ring; then the conception of that creature would 

 be that leugth measured witn the circular 

 ring was infinite, yet we know tho circular ring would 

 have a certain measurable size. Prof. Clifford, the 

 great mathematician of Eugluud, one of the leading 

 mathematicians, one of tho rising mathematicians of 

 our day, has pictured the case of a creature having only 

 length and breadth, living on the surface of a 

 sphere. Then to creatures of that kiud tho 

 idea would be presented that surface was infinite, Just 

 as to us the idea is presented that space is infinite, and 

 yet their surface would be the surface of a sphere ; and, 

 although it would havo no limits, as we know that the 

 surface of a sphere has no limits, yet it would not be 

 infinite in dimension. So says Pr.if. Clifford auJ so say 

 the German mathematicians, from whom tnat idea has 

 been borrowed ; so it may be possible that it is only our 

 limited conception which gives us the idea that space is 

 infinite. 



IS MATTER AS INFINITE AS SPACE 7 



Well, I pass from these conceptions with tho remark 

 that to me they seem not a whit less inconceivable than 

 the absolute, infinity of space. And it api>;trs to me 

 that so far from high matuematical power forcing upon 

 us the possibility of such conceptions, that as soon as we 

 take the rationale of the matter, tho ordinary, simple 

 explanation of tacts, we are bound to admit that space 

 of three dimensions includes the whole or possible space. 

 You will have length aud breadth, and you will havi- 

 everything that lies above it or uclow it. In otuer 

 words, if you have added to length and breadth the con- 

 ception of thickness, you have the whole of space. Wo 

 Lave then infinite space. Wo have brought Us fore us, 



