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THE POPULAR SCIENCE MONTHLY. 



vital condition of our men, resulting from 

 short rations. The fact was, they died from 

 hospital diseases. General Sherman's army, 

 just arrived from Mississippi, without hos- 

 pitals, treated their wounded in the field, 

 and the proportion of recoveries was aston- 

 ishingly great. They were cured by fresh 

 air. At the battle of Peach-Tree Creek, a 

 very worthy staff- officer of mine was se- 

 riously, although not dangerously, wounded 

 in the abdomen. The medical rules were 

 very strict, but, by sending messengers all 

 night, I got authority to send him home to 

 the North, without his going to the hospital. 

 Arriving at Nashville, and being unable to 

 proceed without further medical authoiity, 

 he was taken charge of, and put into one 

 of their comfortable hospitals. In a few 

 days he became terribly afliicted with gan- 

 grene, and only escaped with his life after a 

 perilous and racking illness." 



These observations are doubtless familiar 

 to surgeons ; but if, with Tyndall's experi- 

 ments, they are found to be absolutely cor- 

 rect, does it not become necessary to exam- 

 ine into the condition of the various hospi- 

 tals throughout the country, and to provide 

 at least some special conditions for the treat- 

 ment of flesh-wounds an apartment, for 

 example, separated from the main building, 

 which may be deluged at intervals with su- 

 perheated steam to destroy the germs, or 

 such other precaution as shall insure an 

 atmosphere of absolute purity during the 

 dressing of wounds ? 



We would commend this subject to the 

 State Boards of Health. 



Edward S. Morse. 

 Salem, Massachusetts, April 26, 1877. 



THE NEW IDEAS ABOUT SPACE. 



To the EdUor of the Popular Science Monthly. 



The great attention now given to this 

 subject in Europe seems to render appro- 

 priate a short communication to bring it 

 more directly before Americans. In point 

 of fact, the mathematicians have been 

 making a conquering migration into the 

 fair fields of philosophy, and instead of any 

 longer being content to receive from Meta- 

 physics her definitions of space, they have 

 for themselves attacked the question by 

 the methods furnished by two thousand 

 years of advance in their own science. Al- 

 ready they have made some wonderful 

 strides toward the solution, and the new 

 notions are very fascinating. 



It is, perhaps, daring to attempt to give 

 an adequate idea of some of these without 

 the use of mathematical symbols and ana- 

 lytic geometry ; still it seems desirable for 

 each of the special sciences to be able to 

 express results in untechnical language, and 

 we will try. 



Every schoolboy knows that what is 

 called multiplying a linear inch by a linear 

 inch gives a square inch, and that again 

 multiplying this square inch by a linear 

 inch gives a cubic inch. Now, I suppose, 

 many of the most original boys may have 

 asked themselves, "What would be the re- 

 sult of multiplying this cubic inch again by a 

 linear inch ? " Up to this nineteenth century 

 the answer has probably always been, that 

 the thing was unthinkable and inexpressible, 

 and that, although by analogy we see no 

 reason for being stopped so abruptly, yet 

 such is our invariable experience. 



Now, the two men who first and inde- 

 pendently stepped over this mental fence 

 were the great Gauss whom Germany is now 

 celebrating, and a Russian named Lobat- 

 chewsky. They both said that the space 

 with which we are familiar is only one kind 

 of space out of a number of possible spaces, 

 each logically self-consistent ; but that, from 

 the fact of all our ages of experience being 

 in this particular space, we cannot perfectly 

 picture to ourselves any one of the other 

 kinds, though they are entirely expressible 

 in analytic geometry. 



Now, it has often been remarked that 

 in things very familiar to us we see nothing 

 noteworthy. So we see nothing strange in 

 our conception of a straight line and a plane, 

 yet we may think it strange when we are 

 told that this peculiar notion of straight- 

 ness, smoothness, or flatness, is also inherent 

 in our ideas of our space. This was dis- 

 covered many years ago by Prof Sylvester, 

 and, to denote it, he called our space a hom- 

 aloid, or a homaloidal space. To us it al- 

 ways has three dimensions, and no more; 

 and, just here, all readers may be advised 

 not to try to jndure to themselves any 

 higher kind of space, since they must fail 

 as utterly as they fail to see the ultra-violet 

 rays of the spectrum. Moreover, it has not 

 yet been demonstrated that any other kind 

 of space actually exists in the physical 

 world. This is a matter which can only be 

 settled by physical experiments ; and per- 

 haps it is to be hoped that our old space 

 will stand all tests, for, should it not, then 

 all our science would have to be put on a 

 new basis, at least in so far as related to 

 space. So, you see, no one need be dis- 

 couraged at his inability to perfectly con- 

 ceive any other space than our common one. 

 But, as the others are logically possible and 

 mathematically true, and are necessary to 

 get a complete knowledge of our own space, 

 we will attempt to convey some notion of 

 them. In our space we have length, breadth, 

 and height, and to each of these corre- 

 sponds a coordinate in analytic geometry. 

 This is why we call ours a space of three 

 dimensions, and we cannot picture any other 

 dimension. But we find analytic geometry 

 just as ready to deal with a space which 



