Page:Popular Science Monthly Volume 11.djvu/378

364 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 hospitals, treated their wounded in the field, and the proportion of recoveries was astonishingly great. They were cured by fresh air. At the battle of Peach-Tree Creek, a very worthy staff-officer of mine was seriously, 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 authority, he was taken charge of, and put into one of their comfortable hospitals. In a few days he became terribly afflicted with gangrene, and only escaped with his life after a perilous and racking illness."

These observations are doubtless familiar to surgeons; but if, with Tyndall's experiments, they are found to be absolutely correct, does it not become necessary to examine into the condition of the various hospitals throughout the country, and to provide at least some special conditions for the treatment of flesh-wounds—an apartment, for example, separated from the main building, which may be deluged at intervals with superheated 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.

To the Editor of the Popular Science Monthly.

great attention now given to this subject in Europe seems to render appropriate 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 Metaphysics 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. Already 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 analytic 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 result 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 independently stepped over this mental fence were the great Gauss whom Germany is now celebrating, and a Russian named Lobatchewsky. 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 straightness, smoothness, or flatness, is also inherent in our ideas of our space. This was discovered many years ago by Prof Sylvester, and, to denote it, he called our space a homaloid, or a homaloidal space. To us it always has three dimensions, and no more; and, just here, all readers may be advised not to try to picture 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 perhaps 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 discouraged at his inability to perfectly conceive 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 corresponds a coördinate 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