March 26, 1885] 



NA TURE 



in the moist substance is to keep the bases of the icy filaments, 

 or the lower side of the stratum formed by their agglutination, 

 wet : and congelation of this film appears to be continuous. 



W. J. McGee 

 U.S. Geological Survey, Washington, D.C., U.S.A., 

 February I 



Four-Dimensional Space 



Possibly the question, What is the fourth dimension ? may 

 admit of an indefinite number of answers. I prefer, therefore, 

 in proposing to consider Time as a fourth dimension of our exist- 

 ence, to speak of it as a fourth dimension rather than the fourth 

 dimension. Since this fourth dimension cannot be introduced into 

 space, as commonly understood, we require a new kind of space 

 for its existence, which we may call time-space. There is then 

 no difficulty in conceiving the analogues in this new kind of 

 space, of the things in ordinary space which are known as lines, 

 areas, and solids. A straight line, by moving in any direction 

 not in its own length, generates an area ; if this area moves in any 

 direction not in its own plane it generates a solid ; but if this solid 

 moves in any direction, it still generates a solid, and nothing 

 more. The reason of this is that we have not supposed it to 

 move in the fourth dimension. If the straight line moves in its 

 own direction, it describes only a straight line ; if the area moves 

 in its own plane, it describes only an area ; in each case, motion 

 in the dimensions in which the thing exists, gives us only a 

 thing of the same dimensions ; and, in order to get a thing of 

 higher dimensions, we must have motion in a new dimension. 

 But, as the idea of motion is only applicable in space of three 

 dimensions, we must replace it by another which is applicable in 

 our fourth dimension of time. Such an idea is that of successive 

 existence. We must, therefore, conceive that there is a new 

 three-dimensional space for each successive instant of time ; and, 

 by picturing to ourselves the aggregate formed by the successive 

 positions in time- space of a given solid during a given time, 

 we shall get the idea of a four-dimensional solid, which may be 

 called a sur-solid. It will assist us to get a clearer idea, if we 

 consider a solid which is in a constant state of change, both of 

 magnitude and position ; and an example of a solid which 

 satisfies- this condition sufficiently well, is afforded by the body 

 of each of us. Let any man picture to himself the aggregate 

 of his own bodily forms from birth to the present time, and he 

 will have a clear idea of a sur-solid in time-space. 



Let us now consider the sur-solid formed by the movement, or 

 rather, the successive existence, of a cube in time-space. We are 

 to conceive of the cube, and the whole of the three-dimensional 

 space in which it is situated, as floating away in time-space for 

 a given time ; the cube will then have an initial and a final 

 position, and these will be the end boundaries of the sur-solid. 

 It will therefore have sixteen points, namely, the eight points 

 belonging to the initial cube, and the eight belonging to the 

 final cube. The successive positions (in time-space) of each of 

 the eight points of the cube, will form what may be called a 

 time-line ; and adding to these the twenty-four edges of the 

 initial and final cubes, we see that the sur-solid has thirty-two 

 lines. The successive positions (in time-space) of each of the 

 twelve edges of the cube, will form what may be called a time 

 area; and, adding these to the twelve faces of the initial and 

 final cubes, we see that the sur-solid has twenty-four areas. 

 Lastly, the successive positions (in time-space) of each of the 

 six faces of the cube, will form what may be called a time-solid ; 

 and, adding these to the initial and final cubes, we see that the 

 sur-solid is bounded by eight solids. These results agree with 

 the statements in your article. But it is not permissible to speak 

 of the sur-solid as resting in "space," we must rather say that 

 the section of it by any time is a cube resting (or moving) in 

 "space." S. 



March 16 



The Action of Very Minute Particles on Light 



The action upon transmitted light of very minute particles 

 suspended in a transparent medium is very well known, thanks 

 to the investigations of Briicke, Tyndall, and others, up to a 

 certain point. That is to say, that white light, passing through 

 varying depths of a medium with such particles more or less 

 thickly interspersed, is known to emerge coloured yellow, 

 orange, or red, according to the extent of the action in question. 

 Wishing to illustrate this phenomenon experimentally, I em- 



ployed a very dilute solution of sodium thiosulphate (hyposul 

 phite), which was acidified with hydrochloric or sulphuric acid, 

 and then allowed to stand, observing from time to time the 

 appearances when examined by transmitted light. The solution 

 mentioned is admirably adapted for the purpose, inasmuch as 

 the precipitation of the sulphur proceeds gradually ; and, accord- 

 ing to the greater or less dilution at starting, the completion of 

 the reaction can be spread over a long period of time, in some 

 of my experiments occupying more than forty-eight hours. For 

 a while no turbidity whatever is visible ; then a faint opalescence 

 makesits appearance, and these exceedingly minute particles grow 

 gradually in size, remaining, however, quite uniformly suspended 

 for a considerable period, until a dimension is reached which 

 causes them to settle out of the liquid. In this way I observed 

 with unfailing regularity, and in unvarying order, though with 

 various degrees of rapidity, an extension of the series of colours, 

 which, so far as I am aware, had not previously been noticed, 

 or at any rate published. From orange, the tint passed succes- 

 sively through rose red, purplish rose, to a full purple ; then by 

 insensible gradations to a fine violet, blue, green, greenish 

 yellow, neutral tint, &c. 



The solution was contained in spherical or pear-shaped flasks, 

 or in cells with flat and parallel sides. A solution which was 

 strong enough to give well-marked yellow, orange, and red 

 tints, was not well adapted for the subsequent stages, as it soon 

 became white and opaque, so that the later colours were almost 

 entirely masked. A half litre flask filled with a solution so 

 dilute, that ten minutes or more elapsed after acidifying before 

 opalescence was first visible, gave very feeble yellow and 

 orange ; the rose and rose purple, though decidedly weak, re- 

 minded me in tint of the colours seen towards the upper margin 

 of the recent sky-glows ; but when the full purple, violet, and 

 blue were reached, the colours were very strong and well 

 marked. A gas or candle-flame, viewed through the solution, 

 which was violet by transmitted daylight, appeared emerald 

 green. After passing the blue stage, the colours through green 

 and yellow were much weaker, until, as before mentioned, a 

 neutral tint was reached. Beyond this, with such a dilution, 

 nothing further could be satisfactorily observed ; but by taking 

 a much more capaciou- flask, and using a solution only one-half 

 or one-third the former strength, faint orange and pink were 

 again observed after passing the neutral point. And with these 

 more dilute solutions, very strongly marked secondary effects 

 were noticed after once passing the "blue stage." A distorted 

 image of a window was foimed in the flask, and while the bright 

 portions appeared greenish, those parts where the dark bars of 

 the framework fell, appeared of a fine crimson colour ; after the 

 neutral point had been passed, and the bright parts appeared 

 pink, the dark portion of the image appeared a brilliant emerald 

 green. In either of these stages a part of the solution trans- 

 formed to a tall, but narrow glass cylinder, had not sufficient 

 depth to show any perceptible colour when viewed by transmitted 

 light, but placed on a dark background below a window, showed 

 a crimson or green glow respectively when viewed at a certain 

 angle, and a complementary glow when seen at a different 

 angle (by raising or lowering the level of the eye, the cylinder 

 remaining stationary). 



With the solution in any given stage of development, the 

 effect of increasing the depth of the column through which the 

 light passed was to increase the saturation of the colour to a 

 large extent, and to alter its tint (apparently in the direction of 

 the less refrangible end of the spectrum) to a much smaller 

 degree. That the colour observed at any given stage was owing 

 mainly to the size of the individual particles rather than to then- 

 greater or less proximity, was shown by the fact that, on pour- 

 ing away half or two-thirds of the contents of the vessel, and 

 filling with water, the colour, although much thinner, was nearly 

 of the same tint. 



I am not able to give the proportion by weight of the salt in 

 the solutions experimented with ; but I think about one gramme 

 or less to the litre will be found to give good results. One or 

 two trials, however, would soon indicate the appropriate 

 strength. 



The character of the colours and the whole nature of the phe- 

 nomena led me to infer that they were in all probability caused 

 by the intirference of light ; but as I could not see my way to a 

 rationale of the mode of action, I deferred publication in the 

 hope that by further investigation their exact nature and true 

 cause might be more clearly worked out. The description in 

 last week's Nature (p. 439) of Prof. Kiessling's ingenious 



