NATURE 



[Afay 17, 1877 



" the greater part of these interesting and valuable plants 

 has been destroyed by rain leaking through the roof of 

 the library buildings into the room where they are kept, 

 and by the ravages of moths, &c. In a short time the 

 herbarium will be simply nothing but a mass of unin- 

 teresting fragments. We understand that some time 

 back the Parhament voted a small sum to be expended in 

 putting the herbarium into order. How far anything 

 could possibly have been done by those in charge may be 

 learned from the fact that Dr. Rehman, the Austrian 

 botanist, found whole fasiculi destroyed." 



SPONGY IRON FILTERS 

 TN a paper presented by Prof. Franklaod, F.R.S., and read 

 -'■ before the Royal Society, Mr. Gustav Bischof describes 

 numerous experiments made with spongy iron filters and with 

 charcoal filters. lie states that chemical analysis is incapable of 

 discriminating between living or dead, fresh or putrescent or- 

 ganic matters. The microscope reveals their nature more fully ; 

 but it is nevertheless frequ ntly a matter of great difftcully to 

 decide as to the existence or non-existence of Bacteria of putre- 

 faction, or their germs, in water. 



We must refer our readers to the paper for a full account of 

 the experiments and the conditions under which they were per- 

 formed. Mr. Bischof states that they show that BacUria present 

 in drinking water are not killed in passing through charcoal and 

 are killed in passing through spongy iron. 



He adds : "I believe that the action of spongy iron on 

 organic matters largely consists in a reduction of ferric hydrate 

 by organic impurities in water. We know that even such 

 organic matters as straw or branches are capable of reducing 

 ferric to ferrous hydrate. We know that even such indestructible 

 organic matter as linen and cotton fibres are gradually destroyed 

 by rust stains. This action is slow when experimenting upon 

 ordinary ferric hydrate, but it may, in staht nasccnii, be very 

 energetic, the more so if we consider the nature of the organic 

 matter in water. Ferric hydrate is always formed in the upper 

 part of a layer of spongy iron, when water is passed through 

 that material. The ferrous hydrate resulting from the reduction 

 by organic matter may be re-oxidised by oxygen dissolved in the 

 water, and thus the two reactions repeat themselves. This 

 would explain why the action of spongy iron continues so long. 



" It is, however, quite certain that there is also a reducing 

 action taking place when ordinary water is passed through spongy 

 iron. This is clearly indicated by the reduction of nitrates. 



"Our knowledge of those low organisms, which are believed 

 to be the cause of certain epidemics, is as yet too limited to allow 

 of direct experiments upon them. It is not improbable that, 

 like the Bacteria ol putrefaction, they are rendered harmless 

 when water containing them passes through spongy iron ; but 

 until we possess the means of isolating these organisms, this 

 question can only be definitively settled by practical experience." 



CENTROIDS AND THEIR APPLICATION TO 



SOME MECHANICAL PROBLEMS " 

 'T'HE principal object of the following paper is to suggest the 



-'■ use of a more general form than is commonly employed in 

 the statement of some of the more important theorems of ele- 

 mentary mechanics. Such a generalisation, if in itself satisfac- 

 tory, has two-fold advantages ; it both facilitates the direct 

 solution of problems otherwise apparently complex, and it 

 enables a common method to be employed in an infinite variety 

 of cases, each of which otherwise has to be treated in its own 

 special way. The metliods to be described are purely geometric, 

 and admit in all cases of graphic solutions. In the study of 

 mechanism and in all applications of mechanics to engineering 

 work this is a matter ol considerable importance, for graphic 

 methods have such enormous advantages in these cases that they 

 must supplant all others when they give equally good results. 



By the centroid of any body A relatively to another B is meant 

 the locus of the instantaneous centres of A in its motion relatively 

 to B.^ The expression includes two things, which must be dis- 



» Abstract of a paper read before Section A of the British Association at 

 Glasgow, by Prof. Alex. B. W. Kennedy, C E., of University College, 

 London. 



2 The word r('^:/rt7:V/ was suggested to the author by his colleague, Prof. 

 W. K. CUfford. 



tinguished from each other ; — (i. ) the locus as part of the moving 

 body A, (ii.) the locus as part of the body B relatively to 

 which ^'s motion is observed, and which may for convenience 

 be regarded as fixed. These loci may be entirely different as to 

 form, but in all their properties they are absolutely similar and 

 reciprocal. It would therefore be wrong to give them different 

 names, they can be distinguished, when necessary, as the centroid 

 of a body, and the centroid 7^^ the motion of a hoily respectively. 

 The centroid of A is therefore the locus ispon A of its inst. 

 centres relatively to B ; the centroid for the motion of A is the 

 locus upon B of the same centres. 



The following are the most important characteristics of these 

 curves. As the bodies to which they belong move the centroids 

 roll upon each other, and every point in each becomes in turn 

 the inst. centre. Their rolling, therefore, represents continu- 

 ously the whole motion of the bodies {considered as changes of 

 position merely), quite irrespective of their form ; in other words 

 it defines the path of motion of all points in the bodies. The 

 two centroids have always one point in common — their point of 

 contact — this point being the instantaneous centre. This point 

 may be included in both bodies, and has no motion relatively to 

 either. Any motion which it has must therefore be common to 

 both, so that it may be entirely neglected in investigating their 

 relative motions. In problems affecting the motion of either 

 body relatively to a third this is often of much use. 



For the sake of definiteness it has been presupposed in the 

 foregoing paragraphs that the motions referred to were conplane, 

 or, more generally, took place about some fixed point. When 

 the motion is conplane this point is at infinity, and the centroids 

 are plane curves, sections of the cylindric ruled sur aces formed 

 by the successive positions of the instantaneous axes. When the 

 distance of the point is finite, the centroids are, of course, spheric 

 curves, the instantaneous axes forming c mes of which the point 

 mentioned is the vertex. These theorems were given by Poinsot 

 in his " Theorie Nouvelle de la Rotation des Corps." It may be 

 interesting just to mention also the case of general motion : in 

 space, where (as Belanger seems first tohave pointed out), the solids 

 of instantaneous axes, or cuxoids, as Reuleaux calls them — are 

 general ruled surfaces twisting on each other. Kach generator 

 of the surface is a "screw," and on each in turn a twist occurs. 

 The surfaces are in general non-developable. 



For the sake] of brevity, only conplane motions will be con- 

 sidered in this paper. This class of motions includes nine-tenths 

 of those occurring in mechanism. Two or three special cases 

 of frequent occurrence may first be mentioned. If the rela- 

 tive motion of two bodies be a simple rotation, the centroids 

 are a pair of coincident points, one of which must still be con- 

 sidered to roll on the other. The instantaneous centre here 

 becomes a permanent centre. It is convenient, however, to 

 treat the point not only as a permanent centre, but as a special 

 (limiting) case of the centroid. If all points in a body move in 

 parallel straight lines, the centroid for the motion of the body is 

 a point at infinity, and the centroid of the body is also a point 

 at infinity coincident with the former. If the path of the body 

 were infinitely long, the two points would roll round each other. 

 If, on the other hand, a body move parallel to itself, every point 

 in the centroid for its motion (and therefore all points in its own 

 centroid) must be at infinity. The two centroids must again be 

 coincident, so that the motion is represented by the line at infinity 

 rolling on itself.^ 



Proceeding now to notice the bearing of the theory of cen- 

 troids upon some of the theorems of elementary mechanics, these 

 may be taken in order of simplicity, commencing with those 

 which involve only the notion of change of position. If, then, 

 the line joining any moving point with the point of contact of its 

 centroids be called its instantaneous radius, we can state the 

 general theorem thus : The direction of motion of et'ery point in a 

 body is normal to its instantaneous iadius. \\'hile this obviously 

 includes the simpler special cases already examined, its form 

 allows of direct application to the most general cases, and 

 especially to all cases in mechanism. Two corollaries out 

 of many which are deducible from it may be mentioned as 

 of some special interest : (i. ) The inst. radii of a point moving 

 in a straight line are parallel ; and (ii. ) the inst. radii of a point 

 moving in a circle must pass through one point. In either case 

 the centroids may be quite general curves, as is easily seen. 

 These corollaries have important practical applications in me- 



I Some physical conception of this case can easily be obtained by rolling 

 one hyperbola upon another. The change in the appearance of the rolling 

 as the point of contact recedes along either branch is very striking. 



