ii6 



NA TURE 



[May 31, 1906 



In all these cases of true secular stability, instability 

 supervenes through tidal friction, and not, as in the case 

 ol Roche's problem, through the deformation of figure. 



When Poincar^ announced that there was a figure of 

 equilibrium of a single mass of liquid shaped something 

 like a pear, he also conjectured that the constriction between 

 the stalk and the middle of the pear would become de- 

 veloped until it was a thin neck ; and yet further that the 

 neck might break and the two masses become detached. 

 The present revision of Roche's work was undertaken in 

 the hope that it would throw some light on the pear-shaped 

 figure in the advanced stage of development. 



As a preliminary to greater exactness, the equilibrium is 

 investigated of two masses of liquid each constrainedly 

 spherical, joined by a weightless pipe. , Through such a 

 pipe liquid can pass from one mass to the other, and it 

 will continue to do so until, for given radius vector, the 

 masses of the two spheres bear some definite ratio to one 

 another. In other words, two spherical masses of given 

 ratio can be started to revolve about one another in a 

 circular orbit, without relative motion, at such a distance 

 that liquid will not pass through a pipe from one to the 

 other. 



The condition for equilibrium if found to be expressible 

 in the form of a cubic equation in the radius vector, with 

 coefficients which are functions of the ratio of the masses. 

 Only one of the three roots of the cubic has a physical 

 meaning, and in all cases the two masses are found to be 

 very close together ; but the system can never possess 

 secular stability. 



When the masses are no longer constrainedly spherical 

 the equation of condition for equilibrium, when junction is 

 effected by a weightless pipe, becomes very complicated, 

 and can only be expressed approximately. It appears that 

 in all cases, even of Roche's ellipsoids in limiting stability, 

 the masses are much too far apart to admit of junction 

 bv a pipe}- "but when we consider the unstable series of 

 niuch elongated ellipsoids, it seems that such junction is 

 possible, although the approximation is too imperfect to 

 enable us to draw the figure with any approach to accuracy. 

 If two ellipsoids are unstable when moving detached from 

 one another, junction by a pipe cannot possibly make them 

 stable. This then points to the conclusion that the pear- 

 shaped figure is unstable when so far developed as to be 

 better described as two bulbs joined by a thin neck. 



Mr. Jeans has considered the equilibrium and stability 

 of infinite rotating cylinders of liquid.' This is the two- 

 dimensional analogue of the three-dimensional problem. 

 He found solutions perfectly analogous to Maclaurin's and 

 JacobTs ellipsoids and to the pear-shaped figure, and he 

 was able to follow the development of the cylinder of pear- 

 shaped section until the neck joining the two parts had 

 become quite thin. The analysis, besides, points to the 

 rupture of the neck, although the method fails to afford 

 the actual shapes and dimensions in this last stage of de- 

 velopment. He is able to prove conclusively that the 

 cylinder of pear-shaped section is stable, and it is important 

 to note that he finds no evidence of any break in the 

 stability up to the division of the cylinder into two parts. 



The stability of Maclaurin's and of the shorter Jacobian 

 ellipsoids is well established, and I imagined that I had 

 proved that the pear-shaped figure with incipient furrow- 

 ing was also stable. But M. Liapounoff" now states that 

 he is able to prove the pear-shaped figure to be unstable 

 from the beginning. For the present at least, I still think 

 it is stable, "and this belief receives powerful support from 

 Mr. Jeans's researches. 



But there is another difficulty raised by the present paper. 

 I had fullv expected to obtain an approximation to a stable 

 figure consisting of two bulbs joined by a thin neck, but 

 although the present work indicates the existence of such 

 a figure, it seems conclusive against its stability. If then 

 Mr. Jeans is right in believing in the stable transition from 

 the cylinder of pear-shaped section to two detached 

 cylinders, and if I am now correct, the two problems must 

 part company at some undetermined stage. M. Liapounoff 

 will no doubt contend that it is at the beginning of the 

 pear-shaped series of figures, but for the present I should 

 dissent from that view. 



1 Phil. Trans., k, vol. cc, pp. 67-104. 



- Acad. Imp. des Sci. de St. P^tersbourg, vol. 



NO. 1909, VOL. 74] 



ii.. No. 3, 1905. 



One question remains : If the present conclusions are 

 right, do they entirely destroy the applicability of this 

 group of ideas to the explanation of the birth of satellites 

 or of double stars? I think not, for we see how a ten- 

 dency to fission arises, and it is not impossible that a 

 period of turbulence may naturally supervene in the process 

 of separation. Finally, as Mr. Jeans points out, hetero- 

 geneity introduces new and important differences in the 

 conditions. 



IRE RUSTING OF IRON. 



nPHE first view taken of the atmospheric corrosion or 

 rusting of iron was that it was due to a simple 

 process of oxidation. In 1888 Prof. Crum Brown sug- 

 gested, on the basis of experiments described by Grace 

 Calvert in 1871, that the first stage in the rusting of iron 

 is the production, under the influence of carbonic acid, of 

 ferrous carbonate, which is subsequently converted, by 

 atmospheric oxygen in presence of moisture, into ferric 

 hydroxide or rust. In i8g8, however. Prof. Dunstan, in 

 a lecture delivered to the Royal Artillery Institution, put 

 forward another explanation ; he considered that pure 

 oxygen in presence of water is capable of attacking iron, 

 giving rise to ferrous oxide and hydrogen peroxide, part 

 of the latter then converting the ferrous oxide into rust, 

 while the reinainder directly attacks the iron, giving rise 

 to a fresh quantity of ferrous oxide, which in turn is 

 again oxidised in a similar manner. 



A detailed account of the experiments made in con- 

 junction with Drs. Jowett and Goulding, and of the theory, 

 which may be called the hydrogen peroxide theory of rust- 

 ing, was published in October of last year in the Trans- 

 actions of the Chemical Society (vol. Ixxxvii., p. 1548). 

 The theory was based on certain phenomena of oxidation 

 in which hydrogen peroxide was known to be formed, and 

 on the consideration that certain substances which de- 

 composed hydrogen peroxide were found to prevent the 

 conversion of iron into rust by damp air. The older theory, 

 that rusting was due to carbonic acid, was considered 

 " quite untenable, since it has been shown that rusting 

 can take place in the absence of carbonic acid "; the part 

 played by carbonic acid was regarded as " subsidiary and 

 not essential," and it was held to be proven that the 

 " aerial oxidation of iron can take place in the absence 

 of carbonic acid." This view was arrived at as the results 

 of experiments in which the authors failed, by attempting 

 to exclude carbon dioxide, to prevent iron from rusting in 

 presence of oxygen and water. 



In the .'\pril number of the Transactions of the 

 Chemical Society, however, Dr. G. T. Moody shows that 

 these attempts to prevent iron from rusting were un- 

 sucessful owing to the extreme difficulty of completely ex- 

 cluding traces of carbon dioxide. When very special 

 precautions are taken to eliminate this substance iron may 

 be left in contact with pure oxygen and water for many 

 weeks without undergoing change. In one experiment 

 thirty times the quantity of oxygen necessary to convert 

 the whole of the iron into oxide was passed during the 

 course of five weeks, but not even a speck of rust appeared. 

 On the other hand, by removing the scrubbing arrange- 

 ment by which the air was freed from carbon dioxide, so 

 as to permit the ingress of this gas with the air, rusting 

 commenced almost immediately, and in seventy-two hours 

 the whole of the surface of the metal was seen to be 

 corroded, and a considerable quantity of red rust was 

 formed. Specimens of iron which had been exposed for 

 several weeks to the action of pure oxygen and water with- 

 out rusting were exhibited by Dr. Moody at the recent 

 conversazione of the Royal Society. 



It is also shown by Dr. Moody that while rust is being 

 formed from iron under natural conditions a large propor- 

 tion of ferrous carbonate is produced ; the composition of 

 rust in the course of formation is thus altogether out of 

 harmony with the hydrogen peroxide theory, since this 

 theory postulates that twice as much hydrogen peroxide is 

 produced bv the interaction of iron, oxygen, and water as 

 is necessary completely to oxidise the ferrous oxide to the 

 ferric stated The fact that certain compounds such as the 



