92 



NATURE 



[May 26, 1887 



through the sieve faster. By again sifting the 4 ounces which 

 had passed till 2 ounces passed, a further enrichment was found 

 to have taken place. The 2 ounces were again sifted on the 

 same sieve till i ounce had passed, which was again sifted till 

 i of an ounce passed. This was examined quantitatively, and 

 found to consist of 54 per cent, of quartz and feldspar, and 46 per 

 cent, of dense minerals. By vanning and submitting the residue 

 to the action of a stron?j magnet, almost nothing but zircons and 

 rutiles remained. It is needless to say that much remained 

 with the sand, especially in the latter parts of the operation. 



A current separater was tried, but it seemed more difificult to 

 work, though perhaps it might answer better on a larger scale, 

 where it might be set to work automatically. There was no 

 difficulty in getting a considerable enrichment, but it was evident 

 that a great deal of care would be required in "sizing" the 

 particles before a good separation could be effected. The most 

 hopeful method seemed to be that of washing away the medium- 

 sized grains of sand and afterwards sifting the sediment. 



Perhaps in some of the streams running through the Bagshot 

 or other sands natural eddies may be found or formed artificially 

 from which enriched sand may be dredged, or it may be got on 

 the sea-shore under sand-cliffs. 



The object of the present communication is to draw attention 

 to the matter in hopes that some deposit richer in zircons than 

 the Hampstead sand may be found. Much care must be taken 

 in sampling, because the sands, having been deposited from 

 currents, must vary in composition. A trial is easily made by 

 anyone accustomed to use a microscope and who knows the 

 minerals by sight under such circumstances. A thimbleful of 

 such sand as exists at Hampstead is enough for a trial by vanning, 

 but if one of the dense liquids be used, from 10 to 20 grains by 

 weight of the sand will give a good microscopic slide of the 

 dense minerals. It may of course prove that the Hampstead 

 sand is a residue of denudation in which the denser minerals 

 have accumulated. In that case it is not improbable that other 

 similar deposits may be found, some, perhaps, much more 

 zirconiferous. 



On the whole it appears that the matter is worthy of further 

 attention. In some future communication I hope to be able to 

 give an account of the composition of the matter attracted by a 

 strong magnet, and also of the grains of earthy-looking minerals 

 over the density of 3 '2, and of any richer deposit of zirconiferous 

 sand of which I can obtain reliable samples. 



Allan B. Dick. 



THE ROLLING CONTACT OF BODIES^ 



^XT'HEN two solid bodies roll upon each other, points in the 

 surface of one successively come into contact with corre- 

 sponding points in the surface of the other in a way which differs 

 essentially from that which occurs in sliding contact, and it is 

 the nature of this rolling-contact that the lecturer proposed to 

 discuss in an experimental manner. 



In the first place, it is well to understand clearly the nature of 

 the relative motion of the two points which come into contact 

 when the surfaces are such that no appreciable distortion of them 

 takes place, and for this purpose one of the two bodies mu't be 

 at rest. These may respectively be taken as the plane surface of 

 the ground and a circular disk rolling upon it. An approxi- 

 mate representation of this motion is given by the end of the 

 spokes of a wheel without its tyre. In this case it is seen that a 

 pomt of the rolling body, when it is just coming into contact 

 with the fixed surface, does so in a direction at right angles to 

 the surface at rest, and also leaves it in the same direction. This 

 action is very similar in kind to that which occurs with the con- 

 tinuous circle formed by the tyre. The path of a point in the 

 rim can be drawn in a way visible to the audience by means of a 

 piece of apparatus consisting of two circular glass plates held 

 together by a hollow brass spindle in which slides an arm carry- 

 ing a brush. The brush traces the well-known cycloid, of which 

 the only portion now to be considered is that where it directly 

 approaches the surface beneath. This part is perpendicular to 

 that surface, and when epicycloids are drawn, by rolling the 

 disk upon the arc of a circle, the saine fact is brought out. 



One body may, however, not merely roll upon another, and 

 a normal pressure be exerted, but they may exert a tangential 

 force upon each other. It is convenient to keep these two cases 

 separate ; examples of them being respectively the wheels of a 



' Abstract of Lecture delivered at the Royal Institution, by Prof. HeU 

 bhaw, on April 29. 



railway carriage and those of the locomotive which draws it 

 along. It is to be noted that the object in the former case is to 

 permit one body to move relatively to another without permitting 

 sliding contact of their surfaces, whilst, in the latter case, in 

 addition to this, the object is to obtain such motion. There are, 

 however, many cases in which it is merely the motion of a body 

 about one point which is required, such as when motion is trans- 

 mitted from the edge of one rotating disk to another, and then 

 this distinction still more closely holds, as the normal pressure 

 is only obtained so as to insure the necessary tangential resist- 

 ance. Thus the objects of rolling motion may be classed as 

 being — 



(i) To allow the relative motion of one body to another with 

 whic?i it is in contact without permitting relative motion of that 

 part of their surfaces in actual contact. 



(2) To obtain the relative motion of such parts of the surfaces 

 of bodies as are not in contact by means of statical contact of 

 the parts which are. 



The lecturer then proceeded to consider the practical proofs 

 of the smallne-s of the resistance to rolling in cases where the 

 distortion of the surfaces in contact is very small, as illustrated 

 by the small tractive force required for heavy bodies properly 

 mounted on wheels or on roller-bearings ; mentioning the case 

 of a i2-horse-power engine, the shaft of which continued to 

 rotate for three-quarters of an hour after the motive power was 

 withdrawn ; and another case, of a turntable weighing 14 tons, 

 which was kept in motion by a weight of 3^ pounds acting 

 upon it by means of a cord passing over a pulley. The small 

 distortion of such surfaces when transmitting motion requiring 

 expenditure of energy to maintain, was next made clear by 

 giving certain facts as to the accuracy with which one surface 

 was developed or measured out upon another. An account was 

 given of experiments made with apparatus specially prepared by 

 the lecturer to investigate this point. This apparatus consisted 

 of two accurately turned brass disks properly mounted upon a 

 frame, and the relative positions of these disks could be inter- 

 changed so that any minute differences in their peripheries 

 could be detected. The experiments, which were very diffi- 

 cult to carry out accurately,- showed that under the best cir- 

 cumstances, motion with an error of only i in 300,000 of the 

 distance passed over could be obtained. This accurate measur- 

 ing out of the surfaces one upon another was employed in various 

 ways for purposes of measurement, and these, by means of 

 models and diagrams, were briefly explained. 



Although the foregoing facts prove that, under suitable con- 

 ditions, distortion at the points of contact is very small, yet 

 some resistance at these points always occurs, because no bodies 

 are perfectly hard ; and the nature of this distortion and conse- 

 quent resistance was next discussed. 



The explanation of the resistance opposed by a soft surface to 

 a hard body rolling upon it, as first given by Prof Osborne 

 Reynolds, was applied by the lecturer to account for a very 

 remarkable effect produced in the disk, globe, and cylinder inte- 

 grator of Prof. James Thomson. This effect, which was the 

 turning of the cylinder when the sphere was rolled along it in a 

 horizontal direction, was reproduced by means of a large model. 

 The action of a soft body rolling upon a hard surface was 

 next considered, with the result of showing that the same 

 reasoning would not account for the turning of the cylinder in 

 the same direction as before with the above model, and the 

 lecturer then proceeded, by means of diagrams, to offer an 

 explanation of this and other phenomena. The various effects 

 obtained with bodies of different relative degrees of hardness 

 were discussed at length, but figures would be needed to make 

 these points clear. Finally, an explanation was given of the 

 cause of an error which always appeared in a certain important 

 class of integrators caused by the slipping of the edge of a disk 

 over a surface on which it rolled in circumstances under which 

 it had apparently never been suspected that slipping did actually 

 take place. This the lecturer had been enabled to discover and 

 measure by means of a special piece of apparatus, a model of 

 which was exhibited and the effects shown by its means. 



The facts and reasoning, which were given in the lecture, all 

 related to the rolling contact of bodies, and the lecturer ventured 

 to think that, imperfect as the treatment of the subject had been, 

 it was one of such importance, not merely from the point of view 

 of the practical applications he had mentioned, but in its scien- 

 j tific aspect, dealing as it did from a novel point of view with the 

 I nature and properties of solid bodies, as to be worthy of being 

 thus brought before the Royal Institution. 



