April 



1920 



NATURE 



199 



approximation we find that the apsidal progress per 

 revolution is . 



The observed value requires that A should be nearly 

 T^l2^ and if 3/2 is taken, we get the result obtained by 

 Prof. Einstein by his new specification and principles. 



It may be observed that the above specification by 

 the Lagrangean function could be generalised for any 

 number of particles, and that it involves no departure 

 from recognised dynamics or the normal views of space 

 and time. It does, however, involve the conclusion that 

 the interaction of bodies through the aether, vaguely 

 called "gravitation," is to a very slight degree not 

 exactly in accordance with Newton's specification. 

 Whether such conclusion is really necessary seems still 

 n matter of doubt. 



I have not seen any discussion of the problem of 

 two bodies on Prof. Einstein's specification, but it 

 appears to me that an exact determination of the 

 relative orbit when jw, and m„ are comparable quanti- 

 ties is very desirable. " George W. Walker. 



Portsmouth, March 29. 



The Construction of a Magnetic Shell Equivalent to a 

 Given Electric Current. 



.VccoRDiNG to Ampere's theorem, the magnetic field 

 due to an electric current flowing in any circuit is 

 equivalent at external points to that due to a simple 

 magnetic shell the bounding edge of which coincides 

 with the conductor, and the strength of which is 

 equal to the strength of the current. 



It is generally understood that any surface having 

 the circuit as its boundary will serve as the surface 

 of an equivalent magnetic shell, and the fact that 

 there is a restriction on the nature of the surface 

 does not appear generally to be recognised. 



Thus, for example, in Maxwell's treatise (vol. ii., 

 p. 142) we find the following :— " Conceive any sur- 

 face S bounded by the circuit and not passing through 

 the point P " ; while further on he says : " It is 

 manifest that the action of the circuit is independent 

 of the form of the surface S, which was drawn in a 

 perfectly arbitrary manner so as to fill it up." 



I propose to show by means of a simple example 

 that the surface is not drawn in a "perfectly 

 arbitrary " manner. 



Consider a narrow, rectangular strip of paper the 

 opposite edges of which we shall denote bv a and b, 

 its opposite faces by A and B, and its two ends by 

 I and 2. We shall represent the ends of the edges 

 by a,, b,, a^, bj, where the suffixes refer to the corre- 

 sponding ends of the strip. Now let one end of the 

 paper be turned round through an angle «■ and joined 

 on to the other end, so that a^ is joined to b, and 

 b, to a,. 



Then, since a, is joined to bj, the edges a and b 

 form one continuous line, and, since b, is joined to a,, 

 this line forms a closed circuit. 



Thus we may bend n wire into the form of the 

 edge, and can imagine an electric current to flow 

 in it. 



Although the electric circuit has the form of the 

 edge, yet we could not have a simple magnetic shell 

 the surface of which was that of the paper. 



This is easilv seen, for since, in addition to the 

 edges, the faces .\ and B have also become continuous 

 one with the other, we can no longer distinguish 

 one as positive and the other as negative. The same 

 thing is seen if we try to imagine the surface divided 

 up into elementary portions, in the manner conceived 



NO. 2633, VOL. 105] 



of by Ampere, with a current equal in strength to the 

 given current flowing round the boundary of each. 



It is easily seen that Ampere's construction fails 

 for such a surface, which is known to mathematicians 

 as a Mobius sheet. 



Although the surface we have described would not 

 serve as the surface of a simple magnetic shell equiva- 

 lent to an electric current flowing round its boundary, 

 yet it is possible to construct other surfaces having 

 this boundary which would serve as surfaces of 

 equivalent magnetic shells. 



If we have one suitable surface we can obtain any 

 number of others from it by continuous deformation 

 while the edge remains fixed. 



It is, therefore, desirable to give a general method 

 of constructing a magnetic shell equivalent to a given 

 electric circuit. The following appears to give a sur- 

 face having the required property : — 



Let O be a fixed point external to the circuit, and 

 let P be a variable point. Let P travel once com- 

 pletely round the circuit, so that the radius vector OP 

 traces out some conical surface. 



The portion of this conical surface containing O 

 and bounded by the circuit might then be taken as 

 the surface of the equivalent magnetic shell. 



In the particular case of the circuit we have con- 

 sidered (as well as in many others) the surface will 

 cut itself, but will, nevertheless, have two distinct 

 faces, one of which may be taken as positive and the 

 other as negative. It thus appears to satisfy the 

 necessary conditions. A. A. Robb. 



March 30. 



Volcanic Rocks in the Anglo-Egyptian Sudan. 



In connection with Prof. J. W. Gregory's reference 

 in Nature of February 19, p. 667, to the discovery 

 of the Bayuda volcanic field, and Mr. Campbell 

 Smith's record of a riebeckite-rhyolite which con- 

 stituted a number of stone implements found at 

 Jebel Katul, in Northern Kordofan (tbid.,_ February 26, 

 p. 693), some further notes may be of interest. 



The rock collected by Sir Herbert Jackson at Merowe 

 is a basaltic scoria, and the specimens either float or 

 just sink in water. A few crystals of olivine are visible 

 to the eve, and, urder the microscope, a regular 

 basaltic ground-mass, including felspar, iron ores, and 

 probablv glass, can be recognised in the powdered 

 rock. The specimens have evidently been transported 

 by a stream system which drains from the south-east 

 and debouches" on the river at the spot where they were 

 found. Save for the neighbourhoods of the river and 

 a few routes bv which travellers avoid the long journey 

 around the Abu Hamod bend of the Nile, the maps 

 of the Bayuda Desert are almost blank. Near one of 

 the routes a surveyor has recorded " Hosh Eddalam, 

 crater," and the name means a dark enclosure. Some 

 of the older travellers mistook ironstone concretions 

 for volcanic bombs, and as the surfaces of many rocks 

 are darkened in the desert such a record of a crater 

 did not call for particular note until evidence of ex- 

 trusive rocks appeared. It is situated in latitude 

 18° 20' N., longitude 32° 31' E., and consequently 

 lies to the west of the route taken by Dr. Chalmers 

 Mitchell. The volcanic field seen from the air probably 

 does not lie on the established routes, as it would 

 certainlv have been referred to in reports, even If it 

 were not described. Presumably there can be no doubt 

 I about the existence of craters seen bv an observer such 

 as Dr. Chalmers Mitchell, but the results of an 

 1 examination on the £/round will be of interest, even if 

 I onlv to know the tvpes of rocks involved. 

 I Mr. Stanlev C. Dunn records the presence of rhyo- 

 i lites and felsites near Jakdul, and these are doubtless 



