528 



NATURE 



[December 22, 192 1 



Letters to the Editor. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake to 

 return, or to correspond with the writers of, rejected manu- 

 scripts intended for this or any other part of Nature, ^'o 

 notice is taken of anonymous communications.] 



The Tendency of Elongated Bodies to Set in the East 

 and West Direction. 



Perhaps readers of Nature will recognise the 

 principle of the Eotvos torsion balance in the com- 

 munication of Sir Arthur Schuster published in 

 Nature of October 20 (p. 240) entitled "The Ten- 

 dency of Elongated Bodies to Set in the North and 

 South Direction." The calculation there given is, 

 however, incomplete, and this causes the sign of the 

 effect to be reversed. For the hypothetical " normal 

 case " a complete calculation shows that the tendency 

 is rather for an elongated body to set itself in an 

 east and west direction. The missing element in the 

 calculation is the difTerence in the directions of the 

 centrifugal force on the different portions of the rod. 

 If we call A the longitude, reckoned from the meridian 

 of the centre of the rod, of an element ds of the rod 

 at distance 5 from the centre, then approximately 

 X = s sin <p/a sin 6, where a is the radius of the earth 

 and the remaining notation is the same as in the 

 original communication. Since A is small, we may 

 write for the horizontal force perpendicular to the 

 meridian of the centre of the rod a-pm^Xds ; its moment 

 is (a- pu)^ Xds)(s cos (p), or, finally, since p = as'm6, the 

 moment of an element of length ds is 

 ctm's'' sin cos ds. 



It is easily seen that the horizontal component of 

 the centrifugal force is always directed outward from 

 the central meridian, and therefore tends to bring the 

 rod into the prime vertical. The above expression 

 combines wdth the moment given in the original 

 communication, namely, cro/s'^ cos^ sin (p cos ^ ds (after 

 correcting an obvious typographical error), giving 



0-0)^5^ sin^ 6 sin (p cos f ds. 

 By integration along the rod we get for the entire 

 turning moment 



Iw' sin* 9 sin (b cos <p, 



where I denotes the moment of inertia, as in the 

 original communication. 



As a matter of fact, we must consider not only the 

 effect of the change in direction and amount of the 

 centrifugal force, but also the changes in gravity due 

 to the departure of the earth from a spherical form. 

 We have, in effect, treated the earth as a spheroid 

 having an elllpticity due only to the direct effect of 

 the centrifugal force — that is, an ellipticity of 

 ta^aJ2g, where g is the acceleration of gravity. We 

 may get the complete expression by writing instead 

 of u)^a/2g the actual ellipticity of the earth, e. (This 

 is not offered as a proof.) The result is 

 {2eglja) sin^ 6 sin cos 0. 



In an article of mine published in the September 

 issue of the American Journal of Science, and briefly 

 noticed in Nature for October 6 (p. 192), I have 

 described the Eotvos balance from a different point of 

 view, and have shown how the rod may be thought 

 of as falling while turning about its axis of suspen- 

 sion, because, owing to the different curvatures of 

 the different vertical planes, it actually diminishes its 

 potential energy in turning. The prime vertical is 

 the vertical plane of minimum curvature in the 

 normal case, and it is towards this vertical plane 

 that the body tends to turn. 



Now experiments with the Eotvos balance have 

 shown that the actual condition at any particular point 

 is generally very far from normal, so much so that it 



NO. 2721, VOL'. 108] 



is quite conceivable that at the place of Mr. Reeves's 

 experiment the tendency should be more nearly 

 towards the meridian than towards the prime vertical. 



The body tends to set itself in the vertical plane of 

 minimum curvature, wherever that may be, and if we 

 reckon the angle from this plane the moment of the 

 force acting is numerically 



^I(i/R-i/N) sin ^ cos 0, 

 where R and N are the minimum and maximum radii 

 of curvature of the level surfaces of the earth's gravity 

 field at the point of observation. For the "normal 

 case " this expression readily reduces to the one 

 already given. Observations with the Eotvos balance 

 enable us to determine for any point the value of 

 i/R-i/N for the level surface passing through the 

 centre of the rod and the directions of the principal 

 planes of curvature of the level surface. There is also 

 a second tyf)e of Eotvos balance in which a mass at 

 one end of the rod is balanced by a weight suspended 

 from the other by a fibre of some length. 



To illustrate the 'erratic nature of the curvatures 

 of the level surfaces near the surface of the earth 

 when these are studied in detail, I take from the 

 work of Prof. Soler (" Prima Campagna con la 

 bilancia di Eotvos nei dintorni di Padova," Venice: 

 Reale Commissione Geodetica Italiana, 1914) the 

 following values of the angle /?, which is the 

 angle between the meridian and the direction in 

 which gravity is increasing most rapidly. The normal 

 value of i8 is zero. The actual values at a number 

 of successive stations, all near Padua, were found to 

 be 189°, 147°, 282°, 306°, 274°, 33°, and 304°. The 

 balance used here was of the second type. 



Although the curvature of any level surface near 

 the earth is very irregular In detail. It is fairly regular 

 on the average. That Is, we may consider the level 

 surface as made by superposing on a fairly smooth 

 surface a number of undulations, short and sharp, 

 but of small amplitude. The Eotvos balance picks 

 up mainly the curvatures of the sharp undulations, 

 while In ordinary geodetic work we get only a sort of 

 average curvature of the surface on which the undula- 

 tions are superposed. Walter D. Lambert. 



U.S. Coast and Geodetic Survey, 



Washington, D.C., November 21. 



Japanese Culture Pearls. 



A notice has recently appeared in the daily Press, 

 signed by a number of jewellers, with reference to 

 Japanese "culture" pearls. This notice, besides en- 

 dorsing the opinion expressed by the diamond, pearl, 

 and precious stones section of the London Chamber 

 of Commerce that "the insertion of foreign matter 

 placed In the oyster " disqualifies the culture pearl 

 from competing with the pearl produced without the 

 aid of man, declares that "cultured" pearls can be 

 distinguished from Indian pearls. 



The first of the above statements was justly ridiculed 

 at the time it was made by Sir Arthur Shipley in a 

 letter to the Times (May 7, 192 1), and Is not likely 

 to be taken seriously by the more intelligent members 

 of the pearl-purchasing public. 



The second statement is, however, sufficiently in- 

 exact to be liable to mislead the public. The only 

 established difference between the culture pearls now 

 on the market and "Indian" pearls, a difference 

 revealed by their different fluorescence under ultra- 

 violet light, is one that holds good also for "naturally 

 produced " pearls from the Japanese pearl oyster, 

 and is due to minute differences in the optical pro- 

 perties of the nacre of the Persian Gulf and Japanese 

 oysters. An attempt Is thus made to depreciate 

 culture pearls by confusing them with naturally pro- 



