24c 



NATURE 



[October 20, 192 1 



tive decline during that period of the optical glass 

 manufacture in this country and the consequent 

 absence of an active and close local liaison between 

 the English mathematicians and opticians on one 

 hand and the optical glass manufacturers on the 

 other? The very presence in a country" of an 

 optical glass factory focusses interest on, and 

 enlarges the conceptions of, the research problems 

 connected with optical glass and its applications to 

 optical instruments. The mathematicians and optical 

 designers who are to open out new paths of advance 

 should have the materials they need at hand' and 

 readily available. To allow the optical glass industry 

 to die out in this country would mean that not only 

 the spirit of invention in this industry, but also much 

 of that spirit in the dependent industry of optical in- 

 strument manufacture, would pass over to the country 

 in which there was close co-operation between these 

 essentially related industries. 



Messrs. Zeiss assert that the practical monopolisa- 

 tion of the glass market by French and English houses 

 between 1848 and 1883 materially hampered the pro- 

 gress of the optical engineer. What reason have we to 

 think that a similar monopolisation to-day by Ger- 

 many would be less detrimental to the development of 

 the optical instrument industry in this country? If 

 Germany were the only source of supply of optical 

 glass, what guarantee have we that preferential treat- 

 ment would not be given to German optical manu- 

 facturers in matters of time, quality, and quantity, 

 to the prejudice of optical manufacturers of other 

 nations? Would the British engineering industry 

 have reached its present excellence if there had been 

 no efficient and vigorous iron and steel industry in 

 this country, and consequently no continuous and 

 intimate co-operation on the spot between the 

 engineer and the iron and steel manufacturer? These 

 considerations do not, of course, apply to all indus- 

 tries. But the optical instrument industry depends, 

 and must depend, on constant and close co-operation 

 and co-ordination between the optician and the mathe- 

 matician on one hand and the manufacturer of optical 

 glass on the other, and this cannot be complete and 

 efficient in a country where the sole source of optical 

 glass is a foreign supply. 



We agree with Messrs. Zeiss 's concluding state- 

 ment that optical mathematicians of all countries need 

 every extension of the choice of glasses at their dis- 

 posal and would deplore their exclusion from any 

 valuable material available to opticians in foreign 

 countries. But there was no proposal in the article 

 in Nature of February 10 last designed or bound to 

 have this effect, and, in any case, it leaves untouched 

 the argument for maintaining, in the interests of 

 British opticians, a healthy and progressive optical 

 glass industry in this country. 



The Writer of the Article. 



The Tendency of Elongated Bodies to set in the North 

 and South Direction. 



At one of the soirees of the Royal Society in 1920, 

 Mr. A. E. Reeves showed an apparatus by means of 

 which he believed he had obtained evidence that 

 under suitable atmospheric conditions freely suspended 

 elongated bodies set themselves with their longer axes 

 in the geographical meridian. The evidence supplied 

 at the time was not very convincing, and I under- 

 stand that the subject is receiving further attention. 

 In the meantime it may be pointed out that the earth's 

 centrifugal force would act in a manner tending in 

 the direction of the alleged effect, though the resulting 



NO. 2712, VOL. 108] 



couple is so minute that it would be extremely difficult 

 to verify it e.xperimentally. 



If a horizontal rod be placed in the north and 

 south direction, its southern end is — in the northern 

 hemisphere — further away from the earth's axis. The 

 centrifugal force is therefore greater at the southern 

 end, and if the rod be slightly displaced, the horizontal 

 component of that force will tend to bring the rod back 

 into the meridian plane. 



If p, be the distance of the centre of the rod from 

 the earth's axis, that of a point at a distance s from 

 the centre will be p = po+s cos 0, where 6 is the co- 

 latitude. 



The horizontal component of the centrifugal force 

 per unit mass at any point of the rod is w^p cos 0. It 

 is obvious that only the variation of the centrifugal 

 force along the rod can produce an effect, so that we 

 may write for its significant part 10 -s cos 6. If the 

 rod be turned through an angle <p we must apply a 

 further factor cos <p, neglecting small quantities of the 

 second order. With a- for the mass per unit length 

 of the rod, the couple acting on it becomes 



j aa>^scos^6 s'm (j) cos (f> ds — I <t>^ cos* s\n (f) cos (f), 



where I is the moment of inertia of the rod about 

 its centre of inertia. The result will be the same foi 

 any lamina, whatever its shape or material. For 

 small values of ^ the vibrations of the rod are deter- 

 mined by : — 



I^ = I<02COS*^.(^, 



which gives the period of a complete oscillation as 

 independent of I and equal to 2n-/to cos 6, or T sec 6, 

 if T be the time of revolution of the earth. W'e find, 

 therefore, that the suspended body tends to perform 

 oscillations round the meridian position, the time of a 

 complete oscillation being the same as that which 

 Foucault's pendulum requires to turn round a com- 

 plete circle, which in our latitude is about 31 hours. 



The maximum torsional couple takes place when 

 the rod is inclined at an angle of 45° to the meridian, 

 and in a latitude of 45° it is |I(o^. If it be desired 

 to demonstrate it experimentally we should naturally 

 turn to quartz fibres on account of their great carry- 

 ing power. According to Sir Richard Threlfall 

 (Phil. Mag., vol. 30, p. 99, 1890), a quartz fibre 

 o-ooi cm. in diameter can carry about 10 grams. A 

 uniform rod of that weight and 30 cm. in length 

 has a moment of inertia 750. By a suitable distribu- 

 tion of the weight of the rod this might be increased 

 to 1000. The numerical value of the resulting couple 

 then becomes 



250 u)^ = 1-3 X 10-*. 



For the couple due to a unit angular torsion of a 

 quartz thread of unit length and radius r, Sir Richard 

 Threlfall gives 4-7r* x 10". If the length of the 

 thread be 47 cm., we find finally 1-3 x lo-*, or about 

 20 seconds of arc for the angular torsion of the thread 

 which balances the couple due to centrifugal force. I 

 believe that the finest threads have a diameter about 

 ten times smaller than that in the example given, but 

 the weights would then have to be divided by 100, 

 and the angular displacement would be between three 

 and four minutes of arc. It is to be noted further 

 that the effect cannot be observed directly because we 

 cannot remove or apply the centrifugal force at will ; 

 the whole apparatus would therefore have to be turned 

 through an angle of 45°, and the difference measured 

 between that angle and the angular displacement of 

 the suspended bodv. Arthur Schuster. 



