NA TURE 



[February ig, i 903 



Januarj 29.—" On Skew Refraction through a Lens, and 

 on the Hollow Pencil given bv an Annulus of a very obliquely 

 placed Lens." By Prof. J. D. Everett, F.R.S. 



The investigation here described was undertaken with 

 the view of finding an explanation of the curious curves 

 :d by receiving on a screen, at certain distances, the 

 hollow pencil which emerges from an annulus of a lens 

 placed at a large obliquity (such as 30 or 45 ) to the 

 incident beam. 



The first requisite is a process for calculating the direction 

 cosines of a ray after refraction at a given surface, when 

 those of the incident ray and of the normal are given, along 

 with the relative index of refraction; and the leading 

 feature of the process here described is, the preliminary 

 calculation of the direction cosines of the tangent to the 

 refracting surface in the plane of refraction. The refracted 

 ray (or unit length of it) is projected on this tangent and 

 on the normal ; and these two projections are themselves 

 projected on the axes of coordinates, and added. This 

 process differs in toto from that devised by Seidel and em- 

 ployed by Steinheil. 



A simple case is chosen for testing the working of the 

 proves? , the case of a narrow and thin annulus of a plano- 

 convex lens, with a parallel pencil incident at 45 on its 

 plane face, the index being i'5, and the sine of the inclin- 

 ation of the normals to the axis o'l. The direction-cosines 

 are found for the emergent rays at twelve equidistant 

 points; and from these, by harmonic reduction, expressions 

 are deduced for the direction-cosines of any emergent ray. 

 From the equations of the rays in terms of the direction- 

 cosines and starting-points, numerous cross-sections are 

 calculated and plotted. 



Each ray intersects two others, and the aggregate of 

 these points of intersection constitutes the two focal lines. 

 The secondary line is found to be nearly straight, and in- 

 clined at about 17 to the original direction of the beam. 

 The primary line is approximately a parabola, the chord 

 joining its ends being about \i the distance of the chord 

 from the vertex. The vertex is next the lens, and is the 

 intersection of the two rays which lie in the principal plane. 

 The rays which intersect at its ends have starting-points 

 79 distant from one of these rays, and 101 from the other. 



Every cross-section shows a double point wherever it 

 meets a focal line ; and at the ends of the two focal lines 

 these double points become cusps. The ends of the primary 

 line have been located, and the rays which pass through 

 them found as above, by means of the conditions for a 

 stationary point, which must always hold at a cusp. 



Chemical Society, February 5. — Dr. E. Divers, F.R.S. , 

 vice-president, in the chair. — The following papers were 

 read : — The solubilities and transition points of lithium 

 nitrate and its hydrates, by Dr. F. G. Donnan and Mr. 

 B C. Burt. Lithium nitrate was found to yield two 

 hydrates, LiN'0 3 ,3H,0 and LiNO.,,iH..O. Determinations 

 of the solubility of these hydrates and of the anhydrous salt 

 were made, and the various quadruple points thus located 

 confirmed by thermometric and dilatometric measurements. 

 — The synthesis of aa-diglutaric acid, by Drs. O. Silberrad 

 and T. H. Easter-Held. — Distillation of chlorine water, by 

 Dr. A. Richardson. When chlorine water is distilled 

 below ioo° C. the distillate contains free chlorine ; the resi- 

 due left in the retort liberates iodine from potassium iodide, 

 bleaches indigo solution immediately and gives the usual 

 rea< lions obtained with hypochlorous acid. Distillation of 

 chlorine water in a current of chlorine gas shows that the 

 hydrochloric acid formed in the residue is equivalent to the 

 hypochlorous acid found in the distillate, indicating that a 

 portion of the chlorine reacts with the water thus, 0,+ 

 H a = HCl+HC10. When chlorine water is heated in a 

 flask provided with a reflux condenser no change in its com- 

 position occurs. — A new vapour density apparatus, by Mr. 

 J. S. Lumsden. This apparatus is based on the principle 

 that the molecular weights of all substances in the state of 

 gas, when occupying the same volume at the same temper- 

 ature, exert the same pressure. From the pressure produced 

 1' vaporising a weighed quantity of a substance the mole- 

 cular weight of which is required, the weight in milligrams 

 which would produce the milligram molecular pressure is 



NO. 1738, VOL. 67] 



calculated and taken as the molecular weight. — A new form 

 of pyrometer, by the same. A further application of the 

 principle employed in the foregoing apparatus. A constant 

 volume instrument, made of glass, porcelain or metal, is 

 used, in which a weighed quantity of a substance is vapor- 

 ised and the pressure measured by a mercury gauge. The 

 pressures produced bv equal weights of substances are pro- 

 portional to the absolute temperatures ; therefore, if at two 

 temperatures the pressures produced by equal weights are 

 measured and one temperature is known, the second is 

 determinate. — Tertiary butyl phenol, by Mr. E. W. Lewis. 

 The non-formation of phenyl-rer-butyl ether when phenol 

 in alcoholic solution is digested with /cr-butyl chloride and 

 alkali affords an instance of the difficulty attending the pre- 

 paration of phenyl ethers containing a tertiary radical in 

 place of the hydrogen atom of the phenolic hydroxy!. 



Mathematical Society, February 12.— Prof. H. Lamb, 

 president, in the chair. — The following papers were com- 

 municated : — Lieut. -Colonel Cunningham, On 41c resi- 

 duarity and reciprocity. The criterion for distinguishing 

 the plus and minus signs in the congruence denoted, after 

 Dirichlet, by (q/p) i = ± 1, is the object of investigation. 

 Reductions of the criterion to convenient forms are given 

 and the properties of the symbol (qlp) 4 are developed. 

 Tables are appended giving the quadratic partitions (when 

 possible) of all primes less than 500. — Mr. E. T. Dixon, 

 Note on a point in a recent paper by Prof. D. Hilbert. It is 

 pointed out that in the non-Pythagorean geometries devised 

 by Hilbert, Helmholtz's axiom of monodromy is not verified, 

 inasmuch as it is possible, by rotation through four right 

 angles, to bring the points of a line into positions which 

 they do not occupy before the rotation. It is pointed out 

 further that, in the same geometries, it is possible to pass 

 from one point to another of a straight line without passing 

 through all intermediate points and without leaving the line. 

 The application of the name " geometry " to systems which 

 admit such possibilities is criticised. — Mr. H. Hilton, Some 

 properties of binodal quartics. Properties of bicircular 

 quartics are deduced from those of spheroconics by stereo- 

 graphic projection, and properties of binodal quartics are 

 then deduced by plane projection. — Prof. A. W. Conway, 

 The field of force due to a moving electron. The electron 

 is treated as a point singularity of the electromagnetic equa- 

 tions, and formula; to express the field of force about the 

 electron, when moving with any velocity, are obtained. 

 The amount of radiation from the electron is calculated. — 

 Prof. W. Burnside, An arithmetical theorem connected 

 with the roots of unity, and its application to group 

 characteristics. 



Royal Microscopical Society, Annual Meeting, January 

 21. — The president, Dr. Hy. Woodward, F.R.S., in the chair. 

 — A series of twenty-four photomicrographs in colour was 

 exhibited by Mr. Albert Norman, who said the examples 

 shown were an application of the Sanger Shepherd process to 

 medical photomicrography. The examples shown comprised 

 histological and pathological sections, malaria and tse-tse fly 

 parasites, and various bacilli, including tetanus and typhoid 

 showing the flagella. — The, President delivered his annual 

 address, its title being "Some Ideas on Life," based on the 

 development of life as shown by fossil organisms found in 

 geological strata. 



Mineralogical Society, February 3. — Prof. H. A. Miers, 

 vice-president, in the chair. — Mr. L. Fletcher gave an 

 account of the fall of a meteoric stone on August 22, 1902, 

 at Caratash, Smyrna, and also contributed a note on the- 

 history of the mass of meteoric iron found in the neighbour- 

 hood of Caperr, Patagonia. — Mr. H. L. Bowman gave the 

 results of determinations of the refractive indices of pyro- 

 morphite and vanadinite by means of artificially ground 

 prisms having an angle of about 30 . For red light the re- 

 fractive indices of pyromorphite were « =2.139, € = 2.124,. 

 and of vanadinite, =2.354, f = 2.299. — Mr. T. V. Barker 

 described quartz crystals of peculiar habit which were col- 

 lected by Lieut. E. G. Spencer-Churchill near De Aar, 

 South Africa. Two crystals were remarkable as exhibiting 

 faces seldom observed on quartz, one face in the zone mz and 

 another in the zone rz. 



