February 9, 1 899] 



NA TURE 



357 



College. To Tuskegee Normal and Industrial School (Booker 

 T. Washington!, I give thirty thousand dollars, on same terms 

 as that to Harvard College. I give to bacteriological laboratory 

 (Harvard Medical School) ten thousand dollars. Mr. Austin 

 was one of the class of East India merchants so prosperous in 

 the first half of this century. He was bi'rn in Portsmouth in 

 1S03, but his childhood was spent in Boston, where also his 

 permanent home and interests were centred. 



SCIENTIFIC SERIALS. 



Anicrkan Journal of Mathematics, vol. x.^i. No. I, January. — 

 Systems of revolution and their relation to conical systems in 

 the theory of Lame's products, by F. H. S.ifford. In problems 

 requiring the solution of Laplace's equation, it is often possible 

 (the author remarks) to obtain a solution by transferring to 

 curvilinear coordinates. A, ^, v, and assuming that \" is a pro- 

 duct of three factors, i.e. \ = L.M.N, where L, M, N are 

 functions of X, /I, J* respectively. Such an expression for \' is 

 called a Lame's product. The problem treated is an appli- 

 cation of a theorem due to Lord Kelvin, by means of which, 

 from a known solution, V, of Laplace's equation in terms of 

 coordinates corresponding to a system of mutually orthogonal 

 surfaces, a solution may be readily deduced for a new system 

 of surfaces obtained from the first by inversion. The theorem 

 is used in an extended sense, so that real surfaces have been 

 obtained from imaginary surfaces by inversions with regard to 

 imaginary points as centres. A. Wangerin, in his " Reduction 

 der Potential-Gleichung " (Leipzig, 1875), has discussed many 

 of the topics considered here with the aid of elliptic functions. 

 The use of these functions is avoided in the present paper. 

 Wangerin states that the most general surfaces of revolution 

 for which Lame's products, with an extraneous factor, exist, 

 are those whose meridian curves are obtained from the curves 

 (got by equating the real and imaginary parts of the equation 

 .V 4- ;■/ = f(t + m), where /'is either sn or oi) by an inversion 

 with respect to a point on the axis of revolution. The same 

 topics are treated by Haentzschel in his " Reduction der 

 Potential-Gleichung" (Berlin, 1863), but he obtains surfaces 

 of revolution of the thirty-second degree. — A. L. Baker con- 

 tributes a short elementary proof of Cauchy's theorem, 



W'= / (AV = / wdz, taken around a closed curve enclosing no 



point where w = 00 is zero. — The number is closed with a 

 long essay (pp. 25-84), by C. L. Bouton, entitled " Invariants 

 of the general linear dilterential equation and their relation 

 to the theory of continuous groups." The titles of the chapters 

 will indicate the line of work. Cap I. Cockle's work("Criti- 

 coids") and differential covariants. Cap 2. Cockle's results by 

 Lie's methods. Cap 3. Invariants of the general linear differ- 

 ential equation in two variables for transformation of both 

 variables. Cap 4. Consideration of a subgroup. Cap 5. Differ- 

 ential equation in canonical form (complete solution in explicit 

 form of the problem of finding all the covariants and invariants 

 of the equation in its canonical form (Forsyth's "Identical 

 Covariants," &c. ). The bibliographical references and the con- 

 sideration of Sir J. Cockle's scattered results (the first dating 

 from 1862) are a very useful feature of the memoir. — The 

 pictorial accompaniment of the initial number of the new volume 

 is a photograph, from a painting, of Prof, Simon Newcomb. 



ll'ic-i/emaiiii's Annalen der Physik und Chemie (Supple- 

 mentary Number, 1898).— Mobilities of electric ions, by F. 

 Kohlrausch. The conductivities of very dilute solutions may 

 be theoretically determined from their concentrations by adding 

 up the separate mobilities of the ions constituting the molecule. 

 The author gives tables of mobilities from which the conduc- 

 tivities of monovalent salt solutions can be calculated down to 

 concentrations of decinormal strength. — Kinetic theory of 

 liquids, by C. Dieterici. It is shown that by applying the 

 methods and data of the kinetic theory of gases, the. properties 

 of liquids may be to a large extent mathematicallj' deduced. 

 The size of the molecules exerts of course a great effect, and it 

 will have to be more definitely known before the liquid theory 

 is complete.— Magnetisation by alternating currents, by Max 

 Wien. Toroids of soft iron wire, exposed to alternations of 12S, 

 256, or 512 per second, provided by an alternate current siren, 

 are not capable of following those frequencies by corresponding 



magnetic inductions. Eddy currents of higher periods are 

 developed, and the soft iron becomes magnetically harder. — 

 Reaction pressure of kathode rays, by E. Riecke. An ordinary 

 radiometer is used to determine the reaction pressure, the 

 vanes acting as kathodes. The pressure is proportional to 

 the current intensity, with a current of 3 x lo"" absolute 

 units the pressure is 004 dynes per square cm. — Induction 

 coils, by W. Hess. The discharge of an induction coil is studied 

 by introducing a liquid condenser in parallel W'ith the spark 

 gap. The liquid condenser contains CS.,, and produces a Kerr 

 effect between two crossed nicols. A strained glass plate is put 

 between the nicols, and converts the dark field into a field of 

 fringes. These are displaced by any fluctuation of potential, 

 and when the displacements of a section of the fringes are photo- 

 graphed, a record is obtained of the whole course of the 

 discharge Some excellent photographs are reproduced. — 

 Effect of Rontgen rays upon spark discharges, by H. Starke. 

 Like ultra-violet light, Rontgen rays are capable of reducing the 

 discharge potential between terminals upon which they impinge. 

 But, unlike ultra-violet rays, they are indifferent as to the sign 

 of the terminal impinged upon. — A new method of demonstrat- 

 ing Hertz's experiments, by J. Precht. The sections of a 

 Hertzian resonator provided with a parabolic mirror are con- 

 nected with a spark gap having a blunt kathode and a pointed 

 anode. A steady discharge from an influence machine traverses 

 the spark gap, and the gap is so adjusted that only a glow dis- 

 charge passes. Any electromagnetic waves received by the 

 mirror convert the glow into a shower of sparks, and at the 

 same time the discharge potential is diminished. — Use of the 

 coherer, by O. Behrendsen. For showing the reflection of 

 electromagnetic waves, it is necessary to use a coherer which is 

 not very sensitive, and to avoid single wires. The author uses a 

 coherer made of powdered arc carbon. — Pyro-electricity and 

 piezo-electricity, by W. Voigt. The question is raised whether 

 the whole of the pyroelectric charge of a crystal can be 

 described as piezo-electric, and as due to the change of volume 

 which accompanies every change of temperature. The author 

 shows that in tourmaline and other crystals with a singular axis, 

 about 20 per cent, of the charge is purely pyro-electric. In the 

 other crystals it is altogether piezo electric. — Gliding discharge 

 along pure glass surfaces, by M. Toepler. The length of sparks 

 in air may be considerably extended by making them pass along 

 glass surfaces backed by tinfoil, which is in metallic connection 

 with one of the terminals. — Magnetisation of crystals indifferent 

 directions as depending upon temperature, by Ascan Lutteroth. 

 Faraday found that the orientation of a crystal in a magnetic 

 field is less pronounced at higher than at lower temperatures. 

 The author shows by experiments on various sulphates that this 

 may or may not be true according to the choice of the axis of 

 suspension, and explains his observations on the basis of 

 molecular magnets. — Conduction of electricity by thin sheets of 

 dielectrics, by W. Leick. Gutta-percha, paraffin, and sulphur 

 show greater conductivity in thin layers than in thick layers. 

 The conductivity depends upon the current strength, the resist- 

 ance decreasing as the current increases. Gutta-percha and 

 paraffin do not show any polarisation, but sulphur does. — 

 Absorption of uranyl salts, by Ernst Deussen. Kundt's law of 

 dispersion does not apply to the more easily soluble uranyl salts 

 such as the nitrate and the chloride. But it holds for the nitrate 

 in glycerin, and for the chloride in alcohol. In the case of 

 the less soluble salts, such as the sulphate, acetate, and oxalate, 

 the bands are displaced towards the red. — Effect of gases and 

 metals upon the photographic plate, by B. von Lengyel. 

 Hydrogen is capable of modifying silver bromide so as to 

 give images on development. Metals which, like zinc, are 

 capable of disengaging hydrogen from moist air, also exert 

 an effect upon the sensitive plate. The Becquerel rays of 

 uranium and thorium are, however, a pure radiation. — Visi- 

 bility of Rontgen rays, by E. Dorn. The X-rays are not only 

 visible to the ordinary eye, but to totally colour-blind eyes, 

 sometimes appearing exceedingly bright, but always diffused 

 owing to the absence of refraction. "The rods of the retina 

 are more affected by them than the cones. — A new electro- 

 magnetic string interrupter, by L. Arons. This interrupter 

 dispenses with electromagnets, the vibrating string being 

 attracted by a permanent magnet, which breaks the circuit by 

 withdrawing a platinum wire attached to the string from a 

 mercury surface. The attraction is electrodynamic. Since 

 the self-induction of the circuit can be thus made very small, 

 very high frequencies can be attained. 



NO. 1528, VOL. 59] 



