176 



NA TURE 



[December 9, 1909 



metals and ammonium, and the nature of the isomorphism 

 existing between the salts of these various bases. A largi? 

 number of crystal measurements and determinations of 

 physical constants are recorded in the paper. The main 

 conclusion is that the morphological and physical proper- 

 ties of the crystals of these thalliuin double salts are such 

 as quite entitle them to inclusion in the monoclinic 

 isomorphous series of the general formula above given, 

 but not to places in the more exclusive eutropic series 

 within that isomorphous series. This eutropic inner series 

 is confined to the salts the interchangeable metals of which 

 belong to the same family group of the periodic classifica- 

 tion, namely, to those of potassium, rubidium, and caesium, 

 the crystals of which exhibit the regular progression of 

 angles and physical constants, according to the atomic 

 weight of the metal, already pointed out by the author in 

 previous communications. The crystals of the thallium 

 salts resemble very closely those of the ammonium salts — 

 which are also outside the eutropic series, but are included 

 in the isomorphous series — except as regards one outstand- 

 ing specific property, that of refraction ; for the crystals of 

 the thallium double salts, like those of the simple sulphate 

 and selenate of thallium, exhibit transcendent refractive 

 power, which proves to be a characteristic property of the 

 crystals of all the thallium salts yet studied by the author. 

 — P. F. Everitt : The nature of the diffraction figures due 

 to the heliometer. This paper contains a discussion of the 

 heliometer diffraction fringes. The matter is one of con- 

 siderable importance, owing to its bearing on astronomical 

 measurements taken with this instrument. A difficulty 

 arose owing to the appearance of these fringes in helio- 

 meter work on an artificial double star. It was then found 

 that, although the subject had been discussed by Bessel, 

 Hansen, and Gauss, a good photograph of tlie actual 

 fringes obtained by Scheiner and Hiravama, and a series 

 given for the calculation of the fringes by Bruns, all 

 attempts at their actual numerical determination had failed, 

 owing to the extremely slow convergence of the series 

 adopted, at a small distance from the centre of the system. 

 By the adoption of a semi-graphic method, and the use 

 of mechanical integrators, it has been found possible to 

 carry out the calculations needful in order to obtain an 

 accurate picture of the fringes. Photographs were taken 

 of the fringes, and these, taken by the author, as well as 

 the photograph taken bv Scheiner and Hiravama, show a 

 close agreement with the calculated contours, and enable 

 one to obtain the proportions of the central (non-elliptic) 

 oval, with which observers are chieflv concerned. The 

 close agreement between the calculated and theoretical 

 values of the different parts of the svstem is a further 

 proof that the old undulatory theory suffices to determine 

 in practice the true dimensions of such diffraction figures 

 — fc.. Cunningrham : The motional effects of the Maxwell 

 ffither-stress. There is an outstanding gap in electro- 

 magnetic theory in respect to the attempt to reconcile the 

 analysis of sthereal stress on the lines initiated bv Max- 

 well with Newton's third law and with tne law 'of the 

 conservation of energy. In the present condition of theorv 

 there are assigned to the a;ther certain distributions of 

 electromagnetic energy and momentum. The hypothetical 

 distribution of energy is necessarily associated with the 

 i^oynting vector which measures its rate of transference 

 itie distribution of momentum is so defined that the rate 

 ot increase of the total amount within any given volume 

 supposed at rest in the aether is equivalent to the resultant 

 of the Maxwell stresses on the bounding surface There 

 IS, however, no connection established between the trans- 

 ference of energy across an area and the stress across that 

 area. .Such a connection would require that it should 

 be possible to assign to the medium in which stress and 

 energy reside a state of motion whereby the stresses might 

 do the necessary amount of work ; and this again, would 

 require the revision of the specification of stress, inasmuch 

 as the ordinary expressions are computed for an element 

 of surface which is at rest. In the first section of the 

 present paper it is shown that, if ^ is the intensity of 

 electromagnetic momentum (\¥A\\j i,T,c) and -w the energy 

 intensity ([E=-f H=]/S7r). and the velocity u is taken in the 

 direction of g of magnitude, such that (c=-i-x'=)^=2-jW, the 

 same stress system which would account for the transfer 

 of momentum will account for the transfer of energy, pro- 

 NO. 2093, VOL. 82] 



vided the fether is assumed to be moving with velocity ii. 

 The stress system is not the ordinary Maxwell one, but 

 reduces to it in the electrostatic case. In this case it is 

 known that the Maxwell stress may be analysed into a 

 tension along the lines of force, together with a uniform 

 pressure at right angles to those lines. This property of 

 the stress system, commonly given, is not true of the total 

 stress (electric and magnetic) in the general field. It is 

 shown, however, that the stress system obtained in the 

 paper can always be reduced to this form. The direction 

 of one of the principal stresses is always along the 

 velocity v. It is shown, further, that at the surface of a 

 perfect reflector, stationary or moving, the velocity v is 

 equal to that of the reflector combined with a ' velocity 

 tangential to it, that is to say, a perfect reflector is 

 analogous to an impenetrable boundary. In the second 

 part of the paper a similar analysis is applied to radiation 

 such as would exist in the interior of a cavity the walls 

 of which are moving, so that, although the electric and 

 magnetic forces vary extremely rapidly and in an irregular 

 manner, there is necessarily a transfer of energy. Taking 

 £ and 7 as the mean values of the energy and momentum 

 over intervals of time, which are short as compared with 

 those which are appreciable bv mechanical means, but 

 long as compared with the period of the irregular fluctua- 

 tions which constitute natural radiation, it is found that 

 the mechanical properties of the radiation may be repre- 

 sented as those of a continuous quasi-fluid, in which there 

 is a definite pressure ^ at every point (the same in all 

 directions) and a definite velocity v, the relations connect- 

 ing the several quantities being 



ip^e-vy (I) 



c-y = vU^p') (2) 



If a small volume V is followed in its motion with the 

 quasi-fluid, it is found that the quantity 



^V4/V-^'=)-=" (3) 



remains constant. If v^ is neglected this becomes the 

 known equation connecting the pressure and volume of 

 steady radiation for adiabatic changes. Finally, it is 

 shown that if a state of the radiation differing slightly 

 from the actual is conceived, and dQ is the difference in 

 the energy of the small volume V, after allowing for the 

 change due to mechanical causes, such as increase of 

 momentum and volume, the condition that the expression 

 dQ/T should be a perfect differential is that 



p(fi~zl'-f = k-Y* (4) 



This with (3) involves the equation 



/V/r^ constant. 



— Dr. H. C. Pocklington : The aberrations of a sym- 

 metrical optical instrument. The doubly modified charac- 

 teristic function is written down, and the singly modified 

 function derived from it correct to terms of the fourth 

 order of small quantities. This is transformed so as to 

 take account of the existence of an exit pupil, and formulae 

 are found giving the aberrations for any position of the 

 object and pupil in terms of the six coefficients of aberra- 

 tion of the system. Some relations are found between 

 these aberrations, and connection is established with the 

 methods of numerical calculation given in Whittaker's 

 tract on "The Theory of Optical Instruments." — H. E. 

 Watson: The spectrum of radium emanation. — Prof. 

 E. G. Hill and Dr. .\. P. Sirkar ; The electric conductivity 

 and density of solutions of hydrogen fluoride. — Sir David 

 Bruce, Captains A. E. Hamerton and H. R. Bateman, 

 and Captain F. P. Mackie : Sleeping sickness in Uganda. 

 Duration of the infectivity of the Glossina palpalis after 

 the removal of the lake-shore population. 



Institution of Mininpand Metallurgy, November i8. — 

 Mr. Edgar Taylor, president, in the chair. — L. D. 

 Ricketts : Experiments in reverberatory practice at 

 Cananea, Mexico. A detailed description of the installa- 

 tion of a reverberatory furnace and McDougal calciners 

 at the Cananea Consoiidated Copper Co.'s Works, and of 

 the difficulties that were encountered in connection with 



