These distances expressed as D may be easily converted into angular distances by means of (18). For comparison I give here the corresponding distances for two luminous points of equal brightness on a dark background from my paper "Diffraction Pattern in a case of two very close PointLight Sources" *: If we admit, rather arbitrarily, the limit of contrast sensibility of the eye for the case of diffraction image of two planes with a band between them to be 10-15 per cent., we shall have that two planes with a dark band between them (b=0) are resolved 9-6 times easier than two points, if generally the conditions of resolution of two planes and two points may be considered identical. For b>0 the distances between two planes to be resolved must be greater (see Table IV.). When a-b is less than the assumed limit value of contrast sensibility of the eye, two planes cannot be resolved (see the last line of Table IV.). A diffraction image of two luminous planes with a dark band or a band of some brightness between them may serve as a convenient object for determining the contrast sensibility of the eye, as we can vary the contrasts within large limits, their calculation is very simple and generally the distribution of illumination in such a diffraction image is clearly definite as all the isophotes are straight lines. The author is much indebted to Mr. G. Wahrlich for the execution of the drawings. Phil. Mag. xlvi. p. 29 (1923). XC. Note on the Striking Potential necessary to produce a Persistent Are in Vacuum. By F. SIMEON, B.Sc., F.Inst.P., Physicist in the Research Laboratories of Adam Hilger, Ltd. HE ease with which an arc can be struck in air between and the convenience of such an arc as a light source in spectroscopy, have suggested to those who have experimented in vacuum spectroscopy that an arc in vacuo would be convenient and desirable in that region also. When tried, however, it is found that with a number of substances the arc is intermittent when the voltage available for striking is of the order of 100-200 volts. In addition, it is well known that ares in vacuo emit radiations corresponding to the spark lines of the element in question. In the course of some experiments on the spectrum of carbon in vacuum, its appearance was noted when the applied voltage had several values. For 40 volts or more the arc was as persistent as in air, but the distance between the electrodes could not be made so great, this distance depending upon the voltage and the time the are had been running (i. e., probably on the temperature of the electrodes). When the striking potential was reduced to 30 volts, the arc would no longer persist, a momentary flash only being produced when the electrodes were slightly separated after being touched together, the appearance being similar to that obtained with two copper electrodes for a striking potential of 220 volts. A marked change in the spectrum of the are occurred simultaneously with the change in appearance. A striking potential of 40 volts was sufficient to excite the complete spectrum as given by 220 volts, including the lines near 385A, identified by Millikan† as the La lines of carbon: but with 30 volts the La and some associated lines were suppressed, still leaving, however, a number of recognized spark lines-e. g., 2297, 2509, and 2512 A. This shows that the lower potential is sufficient to ionize carbon atoms by removal of one of the outer electrons, but insufficient to excite radiation corresponding to the L levels. To test whether there is a connexion between L radiation and the persistence of the arc in vacuo, arcs were formed *Communicated by Prof. A. W. Porter, D.Sc., F.R.S. † Millikan, Astrophys. Journ. lii. pp. 47-64 (July 1920). with the elements Cu, Al, Si, and Na. The results are: The second column gives the limits within which the voltage corresponding to the beginning of persistence could be decided on. Means were not to hand for obtaining direct current at about 1000 volts, so that in the case of copper the probable value could not be approached, and only a transitory flash could be obtained on touching the electrodes. together and separating them. The limits given for aluminium are wider than for the remaining two elements because of the " sticky" nature of the arc, the electrodes appearing to fuse together at the point of contact, so that the effort to separate them often caused the arc to be made longer than could be maintained. The numbers given in the third column of the table are obtained from the quantum relation Ve=hv, the value assigned to being that corresponding to the L lines of the element in question. Siegbahn's value of wave-length 13-309 A. was used for copper, and Millikan's † value 372 A. for sodium. The approximate values for aluminium and silicon were obtained by means of Kossel's Combination Principle, La=KB-Ka. A check value for aluminium was obtained by taking Millikan's line at 136 A. as the limit for this metal, the corresponding voltage being 92. It is interesting to compare these results in one or two instances with corresponding results for an are in air at ordinary pressures. An immense amount of work has been done on the carbon arc, and various formulæ given connecting the applied voltage and the length of the arc. Fröhlich established the linear relation V=m+nl, in which m and n are constants. Von Lang has determined *Siegbahn, Jarhb. d. Rad. xviii. (3) pp. 240-292 (1921). Phil. Mag. Ser. 6. Vol. 46. No. 275. Nov. 1923. 3 G the value m=35 volts for carbon. More recently Steinmetz* has given the formula V=V2+a (1+b) in which i is the current and Vo, a and b constants. For carbon he gives Vo=36 volts. In this case, therefore, there is good agreement with the vacuum value for carbon (>30 <40) and with that given by the quantum relation for the limit of the carbon spectrum as determined by Millikan † at 360 A., viz. 35 volts. In the case of copper the evidence is conflicting. Von Lang has determined m in Fröhlich's formula as 23.86 volts, while Arons has found the potential difference required to produce an arc 1.5 mm. long carrying a current of 45 amperes to be 27 volts in air and 30 volts in pure nitrogen. The low value given by v. Lang is probably explained as being a constant found by extrapolation upon plotting results obtained with arcs of various lengths which had been established sufficiently long to have a plentiful supply of electrons of thermionic origin. The value thus obtained would represent the voltage required to maintain an arc of zero length which had already been formed. It seemed best in this case to observe the appearance of the flash produced when two clean copper electrodes were touched together in air. For a potential difference of 10 volts a small spark was produced which did not have the characteristic green colour of the copper arc, which colour did not appear until about 25 volts difference of potential was attained. When the difference had increased to 30 volts, the arc would almost persist, and did persist at 35 volts. Identical observations were made in the case of aluminium, although for this metal Arons gives the values 39 volts for air and 27 for nitrogen. It is at least clear from these results of v. Lang and Arons that the potential difference required to initiate a persistent arc in air is not determined by the excitation of the L-series corresponding to the electrodes, but is almost, if not quite, a constant quantity. It would therefore seem that in air the nature of the electrodes is not of importance as regards the voltage required to establish an arc, but that this depends chiefly upon the atmosphere in which it is formed. Steinmetz, cf. Pidduck's Electricity,' p. 361 (Camb. Univ. Press, 1916). + Millikan, Astrophys. Journ, lii. pp. 47-64 (July 1920). Arons, Aun. der Phys. i. p. 700 (1900). But it does not seem to be necessary in this case to excite the L-series of the gases in the atmosphere, for the highest value given (i. e. Arons' value for aluminium in air) is less than the expected value for nitrogen, and still less than that for oxygen. For the latter gas the limit of the L-series is placed at 248 A. by Kurth* and at 231 A. by Millikan†, which correspond to voltages of about 50-55. For nitrogen the corresponding value will be intermediate between this and carbon, and will be expected nearer to the former in view of Mohler and Foote's values for the K series. It is to be noticed that no suggestion is made regarding the carriers of current in a fully-established are, a full discussion of which has been given recently by Compton §; but if his views receive acceptance, the above considerations may suggest the origin of the positive ions whose presence gives the positive space-charge which enables sufficient electrons to be present to carry the currents observed in practice. XCI. The Two-Dimensional Motion of a Lamina in a Resisting Medium under the Action of a Propeller Thrust. By S. LISTER, M.Sc. || HE "phugoids," or "flight curves," of a lamina moving than its own weight, have been investigated by F. W. Lanchester and S. Brodetsky. The object of this paper is to extend the investigation by the introduction of a propeller thrust. Under Lanchester's assumptions the body has a vanishingly small moment of inertia, the velocity has a direction fixed in the body, and there is no loss of energy. The lamina thus maintains the same mean level throughout the motion. The assumptions made in this paper are, however, those used by Brodetsky, viz., a large moment of inertia, as in the case of a lamina attached to a heavy engine. Small changes in angular velocity can then be neglected and the lamina rotates with uniform angular velocity, w. *Kurth, Phys. Rev. xviii. pp. 461–476 (1921). + Millikan, Nat. Acad. Sci. Proc. (Oct. 1921). Mohler & Foote, Phys. Rev. xix. pp. 434-435 (1922). $ Compton, Phys. Rev. xxi. (3) pp. 266–291 (March 1923). Communicated by the Author. Lanchester, Aerodonetics.' Constable, pp. 37-65. ** Brodetsky, Proc. Roy. Soc. A. vol. xev. pp. 516-532 (1919) ; Mechanical Principles of the Aeroplane. Churchill, pp. 87-93. |