208 Dr. Fleming : Ratio between Mean Spherical and 



to *64 v . From this it can at once be deduced that '48 of 

 the total energy of the a particle, shot out by radium itself, 

 is absorbed when it ceases to ionize the gas. Now it can 

 be calculated from the heating effect of radium at its 

 minimum activity — 25 gram-calories per hour per gram — 

 that the kinetic energy of the a. particle is 4*7 X 10 -6 erg. 

 The amount of energy absorbed when the a. particles just 

 cease to ionize the gas is 2*3 X 10"" 6 erg. Assuming that this 

 energy is used up in ionization, and remembering that the 

 a. particle from radium itself produces 86,000 ions, the average 

 energy required to produce an ion is 2*7 x 10 _lj erg. This 

 is equivalent to the energy acquired by an ion moving freely 

 between two points differing in potential by 24 volts. 



McGill University, Montreal, 

 May 1, 1905. 



XXVI. On the Ratio between the Mean Spherical and the Mean 

 Horizontal Candle-Power of Incandescent Electric Lamps. 

 By J. A. Fleming, M.A., JD.Sc, FJt.S., Professor of 

 Electrical Engineering in University College, London*. 



A PAPER was read before the Physical Society on 

 November 11th, 1904 f, by Mr. G. B. Dyke, B.Sc, 

 in which, amongst other matters, he gave the results of 

 numerous measurements made in the Pender Electrical 

 Laboratory of University College, London, of the ratio of 

 the mean spherical candle-power of incandescent electric 

 lamps to the mean horizontal candle-power, taken when the 

 lamp was rotating round a vertical axis. In all cases the 

 ratio of the mean spherical to mean horizontal candle-power 

 was experimentally found to be a number near to 0*78 for 

 about nine different types of electric glow-lamps. This 

 constant ratio must depend upon definite optical facts, and 

 cannot be a matter of accident. That this is the case can be 

 shown by considering a typical instance. 



Let us suppose a short straight filament a b (fig. 1) ren- 

 dered incandescent to be placed vertically in the centre of a 

 sphere described by the revolution of a semicircle PHQ 

 round a diameter P Q, coinciding with the direction of the 

 filament. Let the length of the filament be small compared 

 with the radius FH=r of the sphere. Let Ih represent the 



* Communicated by the Physical Society : read June 16, 1905. 



t See Mr, G. B. Dyke, " On the Practical Determination of the Mean 

 Spherical Candle-Power of Incandescent and Arc Lamps," Phil. Mao-, 

 ser. 6, vol. ix. p. 136, Jan. 1905 ; also Proc. Phys. Soc. vol. xix. p. 399 



(19U5). 



