with Mercury contained In Tubes. 523 



communicate with it by constricted openings ; this steadies 

 tlie liquid and prevents rapid oscillations of the columns. 

 In such lamps difficulty arose owing to the hotter electrode 

 becoming depleted of mercury which deposited on the cooler 

 negative electrode, so that the arc gradually passed towards 

 the positive end of the tube. This was overcome in a very 

 elegant manner by so forming the tube of the lamp that the 

 part where the positive electrode is situated is brought near 

 to or is made to touch the portion occupied by the negative 

 end of the arc. The difficulty could also be overcome by 

 employing a suitably placed subsidiary heating coil. 



The author is indebted to Mr. H. G. Lacell for further 

 information about these lamps. They are usually constructed 

 to operate on a 500 volt circuit, but lamps suitable for lower 

 voltages have been made. Like most other mercury lamps 

 they will not light on alternating current. The ultra-violet 

 light emitted is so intense as to colour glass globes a deep 

 purple. The tubes in which the arc plays have normally an 

 internal diameter of: several millimetres. 



If we regard the motion of the ends of the mercury 

 columns in the necklace effect as being a simple harmonic 

 motion, then, since experiment shows that the period varies 

 as the square root of the length of the columns, we may 

 regard the coefficient of the inertia term as being proportional 

 to this length. The coefficient of damping due to the in- 

 ternal viscosity of the mercury will also be proportional to 

 this length. The possibility of oscillatory motion depends 

 on the relative magnitude of the square of the coefficient of 

 darnprig and of the coefficient of inertia. So that, if the 

 " Spring " be the same, then we can obtain a dead-beat 

 motion by simply increasing the length without introducing 

 any constriction into it. 



Now the k ' Spring" is, as shown previously, largely settled 

 by the external pressure. It is also affected by the mean 

 current and arc length ; but assuming that the " Spring " is 

 chiefly decided by the pressure, then we can obtain a dead- 

 beat motion by decreasing the pressure. These considera- 

 tions suggest that increasing the length of the tube or 

 decreasing the hydrostatic pressure should result in the 

 formation of an arc of constant length. Both these con- 

 clusions are justified by experiment. 



When the arc is of constant length, the effect observed in a 

 rotating mirror is that of a ribbon of light. Fig. 14 (PI. VI.) 

 is the photograph of such a ribbon taken on a moving plate. 

 The tube was of quartz (4 cm., 4'2 mm., *55 mm., 102 volts, 

 210 ohms), the current was '1 ampere and the volts across 



