320 Dr. 8. R. Miliier on an 



quickly to the level of c, and from that point slowly until the 

 contact U V is made. It is true that the rate of removal of 

 the air from the apparatus by the water-pump is diminished 

 by this addition, since the air has now to be drawn aWay at the 

 lower pressure of W,but this effect is counterbalanced by the 

 water-pump being now ke])t in practical operation during 

 the up-stroke, as well as the down-stroke, of the mercury, 

 and there is no appreciable increase in the period of a stroke. 

 Thus the net result of the addition of W is that the period of 

 contact of the vacuum-tube with the pump-bulb is materially 

 increased without affecting the period of a stroke, which is 

 exactly what is wanted at high exhaustions. 



In the instrument, hd is 58, ee' 17, and he 39 cms., and the 

 pump-bulb has a capacity of about 250 c.c. A water-pump 

 on the ordinary town supply gives a partial stroke in 25 

 seconds, and a complete one in 33, when a 5 seconds' interval 

 of contact is allowed of the vacuum-tube with the pump-bulb. 

 The interval may be given any value by altering the position 

 of the wire V, which is adjustable. 



It may also be worth noting that the use of a small pump- 

 bulb, with its consequent saving in mercury, although of 

 course it would be intolerable in the case of a hand-worked 

 instrument, is advantageous in all respects when the action is 

 automatic. For wdth an automatic instrument the time of a 

 stroke is generally roughly proportional to the volume of the 

 pump-bulb, and under these conditions the rate of exhaustion 

 is greater with a small than wdth a large bulb. In fact, if 

 we put V for the volume of the vacuum-tube, v=.oN for 

 that of the pump-bulb^ and /ju be the time occupied by a 

 stroke (proportional to v), the theoretical ratio in which the 

 pressure is reduced after pumping for the time t is 



t 

 (l-}-.^')~ icxs . 



t_ 

 This expression has its minimum value e~ ^^ when .i' = 0, 

 and tends towards unity as x increases indefinitely. The 

 result of this reasoning is unaffected by the fact that at 

 high exhaustions it is necessary to allow between the strokes 

 a considerable interval of contact of the vacuum-tube with 

 the pump-bulb, to let the air drain into the latter, as this 

 interval should also clearly be made roughly proportional to 

 the volume of the pump-bulb. Moreover, with instruments 

 worked by a water-pump I find that in practice the time 

 required for the stroke with a bulb of 250 c.c. can be made 

 less than half that necessary with a bulb of 500 c.c, in 

 consequence of the greater height he obtainable, and the 



