If the bell is placed on the plate of a pneumatic machine, initially the pressure inside it is the same as the pressure on the outside and the mercury in the cup and the branch adjacent to the manometer remain at the same level, while between the two branches of the siphon barometer there is a difference that measures atmospheric pressure.
When the pneumatic machine is started up the mercury goes down in the siphon barometer and rises in the free air manometer.
If within a certain time interval the difference in level of the siphon barometer that measures the pressure in the bell decreases, in the same time interval the difference in level in the free air manometer that measures the difference in pressure between the inside and the outside of the bell undergoes an increase equal to the decrease in the barometer.
Instant by instant the difference in level in the siphon barometer is exactly equal to the part lacking in the difference in level in the manometer in that it measures atmospheric pressure.