How do I find the atmospheric pressure of the following?

A uniform capillary tube, closed at one end, contained air trapped by a thread of mercury 85mm long. When the tube was held horizontally, the length of the air column was 50mm, when it was held vertically with the closed end downwards, the lenght was 45mm.

Thx.

Boyle's law states that the product of the pressure of a gas times it's volume (P*V) is a constant as long as the temperature remains constant. When the tube is held horizontally, the length of the air column was 50 mm. The air is at atmospheric pressure (P_a)in this position, since the mercury column does not add or subtract any pressure to the air (since gravity does not act horizontally). With the closed end down, the air column length was 45 mm, which means the volume of the air decreased, hence it's pressure increased. Now since P*V is always constant, and since V can be determined from the air column length, we have

P_a*V_a = (P_a +85)*V₂
P_a*50 = (P_a +85)*45
solving,
50P_a=45P_a + 3825
5P_a = 3825
P_a= 765 mm of mercury.
Depending on what country you are from, you should convert this to standardized pressure readings. In the USA, 765 mm Mercury is 30.12 inches mercury air pressure.