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Boyle's Law applies to the expansion and contraction of gases within the body due to external pressure changes:
    PV = constant
If the pressure starts out as one atmosphere at the surface, it increases linearly with depth under water depending upon the density of the water:
    PATA = 1 + (depth/kappa)

      where kappa depends on the density of the water and units of depth:

  Value of kappa
  Depth in feet Depth in meters
fresh water 33.8 10.3
sea water 33.1 10.1

Dalton's Law states that in a mixture of n gases the partial pressure of each gas [Pi] is proportional to the molar fraction of each gas [Yi] that makes up the total:
    PTotal = P1 + P2 + ... + Pn = Y1PTotal + Y2PTotal + ... + YnPTotal

Dalton's Law can be used to determine how much nitrogen, oxygen, or carbon dioxide is in the ambient air at any hyperbaric pressure underwater.

Henry's Law states a gas will dissolve into a liquid in proportion to its partial pressure in the air and its solubility in the liquid.
    Ci in solution = Si × Pi

    where Si = solubility coefficient of gas i in a given solute, cc/mL/atm.
Henry's Law can predict the body's absorption of inert gases into and back from the body at any pressure or depth.

Table 1
Increasing severity of nitrogen narcosis symptoms with depth in feet and pressures in atmospheres.(1,3,6)
Depth P Total P N2 Symptoms
100 4.0 3.0 Reasoning measurably slowed.
150 5.5 4.3 Joviality; reflexes slowed; idea fixation.
200 7.1 5.5 Euphoria; impaired concentration; drowsiness.
250 8.3 6.4 Mental confusion; inaccurate observations.
300 10. 7.9 Stupefaction; loss of perceptual faculties.

Table 2
Symptoms and terminology of DCS.
Location of Bubbles Symptom(s) DCS Type Common Term
Joints Pain upon flexure. I Bends
Skin Altered skin sensation, itching, or rash. I  
Brain-spine Dizziness, headache, loss of coordination, weakness. II Staggers
Chest Cough, dyspnea, pain upon breathing. II Chokes