There are three kinds of breathing: (1) the diaphragmatic or low breath, (2) the intercostal or middle breath, (3) the clavicular or high breath. All three together mean full contraction of all the inspiratory muscles, necessary for the singer's health. However, for the purposes of singing, the combined diaphragmatic and intercostal breath is to be used.
It is advisable to have the pupil practice this kind of breathing on a divan with the following scheme: 12 waves inhaling and exhaling (diaphragmatic breath exclusively), 6 waves (diaphragmatic and intercostal breath combined), 2 waves full respiration (for health's sake, 7 counts in, 7 counts out).
The first attempt to apply the correct procedure of breathing is 4 counts in—4 counts hold (hands on lower ribs) and then from 4 to 24 counts exhale on ZZZZZZZZZZZZ like a humming bee. After this exercise, the pupil may learn to sing sustained tones in the middle or lower range (according to the quality of the voice, on "OH" or "OOH" or just humming.
From Reminiscences of a Vocal Teacher (1941) by Emi de Bidoli, student of Pauline Viardot-García and her pupil Aglaja Orgeni.
It should be noted that Viardot-García also had her students perform their first breathing exercises with a closed mouth, that is, by breathing through the nose. For more details, see Viardot-García's Hour of Study in the download section in the right hand column.