T.S. of Pons Varolli

   The pons varolli lies just cranial to the medulla oblongata. It is about an inch long.
    In section the pons shows cerebellar peduncles which connect the cerebellum to the pons and midbrain. The pons contains many important cranial neve nuclei. It also contains the pneumotaxic centre.
   The pneumotaxic center mediates the change from inspiration to expiration. You must be wondering : How does the pneumotaxic centre perform this function? Well, the process is really simple. The diaphragm is the main muscle that causes inspiration. It is a dome - shaped muscle that lies attached to the inner surfaces of the lower ribs. When it contacts, the summit of the dome is pulled downwards, thus increasing the size of the thoracic cavity. Thus the bases of the lungs expand downwards and they expand. Normally the diaphragm summit descends by around 1.5 cm in quiet breathing but can descend upto 7cm in deep breathing. The diaphragm is supplied by the phrenic nerve.
   This pneumotaxic centre decreases the strength of signals (in the form of action potentials) in the phrenic nerve. Thus, the diaphragm contracts to a lesser extent, meaning that it relaxes and thus mediates expiration. Thus, you're question is answered. :)
   The sections are taken at the levels of facial colliculus and trigeminal nerve (upper pons). I am really sorry about the short forms! Here are their full forms though -
ICP=Inferior Cerebellar Peduncle
MCP=Middle Cerebellar Peduncle
LST=Lateral Spino Thalamic
Roman numerals=number of the cranial nerve
SON=Superior Olivary Nucleus
LL=Lateral Lemniscus
SSN=Superior Sensory Nucleus
MLB=Medial Longitudinal Bundle
TS=Tecto Spinal
RS=Reticulo Spinal
SCP=Superior Cerebellar Peduncle
MTSL ( mnemonic  because it looks like MTNL)
   =Medial, Trigeminal, Spinal and Lateral lemniscus
MS=superior sensory nucleus of trigeminal nerve
M=Mesencephalic nucleus of trigeminal nerve
TzBody=Trapezoid Body