What is the second sympathetic nerve and fifteenth sympathetic nerve? What do they do?

The Sympathetic Nervous System (SNS) is a branch of the autonomic nervous system along with the enteric nervous system and parasympathetic nervous system. It is always active at a basal level (called sympathetic tone) and becomes more active during times of stress. Its actions during the stress response comprise the fight-or-flight response.

Like other parts of the nervous system, the sympathetic nervous system operates through a series of interconnected neurons. Sympathetic neurons are frequently considered part of the peripheral nervous system (PNS), although many lie within the central nervous system (CNS). Sympathetic neurons of the spinal cord (which is part of the CNS) communicate with peripheral sympathetic neurons via a series of sympathetic ganglia. Within the ganglia, spinal cord sympathetic neurons join peripheral sympathetic neurons through chemical synapses. Spinal cord sympathetic neurons are therefore called pre-synaptic (or pre-ganglionic) neurons, while peripheral sympathetic neurons are called post-synaptic (or post-ganglionic) neurons

The sympathetic nervous system involves spinal nerves T1 to L2 or L3.