A cooling system for an aircraft gas turbine engine, the cooling system comprising: a core casing configured to house a compressor (12, 13), a combustion chamber, and a turbine (15, 16); a tail cone configured to form at least part of an exhaust passage of the turbine (15, 16) together with the core casing; struts configured to connect between the core casing with a support body of the tail cone; a housing installed in the tail cone, configured to house an electrical apparatus; and at least one primary duct configured, when the cooling system is installed in the aircraft gas turbine engine, to connect between an internal space of the housing and an outlet passage of the compressor or a discharge port of a blower installed in the gas turbine engine via at least one of the struts and a radial outside of the core casing, characterized by: an electric wire configured to connect to the electrical apparatus; wherein the primary duct includes: a front primary duct connected to the outlet passage of the compressor or the discharge port of the blower; a rear primary duct connected to the housing; and an inter-connecting box provided radially outward of the core casing and contacting between the front primary duct and the rear primary duct; and the inter-connecting box includes a terminal board; and the electric wire is connected from the terminal board to the electric apparatus through the rear primary duct. a core casing configured to house a compressor (12, 13), a combustion chamber, and a turbine (15, 16); a tail cone configured to form at least part of an exhaust passage of the turbine (15, 16) together with the core casing; struts configured to connect between the core casing with a support body of the tail cone; a housing installed in the tail cone, configured to house an electrical apparatus; and at least one primary duct configured, when the cooling system is installed in the aircraft gas turbine engine, to connect between an internal space of the housing and an outlet passage of the compressor or a discharge port of a blower installed in the gas turbine engine via at least one of the struts and a radial outside of the core casing, characterized by: an electric wire configured to connect to the electrical apparatus; wherein the primary duct includes: a front primary duct connected to the outlet passage of the compressor or the discharge port of the blower; a rear primary duct connected to the housing; and an inter-connecting box provided radially outward of the core casing and contacting between the front primary duct and the rear primary duct; and the inter-connecting box includes a terminal board; and the electric wire is connected from the terminal board to the electric apparatus through the rear primary duct. an electric wire configured to connect to the electrical apparatus; wherein the primary duct includes: a front primary duct connected to the outlet passage of the compressor or the discharge port of the blower; a rear primary duct connected to the housing; and an inter-connecting box provided radially outward of the core casing and contacting between the front primary duct and the rear primary duct; and the inter-connecting box includes a terminal board; and the electric wire is connected from the terminal board to the electric apparatus through the rear primary duct. a front primary duct connected to the outlet passage of the compressor or the discharge port of the blower; a rear primary duct connected to the housing; and an inter-connecting box provided radially outward of the core casing and contacting between the front primary duct and the rear primary duct; and the inter-connecting box includes a terminal board; and the electric wire is connected from the terminal board to the electric apparatus through the rear primary duct.