Developer replenishing cartridge and developer replenishing method

A developer replenishing method, comprising:

• using a developer replenishing cartridge;
• wherein:
• the developer replenishing cartridge contains a developer replenishing container and a developer, the developer replenishing cartridge being removably mountable to a developer replenishing apparatus;
• the developer replenishing container includes
• (i) a developer containing portion for containing the developer,
• (ii) a discharge port for discharging the developer contained in the developer containing portion, and
• (iii) a pump portion that operates so that a state where an internal pressure of the developer containing portion is lower than an atmospheric pressure and a state where the internal pressure is higher than the atmospheric pressure alternately repeatedly switch with each other;
• the developer contains toner;
• the toner includes toner particles each containing a binder resin and a wax, and silica fine particles present on surfaces of the toner particles;
• the silica fine particles have a number-average particle diameter of primary particles of 60 nm or more and 300 nm or less;
• a coverage rate of the surfaces of the toner particles with the silica fine particles is 15% or more and 95% or less;
• the toner has a uniaxial collapse stress at a maximum consolidation stress of 10.0 kPa, of 2.5 kPa or more and 3.5 kPa or less;
• and
• the developer is contained in the developer containing portion of the developer replenishing container.