June is named after the Roman Great Mother goddess, Juno. As ruler of the high point of the year, the time of maximum sunlight and minimum darkness, Juno is the light counterpart of Janus, the ruler of the New Year period. Because Juno is the divine watcher over the female sex, the month of June is held to be the most favorable for marrying.
On June 21st is the summer solstice, the festival of Midsummer. The month of June is 'the door of the year,' the gateway to the inner realms, opening to let the sun shine in.
Socrates was born on June 4th, in 470 B.C.E. June 21st--Midsummer, the summer solstice. June 24th--St. John the Baptist's Day/Old Midsummer. It was customary on this day to light midsummer bonfires on high points to celebrate the high point of the year and of solar light.
July is named for Julius Caesar, who reorganized the previously chaotic Roman calendar with the help of Alexandrian sages to form the Julian calendar. This new calendar was instituted in the year 46 B.C.E., known as the year of confusion after the chaos caused by changing from one calendar to another. The Julian calendar became the main calendar in the West for the next 1600 years. It was current in Britain until 1752. When the new Gregorian calendar was set up, Julius's name remained on the seventh month in commemoration of his work.