The practice of double dating resulted from the switch from the Julian to the Gregorian calendar.

The first Roman Calendar (introduced in 535BC) had 10 months, with 304 days in a year that began in March (January and February were added only later). In 46BC, Julius Caesar created "The Year of Confusion" by adding 80 days to the year making it 445 days long to bring the calendar back in step with the seasons. The solar year - with the value of 365 days and 6 hours - was made the basis of the calendar. To take care of the 6 hours, every 4th year was made a 366-day year. It was then that Caesar decreed that the year begins with the 1st of January.

In 325AD Constantine the Great, the first Christian Roman emperor, introduced Sunday as a holy day in a new 7-day week. He also introduced movable (Easter) and immovable feasts (Christmas). In 1545 the Council of Trent authorised Pope Paul III to reform the calendar once more. 

In 1582, Pope Gregory XIII determined that the Julian calendar was off by 11 minutes and 14 seconds. Advised by astronomer Father Christopher Clavius and physician Aloysius Lilius, Pope Gregory XIII ordered that Thursday, 4 October 1582 was to be the last day of the Julian calendar. The next day was Friday, 15 October. The new Gregorian calendar resolved the discrepancy and declared January 1 as the first of the year. For long-term accuracy, every 4th year was made a leap year unless it is a century year like 1700 or 1800. Century years can be leap years only when they are divisible by 400 (e.g. 1600). This rule eliminates three leap years in four centuries, making the calendar sufficiently correct for all ordinary purposes. Protestant rulers ignored the new calendar that the Pope ordered. 

In spite of the leap year, the Gregorian year is about 26 seconds longer than the earth's orbital period. Thus the beginning of the third millennium should have been celebrated at 9:01pm on 31 December 1999. But considering that the Gregorian calendar starts with Year 1, and not Year 0, adding 2000 years means that the third millennium started at 21h00:34s on 31 December 2000. However, because Dionysis Exeguus - the 6th Century monk whose task it was to pivot the calendar around the birth of Jesus Christ - miscalculated the founding of Rome by about 4 years (and left out the year 0), the TRUE THIRD MILLENNIUM actually started on 31 December 1995.

As mentioned, Britain made the change only in 1752. Russia adopted the new calendar in 1918, China in 1949. 

Not all countries accepted this calendar at the same time. In fact, it was not until 1698 that Germany and the Netherlands changed to the Gregorian calendar. England and the American colonies didn't accept it until 1752. Before that date, the government observed March 25 as the first of the year, but most of the population observed January 1 as the first of the year. So, many people included both years when writing dates falling between January 1 and March 25, as in the following examples.

Julian or old style               Gregorian or new style              Double date
25 December 1718               25 December 1718                      25 December 1718
1 January 1718                     1 January 1719                            1 January 1718/19
2 February 1718                    2 February 1719                           2 February 1718/19
25 March 1719                      25 March 1719                            25 March 1719

To make life a little easier, the Kinnaird Worldwide dates are all Gregorian or they are the dates as published in IGI or other records or they are the dates as provided by family members..