Date and Year Calculation:
To determine the day of the week for a specific date, we can use various methods including the Zeller's Congruence algorithm or a perpetual calendar. However, since the provided date, 2nd October 1869, is within the range of the Gregorian calendar, we can use a simplified approach to find the day of the week.

Gregorian Calendar:
The Gregorian calendar, which is the most widely used calendar system today, was introduced by Pope Gregory XIII in 1582. It replaced the Julian calendar and brought about a more accurate calculation of leap years.

Calculating the Day of the Week:
To find the day of the week for a given date, we need to consider the number of days that have passed since a known reference day. In this case, we'll use the reference day as 1st January 1800, which was a Wednesday.

Calculating the Number of Days:
To calculate the number of days between 1st January 1800 and 2nd October 1869, we need to consider the following factors:

1. Years: 1869 - 1800 = 69 years
2. Leap Years: There were 17 leap years within the given range (1804, 1808, 1812, ..., 1868).
3. Non-Leap Years: There were 52 non-leap years within the given range (1800, 1801, 1802, ..., 1869).
4. Days in Each Year: Each non-leap year consists of 365 days, and each leap year consists of 366 days.

Using these factors, we can calculate the total number of days between 1st January 1800 and 2nd October 1869.

Total Days = (69 * 365) + 17 + 52 = 25215 days

Determining the Day of the Week:
Now that we have the total number of days, we can find the corresponding day of the week. Since 25215 is divisible by 7, we know that the remainder will be 0. This means that if 1st January 1800 was a Wednesday, then 2nd October 1869 will also be a Wednesday.

Conclusion:
Therefore, the correct answer is option 'D' as 2nd October 1869 fell on a Wednesday.