To determine the day of the week on 17th June 1998, we can use the concept of the Gregorian calendar and the knowledge of leap years.

# Gregorian Calendar
The Gregorian calendar is the calendar system used in most of the world today. It was introduced by Pope Gregory XIII in 1582 to fix the inaccuracies in the previously used Julian calendar. The Gregorian calendar is a solar calendar that divides the year into 365 days, with an additional leap day added to February every four years.

# Leap Year Rule
The rule for determining leap years in the Gregorian calendar is as follows:
- A year that is divisible by 4 is a leap year, except for years that are divisible by 100.
- However, years that are divisible by 400 are still leap years.

# Calculation
1. Determine if the year 1998 is a leap year:
- Since 1998 is not divisible by 4, it is not a leap year.

2. Calculate the number of days from a known reference date to 17th June 1998:
- We can use a known reference date, such as 1st January 1900, which was a Monday.
- From 1st January 1900 to 1st January 1998, there are 98 years.
- Since 1900 is not a leap year, there are 365 days in each of those 98 years.
- From 1st January 1998 to 17th June 1998, there are 167 days.
- Therefore, the total number of days is 98 * 365 + 167 = 35947 days.

3. Divide the total number of days by 7 to find the remainder:
- 35947 divided by 7 is 5135 remainder 2.

4. Determine the day of the week based on the remainder:
- Since the reference date (1st January 1900) was a Monday, adding 2 days takes us to Wednesday.

Therefore, the day of the week on 17th June 1998 was Wednesday.