There are exactly 52 Fridays in the year 1878.
The answer to this question is not always simple. Most of the time, it will equal the number of weeks in a year, but that's only true for some of the days of the week.
Most years have 365 days, but a leap year has 366 days. That adds up to 52 weeks (where each week is exactly 7 days) PLUS 1 or 2 additional days. The year 1878 has exactly 365 days.
Now if the year starts on a Friday in a non-leap year, you end up with 53 Fridays. Or if either of the first two days lands on a Friday during a leap year, then you can also get 53 Fridays. Check the calendars below for January and December of 1878 to see exactly where the year starts and ends.
January 1st, 1878 is a Tuesday. It is the 1st day of the year, and in the 1st quarter of the year. There are 31 days in this month. 1878 is not a leap year, so there are 365 days in this year.
December 31st, 1878 is a Tuesday. It is the 365th day of the year, and in the 4th quarter of the year. There are 31 days in this month.
This site provides a tool to count the number of any selected day of the week over an entire year. You can pick any year and find out things like the number of Saturdays in 2020.
Don't forget to check out the other date calculator tools available on the site, like the Days From Today calculator that helps you find the date occurring exactly X days from now. Or if you're trying to count the total number of days between two dates, you can use the Date Difference calculator.