What was the day of the week on 19 August 1837?

Saturday

\(\frac{Date + Month code + Century code + Century upper year + Quotient of Upper year/4}{7}\)

\(\frac{19+2+2+37+9}{7}\)

\(\frac{69}{7}\) =  Remainder 6

The code for 6 is Saturday.

Note:

Code for   

Mon – 1       Tues – 2       Wed – 3      Thurs – 4     Fri – 5         Sat ­­–6            Sun – 0

Code for    

Jan – 0         Feb – 3        Mar – 3

Apr – 6        May – 1       June – 4

July – 6        Aug – 2       Sep – 5

Oct – 0         Nov – 3       Dec – 5

Code for         1800 is 2

                    1900 is 0

                    2000 is 6

                    2100 is 4

                    2200 is 2

                    2300 is 0

                    2400 is 6

                    2500 is 4   and  Likewise