16th July, 1776 mean (1775 years+ 6 months+ 16 days) 

Now, 1600 years have O odd days. 

 100 years have 5 odd days

 75 years contain I 8 leap years and 57 ordinary years

 and therefore (36 + 57) or 93 or 2 odd days. 

$\therefore$ 1775 years given $0 + 5 + 2 = 7$and so 0 odd days.

 Also number of days from IstJan.1776 to 16th July, 1776

$$\begin{gathered} \mathrm{Jan} \mathrm{Feb} \mathrm{March} \mathrm{April} \mathrm{May} \mathrm{June} \mathrm{July} \\ 31 + 29 + 31 + 30 + 31 + 30 + 16 \end{gathered}$$

= 198 days = 28 weeks + 2 days = 2 odd days

$\therefore$ Total number of odd days$= 0 + 2 = 2.$

Hence the day on 16th July, 1776 was 'Tuesday'.