A differential leveling circuit started at BM Hydrant $($elev$.367\mathrm{.}30$ ft $)$ and ended at $B{M}_{\text{M}\text{a}\text{n}\text{t}\text{o}\text{l}\text{e}}($elev$.348\mathrm{.}50ft$ as shown below. All measurements are in feet. Calculate:

a$.(3pts)$ the HI for each set$-$up$,$ and the elevation of each turning point,

b$.(2$ pts$)$ the misclosure, and

c$.(3$ pts$)$ the corrected elevations.

$\backslash$table$[[$Point$,$BS$,$HI$,$FS$,$Elevation,Correction,Corr. Elev.$],[,3\mathrm{.}67,,,,,],[,,,,,,],[$TP ${?}_1,4\mathrm{.}16,,7\mathrm{.}82,1,,],[,,,,,,],[$TP $2,2\mathrm{.}79,,9\mathrm{.}01,-1,,],[,,,,,,],[T{P}_3,2\mathrm{.}05,,8\mathrm{.}11,,,],[,,,,,,],[$Manhole$,,,6\mathrm{.}45,,,]]$