Calculate: $($i$)$ the apparent specific gravity, $($ii$)$ the bulk specific gravity, $($iii$)$ the apparent particle density, and $($iv$)$ the bulk particle density of sand, given the following data:

Mass of sand $($oven$-$dry$)=510$ g

Mass of sand $($SSD$)=530$ g

Mass of pycnometer full of water $=1520$ g

Mass of pycnometer plus sand and topped up with water $=1800$ g