Results from 1036 days of solar neutrino data accumulated in the upgraded Kamiokande detector (Kamiokande III) are presented. The $^{8}\mathrm{B}$ solar neutrino flux observed in Kamiokande III is ${2.82}_{\ensuremath{-}0.24}^{+0.25}$ (stat) \ifmmode\pm\else\textpm\fi{} 0.27 (syst) \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ ${\mathrm{cm}}^{\ensuremath{-}2}$${\mathrm{s}}^{\ensuremath{-}1}$; the combined flux from Kamiokande II and III (2079 days in total) is 2.80 \ifmmode\pm\else\textpm\fi{} 0.19 (stat) \ifmmode\pm\else\textpm\fi{} 0.33 (syst) \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ ${\mathrm{cm}}^{\ensuremath{-}2}$${\mathrm{s}}^{\ensuremath{-}1}$, which is 49% to 64% of the standard solar models. These combined data from January 1987 to February 1995, covering an entire period of solar cycle 22, enabled us to study a correlation between the neutrino flux and the solar activity in detail: no strong correlation of the solar neutrino flux with the sunspot numbers was found within experimental errors. The result on a search for the daytime and nighttime flux difference is also reported.