High-resolution measurements of the differential cross sections for inelastic electron scattering of 183- and 250-MeV electrons by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ were carried out using beams from the Tohoku 300-MeV electron linear accelerator. Peaks were found with the following excitation energies (in MeV), and spins and parities: 3.74($3^{-}$), 3.90($2^{+}$), 4.49($5^{-}$), 5.25($2^{+}$), 5.61($2^{+}$), 5.90($1^{-}$), 6.29($3^{-}$), 6.59($3^{-}$), 6.95($1^{-}$), 7.9($2^{+}$, $4^{+}$), 8.5($2^{+}$, $4^{+}$, $5^{-}$), and others in the giant-resonance region. The cross sections for these states were obtained in the momentum transfer range from 0.5 to 2.2 ${\mathrm{F}}^{-1\mathrm{}}$. The data of the $3^{-}$ and $5^{-}$ states were compared not only with Tassie's vibrational model, but also with the particle-hole model of Gillet et al. The excitations of the dipole states ($T=0\mathrm{}$) are compared with Fujii's calculation. The data have been analyzed by using a distorted-wave code of Tuan, Wright, and Onley to extract the values of the reduced transition probabilities using the transition charge desities ${\rho }_{\mathrm{tr}}$ modified from the Tassie model, and from the particle-hole model. Then, the values of $B\left(\mathrm{EL}\right)\mathrm{}$ obtained from the quite different models are compared. The shapes of ${\rho }_{\mathrm{tr}}$ which provide best fits to the data are presented.

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