A calorimetric method of obtaining directly the fragility of liquids from the fictive temperatures of variably quenched glasses, is outlined. "Steepness indexes" m, have been determined for a group of molecular liquids of diverse character, and vary in the range 50-150. The values obtained mostly agree well with those from earlier studies using dielectric relaxation, heat capacity spectroscopy, and viscosity data. In our method there is the advantage that the fragility is determined from the relaxation process that is basic to the calorimetric glass transition temperature measurement, namely, that of the enthalpy. The calorimetric measurements also yield the liquid and glass heat capacities, and entropies of fusion, permitting relationships between thermodynamic and kinetic responses to be examined simultaneously. We study glycerol, dibutylphthallate, 9-bromophenanthrene, salol, orthoterphenyl, propylene carbonate, decalin and its nitrogen derivative decahydroisoquinoline, and find the latter two to be the most fragile liquids known, m =145 and 128 respectively. Surprisingly, of the liquids studied, decalin has the smallest increase in heat capacity at the glass transition. By contrast, the strongest liquid, glycerol, has the largest increase. However, the thermodynamic fragility of decalin, assessed from the scaled rate of increase of the excess entropy above T-g, is found to be high, due to the unusually small value of the excess entropy at T-g. Conversely, the entropy-based fragility for glycerol is the lowest. Thus the correlation of kinetic and entropy-based thermodynamic fragilities reported in recent work is upheld by data from the present study, while the basis for any correlation with the jump in heat capacity itself is removed.