On Certain Projective Generalizations of Metric Theorems, and the Curves of Darboux and Segre

nificant. The values for platinum, given for comparison, were obtained along with the silicates. Albite and microcline have a smaller proportion of oxygen atoms than silica, and this should bring the theoretical value A, nearer 5.96 for them than for silica. Moreover, the values of Ap given contain the thermal effect of expansion. Allowances made for these two facts bring these substances into a class with the forms of silica, and thus tend to give assurance that the silica results are not exceptional, although the data are too uncertain to add anything to the exactness of our knowledge of the variations from the theoretical curve. Anorthite is given as a type of substances showing above 1000° a much larger increase. This increase, however, is very likely in part the effect of the latent heat from a slight amount of melting, due to a very small amount of impurity. Such effects have regularly been found in other kinds of work on silicates. But while such melting can affect the atomic heat as determined for anorthite and most other substances, which crystallize readily on cooling, it can scarcely do the same for the other silicon compounds given here, all of which are very sluggish in their changes of state, so that any slight portion of them melted at the higher temperatures would in all probability merely cool to a glass during the heat determination in the calorimeter, giving out no latent heat. Indeed, since the effect of impurities in causing melting increases rapidly with the temperature, these substances are very exceptional in their value for demonstrations at high temperatures such as that which is the subject of this paper. Summary.-The specific heats of three forms of silica and two silicates (alkaline feldspars) determined for temperatures up to 1300°, indicate that the atomic heats at constant volume for these substances increase above theoretical value, asymptotic to 5.96, as the heats of metals have been known to do, and hence that such increase is a very general phenomenon, as has been suspected.