Density, Expansivity, and Viscosity of Molten Alkali Silicates 155The fraction of total energy absorbed is defined aswhere Eh is the relative energy occurring at wave length and A h is the fraction absorbed at the same wave length and is calculated from Th (the transmission a t h) by the formula T i being for a 0.65-mm. diameter and further defined as the H. P. Gage, "Glass Color Filters for Special Applications," J . Optical Amer., 27, 161 (1937).Th fraction of impinging radiation that finally emerges in the original direction. Accordingly, due to reflection, Th = (1 -I )~ when Ah = 0; and A h = (1 -I ) when Tx = 0. The function Ah of T i plots as a nearly straight line and is simple to use when so plotted.When infrared transmission data are available for some thickness other than 0.65 mm., they can be converted either by using the expressionwhere 0 is the absorption coefficient and t is the thickness, or by the use of a 06 table published by Gage.3 Table I is a representative calculation for one of the glasses in Fig. 8 and shows (1) appropriate values for Ex and ( 2 ) that all energy beyond 5 microns, except for one reflection, is absorbed completely.densities nd vi cositie of melts in the systems LizO-SiOz, NaaO-SiOn, and K20-Si02 were measured with a restrained sphere apparatus over the temperature range 1000° to 14OO0C. At the higher temperatures in this range the density in each system decreased with increasing alkali content. On a mole basis the thermal expansivity of the potassium silicates was greater than that uf the sodium and lithium silicates. Comparisons on the basis of moles of alkali per unit volume of glass showed that to a first approximation the viscosity of the systems investigated was almost independent of the kind of alkali ion involved.

The densities of liquids in the systems LizOBz03, Na20-B20,, and Kz0-Bz03 were measured by a counterbalanced-sphere method over the approximate temperature range 600" to 1000°C.The room-temperature densities of alkali borate glasses were also measured. Density increased with increasing percentages of alkali oxide below 30 mole yo. At high temperatures the densitycomposition curves showed maxima at about 30 mole yo alkali oxide. Expansivities over various temperature ranges were calculated from change of density with temperature. Expansivities in the liquid range increased with alkali content.In the low-alkali region, expansivity in the liquid range decreased with rising temperature whereas contrary behavior was noted in the high-alkali region. The most striking effect caused by the addition of alkali to Bz03 was a volume contraction. Some reasons were found to account for the lack of agreement with experimental observations of the methods of Huggins and Stevels for calculating densities.

The viscosity and electrical resistance of members of t h e systems Li20-B20a, Na20-Bz03, and K,0-B20s have been measured in the approximate temperature range 600' to 10QO°C. The log viscosity isotherms in the range 700" to 800°C.showed a minimum in the low-alkali region followed by a maximum as the alkali concentration was increased. This behavior could be explained by postulating a n equilibrium between two antithetical effects caused by the addition of alkali oxide to B2O3. The log electrical resistance isotherms decreased rapidly with increased alkali content up to about five equivalents of alkali ions per liter and decreased less rapidly in a linear fashion with further increase in alkali ion concentration. The equivalent conductance increased with alkali concentration, indicating behavior rather typical of liquids of low dielectric constant. The rate of increase of equivalent conductance was greater in the concentration region where the viscosity was increasing than where the viscosity was decreasing, thus illustrating that viscosity is not a controlling factor in electrical conduction. A plot of log R vs. log 7 gave straight lines whose slopes decreased with alkali content. The hypothesis that electrical resistance and viscosity of each glass were both related to the concentration of weak bonds in that glass was advanced to account for the constancy of the relation between the temperature coefficients of the two properties.

The s urface te~sions of a series of lithium, sodium, and potassium silicate melts were measured by a .maxllllum-pull-on-cylinder method. The order Li > Na > K was established for s,u rface tens IOn as well as [01' the algebraic value of t he te mperature coeffi cient of s urface te n s~on.Lithia an.d soda ralse~ th e surface te nsio n, and potash lowered it. The surface tensIOn ?urves of dl.fferent alkah cont~nt cO~1yerged with increasing temperature for li thium and sodIUm, b,ut dlverge.d. for potassIUm slhcates. Liquids containi ng less t ha n 33 mole percent of h thla had P?sltlve temperature coefficients of s urface tension. Correlation was obse,rved between a lka h content, volume expansi vity, and tempflrature coe ffi cient of surface tensIOn.

The viscosities a nd densit ies of 22 op t ical glasses, representin g all ty pes produced at t he National Bureau of Standards, were measured by a co unte rbalanced-sphere method. The densities agreed with those obtained by a vo lumeter method, and t he viscosities showed good agreement with t hose obtained with a small r otation viscometer.Expansivities calulated from density res ults in t he tem peTat ure ran ge 1,000° to 1,200° C showed that flints are low, 15 to 22, barium crowns are in termed iate, 22 to 37 , a nd borosilicate crowns are high , 34 to 40 (m icrons/ meter)/oC . The expansivities showed a posit ive correlat ion with t he slope of the viscosity temperature cur ve.The superiori ty of t he theoreticall y derived Faxen correction of Stokes law over t hat of t he e mpiri cal Francis formula was established b y means of a freely falling sphe re appa ra t us.