Differentiation in Silicate Liquids. 185 



The Viscosity of the Melts. 



If the effect of convection currents in delaying the sinking 

 of crystals in the crucible may be considered negligible it is 

 possible to obtain a rough idea of the order of magnitude of 

 the viscosity of the silicate melts. It must be thoroughly 

 emphasized that the figures so obtained and stated below can- 

 not be considered as having any exact significance. They 

 merely form a basis for the rough comparison of the viscosity 

 of these silicate melts with that of liquids of everyday experi- 

 ence. The rate of sinking of small spheres in a liquid is given 

 by the equation 



__ 2 gr. 2 d — d 



~~ 9 v 



where Fis the terminal velocity; r, the radius of the sphere 

 and cl its density ; -y, the viscosity of the liquid and d' its dens- 

 ity. The rate of sinking of forsterite crystals from the less 

 siliceous melts was approximately 1 cm. per hr., since the sur- 

 face indicating the upper limit of crystals moved downward at 

 approximately that rate. The crystals lying near this limiting 

 surface have an average diameter somewhat less than 0*l mm . 

 The difference in density between forsterite and the liquid at the 

 temperature of the experiment is not known, but since forster- 

 ite does not invert before melting it is probably not far from 

 the difference at room temperature, approximately 0*4. These 

 values would indicate an absolute viscosity of about 8. It is to 

 be noted, however, that the crystals were growing while sinking, 

 and though they grew very quickly at first and were nearly 

 their final size throughout the greater portion of the time it is 

 probable that a viscosity 1/2 as great as that given above 

 would be a fair estimate of its actual value. The viscosity 

 indicated is, therefore, about 4, or approximately 400 times that 

 of water and somewhat less than 1/2 of that of glycerine at 

 room temperature. In so far as the sinking of crystals was 

 interfered with by convection currents this value is to be con- 

 sidered too high and, therefore, a maximum estimate, but the 

 fact that the surface marking the upper level of crystals moves 

 downward as a fairly definite plane indicates that the effects of 

 convection currents in keeping the crystals evenly distributed 

 is negligible. 



For the more siliceous type of mixtures from which pyroxene 

 crystals settled out the viscosity is considerably greater. The 

 difference in density between the crystals and liquid is approxi- 

 mately the same. Crystals of pyroxene of average dimension 

 0*5 mm sink in these liquids only about as fast (l crn per hr.) as 

 did crystals of forsterite 0*l mm in diameter in the less siliceous 

 mixtures. In another case crystals 0'3 mm in diameter sank about 



Am. Jour. Sci.— Fourth Series, Vol. XXXIX. No. 230.— February, 1915. 

 13 



