1904] 



on the Motion of Viscous Substances, 



491 



The upper square is compressed horizontally, the lower is drawn 

 out in the same direction. 



Experiment shows that the rate at which the bar falls at its centre 

 is approximately that given by theory based on similar suppositions 

 to those which were made in the case of traction. 



Fig. 7 shows the time which, according to the theory, should be 

 taken by rods of different lengths in falling at their centres through 

 the same distance. The shorter the bar the slower it falls. The 

 marked points are those actually observed. The agreement is, under 

 the circumstances, satisfactory. 



The results obtained in this way for the viscosity of several 

 materials are exhibited in the tables. When the material of the bar 

 is so soft that it sags too quickly to be easily observed, it may be 

 immersed in a liquid of very nearly its own density. In this way 

 the forces bending it can be made as small as we please and con- 

 sequently the rate at which it sags also. 



Sliape of Falling Stream. 



The shape of a falling stream of a viscous liquid is interesting 

 to observe. It can be well seen when helping oneself to honey. If 

 the liquid is a thick one we have 

 practically a case of simple viscous 

 traction of a rod continued until 

 extreme thinning of the rod is pro- 

 duced. In Fig. 8 is shown the 

 shape taken by such a liquid when 

 falling from a circular hole in the 

 bottom of the containing vessel. 



There is an interesting point 

 in connection with the shape or 

 outline of the falling stream which 

 is at first surprising. It comes out 

 that, when the flow is slow, the 

 same shape ought to be assumed 

 by all substances under the same 

 conditions as to size of orifice and 

 height in containing vessel. This 

 certainly appeared to be so in the 

 case of the substances in the series 

 examined. How this comes about 



will be understood by considering that if the material is removed 

 slowly below owing to high viscosity, it is fed in at the top equally 

 slowly. 



A short length such as marked above draws out as it falls so 

 that it occupies a greater length at subsequent positions. Now 

 if we know the rate at which it is drawn out and the force acting 

 upon it, we can calculate the viscosity just as in the direct experi- 

 ments on traction. 



Vol. XVII. (No. 98.) 2 l 



■rLOWorFTlLUNC COLUMN 



Fig. 8. 



