1879.] Spontaneous Segmentation of a Liquid Annidus. 



51 



.". pressure at A = C 



and at B = C + (---L-.\* i 

 \r R— rj 



where h is a constant, and the difference of pressures at' A and B is 



proportional to 



+ , which is small compared- with 



R + r R— r 



It may, therefore, well happen, as we shall see in the sequel that it 

 does, that the annulus will split spontaneously before any appreciable 

 alteration of its form can be caused by this inequality of pressures ; and 

 this is the more to be expected if the annulus be lying on a horizontal 

 plate, friction with which impedes the motion of the liquid as a mass. 



The method that I have adopted to discover the law of splitting has 

 been to liberate suddenly an annulus of mercury on a horizontal 

 surface of glass or iron. 



The apparatus consisted of a circular plate of iron 15 milllms. thick 

 and 60 millims. in diameter, the lower surface of which was truly 

 plane, and in it were cut various annular grooves, whose cross section 

 was an exact semicircle.- 



This plate is placed' face downwards on a plane horizontal surface of 

 iron or glass, and mercury is poured into one of the grooves through 

 one of two small vertical holes bored through the plate, the second 

 hole allowing the imprisoned air to escape. After removing any 

 excess of mercury that may remain in the holes, the plate is suddenly 

 lifted by a central handle, and a circle of regularly disposed dirops is 

 found lying on the lower plate. 



The following is a table of results obtained in this way, which are 

 recorded without any omissions. The size of the grooves was obtained 

 by direct measurement and by weighing the mercury they contained. 



A fourth groove of '7 millim. thickness was found to be too small 

 to use, being very difficult to fill with mercury. 



Groove No. 1. Diameter (d)= 2*03 millims. 

 Principal radius (R) = 25 ,, 



Method of liberation.. 

 Plate lifted rapidly. .. 



No. of drops. 



17 

 18 

 16 

 17 

 18 



16+(prob. 18) 

 17 

 19 



Remarks. 

 Regular, larger at the holes. 

 Very regular. 



37-25 (+) 



Regular; larger at the holes. 

 Very regular. 



e2 



