1879.] Spontaneous Segmentation of a Liquid Annulus, 59 



Annulus No. 2. 

 (Initial diameter = 7" 4 75 centims.) 







Diameters. 









X-fHULIl Ul 









IV" n mT^PT* 



Remarks. 



J: ail. 













IVlaximum. 



JVLimmum . 



iyxHd.il. 







centims. 



centims. 



centims. 



centims. 







12 



6-85 ' 



6 85 



6 85 



17 



14 masses ; 11 drops 













perfectly regular. 





6 '85 



6 *85 



<Q '85 



16 or 17 



Perfectly circular. 











17 



Probably. 





6-65 



6-65 



6*65 



16 



Probably ; 8 in one 













semicircle ; sand 













rather hard. 





6 65 



6'5 



6-57 



15 or 16 



Sand wetter. 





6 65 



6-65 



6-65 



15 ©r 16 









Mean = 



6-7 



16-1 





It will be observed that, in the case of the smaller annulus, the 

 average experimental value of n is nearly a whole drop below the 

 theoretical value. This points to the possibility of contraction before 

 the segmentations were determined. Such contraction would cause 



a diminution in the value of the ratio — , both by diminishing the 



d 



numerator and increasing the denominator of the fraction, and would 

 produce a corresponding diminution in the number of drops. 



Since the force of contraction is inversely proportional to the princi- 

 pal radius of the annulus, its effect will be more rapid in the smaller 

 annulus, both on this account and because of the smaller mass of 

 liquid to be set in motion..* 



That the annulus sometimes becomes elliptical, is probably due to an 

 uneven distribution of the liquid at starting. When the disk was not 

 quite horizontal the thickest and thinnest portions of the annulus would 

 be opposite to each other, and the segmentation of the latter will be 

 complete before that of the former. This accords with the previous 

 observation that the well and ill-divided parts are always at opposite 

 ends of the same diameter. 



To account for the fact that this diameter is the shortest, it would 



* It should be remembered that the contractive force ceases to act on drops 

 which have assumed the spherical form. Hence the total amount of contraction 

 that is found to have taken place at any time after complete segmentation will depend 

 on the velocity acquired while the force acted, and therefore upon the time required 

 for the process of segmentation. This time will evidently be less in the case of a 

 thinner annulus. 



