Shape of Large Bubbles and Drops. 

 where, for brevity, 



0=1 xydy, B= I s? Ay, A= 1 2«</y, 



Jo Jo Jo 



and s is the length of the arc AOB. 



Fiff. 2. 



513 



Suppose, then, that the coordinates of a large number of 

 points on the photograph of the meridional section of the 

 drop are measured off, and referred to the vertex as origin. 

 Three curves may then be plotted out — one having the 

 values of x and y, a second with the values of x 2 and y, and 

 a third with the values of xy and y, as abscissae and ordinates 1 - 

 respectively. The areas of these curves, taken between 

 proper limits, will then be proportional to the integrals A, 

 B, and C respectively. These areas can be measured with 

 considerable accuracy either by square-counting or by the 

 planimeter, afterwards being reduced to their proper values 

 from a knowledge of the magnification. The length s of the 

 arc AOB may be measured either by a rotating wheel, or by 

 fitting: a flexible rod to the curve. 



If the point (x x , y r ) be chosen so that the tangent is vertical,, 

 equation (x.) simplifies to 



_gp f2C^ 1 2 + AB^-A^ 1 2 z/ 1 



T= — 



x l 



2A- 



%\S 



(xi.) 



a form convenient for the measurement of small drops. 



But if the drop or bubble be so large that its surface may 

 Phil. Mag. S. 6. Vol. 25. No. 148. April 1913. 2 N 



