Shape of Large Bubbles and Drops. 519 



Similarly, by plotting a curve between x 2 and y, estimating 

 its area (99*72 sq. cm.), and taking account o£ magnification, 



B =?w : =- 002405 - 



Similarly, the curve between xy and y (area 72*64 sq. cm.) 

 gave 



79*64 x -05 



c = "-fiw = ' 0008758 - 



Finally, 



s, as actually measured on squared paper = 2 x 7*847 inchest 



And since 1 cm. on graph = *2 cm. on photo, the true 

 value of s on the drop itself 



2 x 7-847 X 2*54 x *2 lofln 



= ^ n n - ='4960 cm. 



lb*U< 



These values, substituted in equation (x.), ghe 



T 981x1*461 , 



1= - ^ Q . =76*0 dyne-cm. \ 

 •218x84 J 



This result, though higher than those obtained by the 

 other methods described by the writer, yet falls within the 

 limits of the varying results made by different experimenters, 

 as previously quoted. And, i£ it be remembered that this 

 particular drop (E in fig. 3) is very small — its maximum 

 diameter being about 4 millimetres — and, further, if the 

 necessary uncertainty in the determination of <f> be taken 

 into account, it is fairly reasonable to assume, especially if 

 the small drops will allow of the use of equation (xi.), that 

 such planimetric measurements will give results that can 

 be relied on in cases where it would be difficult to obtain 

 measurements by any other methods, e. g. in the case of 

 molten metals, or small drops of magnetic liquids in magnetic 

 fields. 



To sum up: — (1) In the present paper methods have been 

 described by means of which approximations to the outlines 

 of large bubbles and drops may readily be made. These 

 approximations differ slightly in their correcting terms from 

 those obtained by other methods. 



(2) A mechanical, or planimetric, method of integration 

 has been described which is applicable to drops and bubbles 

 of all sizes. 



