370 



Mr. A. M. Worthington. 



[June 16, 



" The equation (7) -— =T, 



is true also for drops formed at the mouth of a vertical pipe on the 

 assumption that in consequence of the gradual accession of new fluid the 

 same pressure is found in the interior fluid at the mouth of the pipe as in 

 a level fluid surface''' " The drop goes on increasing till W=0, or till 

 the highest element of the fluid is vertical, and then it falls off. 



" If the radius of the cylinder on which the drop is formed be very 

 small, the weight of the portion of the fluid which remains hanging 

 may be neglected, and the weight of the portion of the drop which 

 falls may be treated as the W in equation (7)." 



He is here speaking of a drop pendent from a tube so small that it 

 wets the outside and hangs as in fig. 3. It is, however, obvious that, 

 under such circumstances, the surface of the liquid, where vertical, 

 shares the curvature of the tube, and that the equation of equilibrium 

 should be 27rrT=W -J- the pressure on the area of the section of 

 radius r, 



or 27rrT=W + 7rr2— , 



r 



or = 1 . 



7TI' 



In other words, Professor Quincke's value of the tension is precisely 

 half what it ought to be. Hence, the very low value that he obtains 

 for the surface tension of water by this method, '0548 as compared 

 with -08253 by other methods. 



He applies the same equation to Professor Guthrie's experimental 

 data, although indeed it is not applicable to the larger terminals used 

 by the latter, so that the approximate agreement of the results with 

 those obtained by other methods is really due to a fortuitous cancelling 

 of errors.* 



I will now explain the mariner in which the tracing may be used 

 for evaluating the pressure at the base, and determining the value of 

 the tension. 



It is convenient to assume first that this pressure is zero, then to 

 introduce in the value of T the correction which is found from an 

 examination of the curve to be necessary. 



Assuming then that the pressure at th e hase is zero, it is evident that if 

 any horizontal section of the drop be made, the vertically resolved 

 part of the surface tension across the circumference of this section is 

 equal to the weight of the portion of the drop below the section, plus 

 the pressure of the head of liquid reaching from the section to the 

 bottom of the tube multiplied by the area of the section on which it 

 acts. 



* " Pogg. Ann.," vol. cxxxi, p. 137. 



