646 DR MATTHEWS DUNCAN ON A LOWER LIMIT TO THE 



the slipping of the membrane. The twenty-second column gives the pressure on 

 a circular surface of 225 inches radius, or equal to the assumed dimensions of 

 the lumen of the passage through which the child is expelled. The twenty-third 

 column gives the tensile strength of the membrane, or, in other words, the weight 

 which a band of it, an inch broad, would bear without giving way. 



Professor Tait has supplied the following formulae from which the columns 

 of the tables are computed : — 



Let b be the height of the barometer, corrected for the short column of mercury 

 in the gauge ; 



/ the length of the air-column before pressure is applied ; 



TV the contraction of the column, when the membrane bursts. 



Then, since the weight of a cubic inch of mercury, at ordinary temperatures, 

 is about 0-49 lbs., we have, for the difference of pressures on opposite sides of the 

 membrane when it bursts, the expression 



„> 0-49 t(j!r x -l) =049^, . (1) 



in pounds per square inch. No sensible correction is required for the length of 

 the water-column, when the mercury in the gauge and the membrane were not 

 exactly at the same level. 



If T be the force in pounds weight which will just snap a band of the mem- 

 brane an inch broad, g the radius of curvature when the membrane bursts, we 

 have, by a known theorem, the membrane being supposed to form approximately 

 a portion of a sphere, 



" = ' (2) - 



To find /o, we remark that the external semidiameter of the apparatus a is the 

 radius of the base of a spherical segment, whose height h is measured; and 

 geometry gives at once the equation 



2f = A + x ( 3 )- 



Hence, the tensile strength of the membrane is 



T = 0123 



&(» + ?)'■ • » 



If we assume that the membrane is usually burst, by natural processes, when a 

 portion of it forms a hemisphere of 2 - 25 inches radius, the requisite pressure in 

 pounds per square inch will be, by (2) and (4) 



0-245 b\ 



&(*-+t) w 



2-25 I- 



and the effective pressure, on a circular surface of 225 inches radius, will then be 

 , o0 .. o 0-245 5x f, o 2 \ - «, b\ (, a 2 \ ,_. 



