256 Mr. K. Honda on a Portable 



the jar respectively : h 2 , 7i 3 be the levels of mercury in the 

 tubes B and C. Let b be the common height o£ the mercury 

 in the tubes, when the jar is not dipped in the water. I£ IT 

 and P be the pressure of the atmosphere and that within the 

 jar respectively, we have 



F = n + h-h 1 = p (h. d -h 2 ) + II, 



where p is the density of mercury,, 



If s u a be the cross-section and the height of the jar, and 

 s 2 , s 3 the cross-sections of the tubes B and C respectively, Ave 

 have, by Boyle's law, 



P{ Si(a — 7i{) + v + s 2 {b — h 2 ) } — const., 



where v is the volume of the lead tubing, plus that of the 

 part of the tube B lying above the level b. 



The differentials of the above two equations are 



dP = dh-<dh 1 =p(dh z -dh a % 



dF{s 1 (a-h 1 )+v + s 2 (b-h 2 )}-Y(s l dh l + s 2 dh 2 ))=Q; 

 we have also the equation of continuity 



s 2 dh 2 = — s B dh s . 

 Eliminating dh^ dh 3 , dV from these equations, we get 

 dh 3 __ 5]P 



dh p(l+ f){s 1 (a-h 1 ) + v + s 2 (b--li 2 ) + Sl P^ + Ps 3 



Since the first three terms in the denominator of the above 

 expression are very small compared with the fourth, we have, 

 neglecting these small terms, 



dh 3 __ 1 



dh~ 



(i+iA + tj 



Hence the motion of the mercury meniscus in the tube C is 

 practically proportional to the change of water-level. We 

 may also infer from the exact expression for dhjdh that the 

 volume of the lead tubing need not be small compared with 

 that of the jar. Even, if the volume of the tubing is equal 

 to that of the jar and the change of the water-level exceeds 

 10 m., the value of dhjdli in my apparatus remains constant 

 up to 06 per cent., which is sufficient for practical purposes. 

 Hence the recording apparatus can be set up at a considerable 

 distance from the beach. 



