SECONDARY UNDULATIONS OF OCEANIC TIDES. 



dP = d/i-M, = p{d/t-,-d/i.^ 

 dP \ s,(a -h,) + v + s,{b - Ji,) \ - P{^,dh, + s.^m = ; 



we liave also the equation of continuity 



,9.,dh. = —sßh^ 

 Eliminating dh^, clh.,, clP from these equations, we get 

 dlh s,P 



dh 



p(l^^^^s,{a-h,) + v-{-s,{h-k^-\-s^P^+Ps, 



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 1 



dh /, s., \ S3 



<i-^î) 



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

 practically proportional to the change of sea level. We may 

 also infer from the exact expression of dli^fdh that tlie volume 

 of the copper tu]:)ing 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 sea level exceeds 3 m., tlio actual 

 value of dhjclh in the present apparatus does not difler from 

 the value given in the last equation by more than 0.2%'. 



The effect of temperature may be calculated in a similar 

 way. For tliis purpose, the product of the volume and the 

 pressure in Boyle's law is put equal to RT, where T is the 

 absolute temperature, and E a constant. Here // is considered 

 to be constant ; we have then the equations 



dP= -dh = pdk(i + ±y 



