42 THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 



theory, got rid of by supposing- the actual tide to be referred to a configuration of the 

 sun and moon anterior by 2J days to the configuration at the time of the tide. But 

 since we refer the effects of parallax and declination to the parallax and declination 

 contemporaneous with the tide, we must look for an analogy only when we do the 

 same in the other case. 



In the semimenstrual inequality, as determined from observation, there is no such 

 discrepancy with theory as compels us to suppose a change in X'. But this forms no 

 objection to our view ; for if, in the course of a semirevolution of the moon, there were 

 a periodical change in V, this must have the same cycle as the change in & — X', and 

 would therefore be confounded with that change, and would not result in a separate 

 foi^m from our discussion. 



But, moreover, the difference of the quantity of the semimenstrual inequality at 

 different places, which we have already show^n to exist, supplies a confirmation of the 

 opinion here put forwards. For this difference implies that the tide travels from one 

 given place to another in different times at different periods of a semibmation ; that 

 is, it implies that the velocity of the tide-w^ave is different in different configura- 

 tions of the sun and moon, that is, under different circumstances of the tide-pro- 

 ducing forces. And this agrees with our doctrine, that the amount of lagging is 

 different under different circumstances of those forces ; for if the amount of lagging 

 of the tide elevation go through a cycle of changes in a certain period, the velocity 

 with which this elevation travels will also go through a cycle of changes in the same 

 period. And this difference of the semimenstrual inequality at different places, does 

 appear to betray a semimenstrual inequality affecting X', the amount of the inequality 

 varying with the place ; and this variation, added to the theoretical semimenstrual 

 inequality which affects d' — X', and which is the same for all places, makes up the 

 empirical semimenstrual inequality of &\ given by our mode of investigation, which 

 thus appears to be different at different places. 



Taking all these reflexions into consideration, there appears to be good reason to 

 believe that the amount of the lagging of the tide behind the equilibrium-tide is 

 really affected by changes in the distances and velocities of the disturbing luminaries. 



There is another circumstance in which the empirical differ from the theoretical 

 laws : the epochs |3, y of the changes due to parallax and declination are different 

 from the epoch a of the semimenstrual inequality. 



The physical statement of this result is, that the time required to transmit to any 

 port the general effect of the tide-producing forces, and the time required to transmit 

 to the same port the effects of particular changes in these forces, are different. And 

 of this result we may say, in the same manner as of the former, that we see far too 

 obscurely the causes which determine the amount of this interval in one case, to assert 

 that it must necessarily be the same under different circumstances. But we may illus- 

 trate this subject somew-hat further. We may suppose an imaginary mean moon, 

 moving uniformly in the equator, at a constant distance from the earth, to produce 

 the mean tide ; another auxiliary moon, by moving directly to or from the earth, in 



