196 FROM NEBULA TO NEBULA 



overweighting that already overweighted side! No, the 

 natural way is for the migrating waters to heap them- 

 selves up at two points on the surface equi-distant from 

 the moon and from each other, forming together, as it 

 were, the three corners of an isosceles triangle. These 

 locations, of course, are ideal rather than actual, inas- 

 much as the moon, because of her monthly revolution, is 

 constantly changing her angular position relatively to 

 the earth and the sun, thus dynamically complicating 

 the phenomena themselves, as well as the mathematics 

 of them, to an extreme degree. 



It is here very important to guard against the mis- 

 take of supposing that the sun's displacing power upon 

 the waters is necessarily always uniform. Were this 

 true in fact, it would but cloud the principle involved. 

 The principle is that the earth must maintain her own 

 and her system's equilibrium, and so she reacts to the 

 attraction only to the extent required by the conditions 

 of the moment. For instance, when the sun is mid-over 

 either ocean, his effect is at a maximum, and when he is 

 looking down upon the continents, at a minimum; like- 

 wise, in winter, when he is farthest south, where the 

 oceans are twice as expansive, the tides are in general 

 higher than when he is north of the equator. The posi- 

 tion of the moon in her orbit is another factor that rules 

 the heights of the tides. When she is in line with the 

 earth and sun, the system is top-heavy, and needs more 

 ballasting than when she is elsewhere, hence it is then 

 that we have our "spring" tides; but when she is at 

 quadrature, the contrary is the case, and we have "neap" 

 tides; and so on. 



This principle of what may be called tidal equili- 

 brism furnishes the sufficient explanation of the singular 

 movements of the inner satellites of Jupiter and of Sa- 

 turn, described by Sir John Herschel in Articles 542 and 

 550, respectively (Outlines of Astronomy) : 



An extremely singular relation subsists between the mean 

 angular velocities or mean motions of the three first satellites of 

 Jupiter. If the mean angular velocity of the first be added to 

 twice that of the third, the sum will equal three times that of the 



