Owing to a variety of causes, such as the rotation of the earth on its axis, which carries the water rapidly round with it; the inertia of the water, preventing it from instantly responding to the tidal force; the irregular shape of the oceans, interrupted on all sides by great areas of land; their varying depth, producing differences of friction, and so on, the tidal waves do not appear directly under, or directly opposite to, the moon, and the calculation of the course and height of the actual tides, at particular points on the earth, becomes one of the most difficult problems in astronomical physics. We now turn to consider the effects of the sun's tidal force in connection with that of the moon. This introduces further complications. The solar tides are only about two-fifths as high as the lunar tides, but they suffice to produce notable effects when they are either combined with, or act in opposition to, the others. They are combined twice a month—once when the moon is between the earth and the sun, at the time of new moon; and again when the moon is in opposition to the sun, at the time of full moon. In these two positions the attractions of the sun and the moon must, so to speak, act together, with the result that the tides produced by them blend into a single greater wave. This combination produces what are called spring tides, the highest of the month. When, on the other hand, the moon is in a position at right angles to the direction of the sun, which happens at the lunar phases named first and last quarters, the solar and the lunar tides have their crests 90° apart, and, in a sense, act against one another, and then we have the neap tides, which are the lowest of the month. Without entering into a demonstration, it may here be stated as a fact to be memorised, that the tidal force exerted by any celestial body varies inversely as the _cube_ of the distance. This is the reason why the sun, although it exceeds the moon in mass more than 25,000,000 times, and is situated only about 400 times as far away from the earth, exercises comparatively so slight a tidal force on the water of the ocean. If the tidal force varied as the _square_ of the distance, like the ordinary effects of gravitation, the tides produced by the sun would be more than 150 times as high as those produced by the moon, and would sweep New York, London, and all the seaports of the world to destruction. In that case it might be possible, by delicate observations, to detect a tidal effect produced upon the oceans of the earth by the planet Jupiter.