106 Baron N. Schilling on the Constant Currents 



attraction of the moon acts at the angle HBb with the earth's 

 ■ gravitation. We thus see that the weight of the water and air 

 becomes greater the further we remove from the point where 

 the moon or the sun is in the zenith. In the points C and D, 

 which are as distant as the centre of the earth, # = 0; therefore 

 the full attraction of the earth corresponds to the weight of the 

 water and air in these points. In the other hemisphere, turned 

 away from the moon, k is a negative quantity, because the centre 

 of the earth is more powerfully attracted than any point of the 

 surface of this hemisphere. But k acts in the same direction 

 with gravitation, and must therefore be added to it in order to 

 determine the weight of a particle in this hemisphere. The 

 point E, most remote from the moon, is the most feebly attracted ; 

 hence in E also the quantity to be added to gravitation is the 

 least, and the weight of a particle in E lighter than in any of the 

 other points of the hemisphere which is turned away from the 

 moon. In the point F, for example, the weight of a particle 

 might be expressed hy g — k 3 . cos OFL ; and it would constantly 

 diminish the more we approached the point E, which has the 

 sun or the moon in the nadir, where its expression would be 

 g—k 4 . When the sun is in question, k 4 is only slightly less 

 than k l ; but the difference is not insignificant when the attrac- 

 tion of the moon is taken into consideration ; the difference be- 

 tween the attraction of the point which has the moon in the 

 zenith and that of the centre of the earth is 1J the difference 

 between the attractions of the centre and the point which has 

 the moon in the nadir. Briefly, in each of the two hemispheres 

 (one turned to the sun or moon, and the other turned from it) 

 the minimum of the' weight is found in the point of the surface 

 which has the sun or moon in the zenith or nadir, but the maxi- 

 mum on the line D M C N, which divides the two hemispheres. 

 The pressure of the greater weight must cause a portion of the 

 water and air to flow into the region where water and air are 

 lighter ; and hence a raising of the level will take place there, 

 corresponding to the less weight, while in the region of the 

 greatest weight the level will sink. Consequently both the sea 

 and the atmosphere must endeavour to take the form of an ellip- 

 soid the summits of which are on the line which passes through 

 the centre of the earth and the moon. By the action of the sun, 

 as by the moon's attraction, an ellipsoid somewhat less elongated 

 will be formed in the sea and the atmosphere, its major axis 

 being on the line which passes through the centre of the earth 

 and the sun. In reality the actions of these two attractions 

 will be combined and form only one tidal ellipsoid, which is most 

 elongated when the actions of the sun and moon coincide — that 

 is, at the times of full and new moon. On the contrary, the 



