December 10, 1915] 



SCIENCE 



831 



since been pleasantly devoted to a study of the 

 tides and other kindred problems. 



In my investigation of tbe tidal problems 

 I have based my work on the two following 

 postulates; namely: 



FmsT : If a solid body of any figure what- 

 ever he covered hy a fluid in equilibrium, the 

 gravity at every point of the surface will be 

 the same; and 



Secoat): If the fluid covering a solid body 

 be free to flow, and the gravity at different 

 points of its surface be disturbed in any man- 

 ner whatever, the fluid will flow from points 

 where gravity is less to points where gravity is 

 greater; and it will continue to flow until the 

 gravity at all points of the surface becomes 

 equal. 



If these postulates in regard to the equilib- 

 rium of fluids be correct the problem of the 

 tides becomes greatly simplified, and instead of 

 being the most difficult, it becomes the simplest 

 problem of celestial mechanics. For it is a 

 very simple problem to calculate just how 

 much the earth's gravity at any point of its 

 surface is affected by the attraction of the 

 sun and moon. ISTow when the sun or moon 

 is overhead we know the gravity at the earth's 

 siu'face directly underneath them is lessened, 

 and we also know that the gravity at all points 

 where the sun or moon is in the horizon is in- 

 creased by their attraction. It therefore fol- 

 lows from the second postulate that the water 

 directly under the sun or moon will flow away 

 towards the horizon in every direction ; and in- 

 stead of being heaped up under the moon as 

 claimed by INewton and his successors, will be 

 dispersed along a great circle of the earth 

 whose pole is directly under the sun or moon, 

 thus making a thin ribbon or narrow zone of 

 high water of uniform depth and extending 

 completely around the earth, instead of being 

 piled up in the form of protuberance under the 

 moon. 



It also follows that there will be a zone of 

 low water directly under the moon instead of a 

 protuberance of high water as claimed by 

 Newton. 



J^ow since there are two disturbing bodies, 

 the sun and the moon, acting independently of 



each other, it is evident that there wiU be two 

 independent high-water waves passing com- 

 pletely around a great circle of the earth; and 

 since all great circles intersect or cross each 

 other at opposite extremities of a diameter, it 

 follows that there wiU. always be two points of 

 intersection, or two places of high water, which 

 may be observed at all times, provided we 

 know where to look for them. It also follows 

 that high tides are not restricted to the times 

 of new and full moon, but exist at all times. 



The problem of the tides is therefore greatly 

 simplified and reduced to one of finding where 

 the high-water waves produced by the attrac- 

 tion of the sun and moon cross each other, for 

 at these points the single wave is equal to the 

 sum of the two separate waves; and the com.- 

 putation of the places where the tidal waves 

 cross each other is very easy and much 

 simpler than the computation of an eclipse. 



The plane of the solar tidal wave is always 

 perpendicular to the ecliptic, and passes 

 through the center of the earth and poles of 

 the ecliptic; and its position is known at all 

 times. The plane of the lunar tidal wave is 

 always perpendicular to the plane of the moon's 

 orbit ; but as the moon's orbit is inclined to the 

 ecliptic by about 5°, it follows that the poles of 

 the moon's orbit are always at a distance of 5° 

 from the poles of the ecliptic. But the inclina- 

 tion of the moon's orbit to the ecliptic is always 

 the same, while the nodes of the orbit on the 

 ecliptic are in motion, and perform a complete 

 revolution in about nineteen years. It follows 

 from this that the poles of the moon's orbit 

 move in a small circle of 5° radius around the 

 poles of the ecliptic, making a revolution in 

 nineteen years. The position of the lunar 

 tidal wave thus becomes known at all times; 

 and since the position of the solar tidal wave 

 is also known at the same time, it becomes an 

 easy matter to calculate the place of their in- 

 tersection, which is the place of high tide. 



'Now since the moon's nodes are moving 

 backward on the ecliptic 1°.5649 during each 

 lunation, it follows that the tides of no two 

 consecutive lunations will be precisely the 

 same; but they may be more easily calculated 

 than most other celestial phenomena. 



