524 THE POPULAR SCIENCE MONTHLY 



motion of the earth to cause the waters of the oceans to oscillate like 

 water contained in vessels of various shapes and sizes. 



While not questioning the fact established by Newton that the tides 

 are primarily due to the attraction of the moon and sun. Admiral Fitz 

 Eoy attempts to explain the tides upon the assumption of stationary 

 waves extending in an east-and-west direction across various portions 

 of the several oceans. His wide experience as a navigator had famil- 

 iarized him with the fact that throughout some extended regions of 

 the ocean, the tides occur at nearly one and the same time; also that 

 even for islands remote from the land, the amount of rise and fall is 

 quite various. 



Sir George B. Airy was the first person to make an extensive mathe- 

 matical study of wave motion implied in tidal phenomena. While he 

 does not point out how the ocean tides are produced, he shows that 

 certain dependent bodies of water, and in particular the Irish Sea, must 

 contain stationary waves. He establishes the theoretical result that 

 the tides in a north-and-south canal extending from the equator to 

 either pole must consist of a stationary wave. 



William Ferrel suggests that, because of their unusual size, the tides 

 of the North Atlantic may depend upon stationary waves extending 

 in an east-and-west direction across the ocean ; and, in particular, upon 

 one extending between the coasts of Ireland and those of Newfound- 

 land. 



These, and other writers who have expressed similar views, failed 

 to consider that an imperfectly bounded strip of the sea must have 

 considerable width (as well as a suitable length) in order to make 

 a stationary wave possible. They also failed to make any connection 

 between the known tidal forces and the times of the tide. 



This brings us to the subject proper, which involves an approximate 

 explanation of the dominant ocean tides, it being manifestly unreason- 

 able to expect accurate mathematical solutions of the problems in- 

 volved. 



It should be noted in passing that although Dr. Berghaus pro- 

 pounded no theories concerning the tides, his cotidal chart constructed 

 in 1889 marks a radical departure from those previously constructed, 

 and is in itself highly suggestive. 



The Tide-producing Forces 



The tide-producing forces of moon and sun can be computed from 

 well-established astronomical data, and there are no uncertainties con- 

 nected with their determination, at least to a moderate degree of re- 

 finement. In this place it is necessary to say only a few words de- 

 scriptive of these forces. The tide-producing force of the moon upon 

 a particle of unit mass is the difference between the moon's attraction 

 upon this mass and upon a unit mass situated at the earth's center; or 



