230 Wisconsin Academy of Sciences, Arts, and Letters. 



We have seen how the moon assumes various positions from 

 south to north of the equator in each revolution about the earth, 

 and we will find that the oceans are differently affected during 

 inferior from superior transits. For we will first suppose the moon 

 in the plane of the equator which occurs at new and full moon in 

 the equinox and in the quadratures at solstices. It is evident that 

 the moon holds the same relative position to the sea under her 

 as the lower transit does to the sea on the remote side, and the result 

 is the same ; but when we consider the moon in maximum north 

 or south declinations then the conditions are entirely changed ; 

 the lower transit of north declination and upper of south declia- 

 tion affect the sea further south than the upper north and lower 

 south so that the results must be different for each pair. In order 

 to illustrate, several tides of Cape Flattery on the Pacific coast are 

 added to the sketch ; these are sketched according to the reported 

 observations of the U. S. coast survey. i 



The wave A 1 arrives arrives ahead of mean time after transit ; 

 B 1 is behind time ; A 2 is separated one lunar day from A 1, 

 and so on. These are the tides of max, decs. The tides A 1, 

 A 2, etc., were formed by an upper transit with the moon at U, 

 N. dec, or by a lower transit with the moon at L, S. decl., and the 

 ocean at E will be affected alike by either ; but since the line 

 from the moon pierces the ocean north of the equator, the tide 

 will be formed north of the mean origin and will come ahead of 

 mean time. On the other hand, the tides B 1, B 2, etc., are 

 formed by an upper transit with the moon at L, S. decl, or by a 

 lower transit with the moon at U, N. decl., and the ocean at Q 

 will also be affected equally by either ; but since the line from the 

 moon pierces the ocean south of the equator the tide will be 

 formed south of the mean origin and will be behind time. The 

 result is obvious ; the wave B 1 being behind its proper place and 

 the wave A 2 in advance, an overlapping takes place and the 

 tides assume a mixed type. The tide travels by the rising of the 

 water in front and the falling to the rear of the crest, hence 

 the tide A in raising the rear slope of the tide B draws upon the 

 volume and causes a degradation of the latter, the distance be- 

 tween B I and A 2 being greater than the mean interval, the 



