MOON'S DECLINATION CONSIDERED. 19 



The second term, which is the variable part, represents 

 the tide-producing part of the force. This is positive as 

 long as the hour angle from the moon is less than 45 on 

 either side ; and in that case from the equator to lat. 45 

 this is an elevating force, being greater as the particles are 

 further from the equator : from 45 to the poles it is 

 depressing. In the remaining quadrants this term is 

 negative. Hence, by 5 and 4, the elevation at the 

 equator (and up to lat. 45) will be greatest (i.e. it will be 

 high water), 90 from the moon. Beyond lat. 45 the 

 depression will be greatest under the same circumstances. 

 In these latitudes, therefore, the effect of the former com- 

 ponent would be partially counteracted. It is easy, 

 however, to see that the variation in the meridional force 

 (and it is only the variation that affects the tide) is in any 

 latitude less than that in the force parallel to the equator 

 in the proportion of sin lat. : 1 ; for the latter varies from 

 H cos lat. to - H cos lat. and the former from H sin lat. 

 cos lat. to - H sin lat. cos lat. Hence while the height of 

 the tide would be lessened, the place of high water would 

 be as before. The actual magnitude of the tide may be 

 ascertained as follows : 



TT 



The force being - - sin 2\ cos 2tn (\ being lat., and m 



6 



hour angle). 



In order to apply the same method of summing as in 

 fig. 5, we write this 



- ^sin 2 A sin 2(45 - w). 



02 



