NEWTON S PRINCIPIA. 293 



while by their vis insita. The luminaries continue to act 

 with great power for a little while after the moment of 

 their greatest strength, and thus continue to raise the tides. 

 But Laplace remarks (Mec. Cel. xiii., chap. 1.) that &quot;vrai- 

 semblable &quot; as this is, it is nevertheless erroneous, for an 

 accurate investigation shows that, notwithstanding this 

 continued action of the luminaries, the greatest full tides 

 should occur exactly at the syzygies and the least exactly 

 at the quadratures, and that therefore the explanation of 

 the delay must be sought for in the accessory circumstances. 

 It is, in fact, due to friction. 



Newton then proceeds to make several &quot; corrections&quot; to 

 this result which he conceives to be necessary. He 

 observes that the luminaries are not in the positions of 

 greatest efficiency at the moments of the greatest high 

 tide at the place under consideration ; that therefore it 

 is not the whole force of these luminaries that is employed 

 to raise the tide, but this force multiplied by the cosines 

 of certain angles. He corrects, therefore, for the instan 

 taneous angular positions of the luminaries at the moment 

 of the greatest tide. He also remarks that changes in the 

 distance of the moon are produced by the inequality in 

 her motion called the &quot; Variation,&quot; and he adds, therefore, 

 another correction for the distance of the luminary at the 

 moment of the greatest tide. But Laplace points out that 

 this correction also is wrong. In fact it contradicts the 

 previous reasoning, for if the tide be due to the accumu 

 lated action of the luminaries during a certain instant, we 

 must not consider it as proportional to the force at the end 

 of that interval. But when all corrections are applied, 

 he finds that the sun s force raises the tides by 1 foot II ^ 

 inches, and the moon s force will therefore raise the same 

 to the height 8 feet 7^ inches, and the joint action of 

 the two to the height 10J feet, and when the moon is 



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