Mr. E. L. Garbett on Popular Difficulties in Tide Theory. 175 



be trifling compared to the earth's rotation. Now let the earth 

 and waters rotate together eastward, as they do, with a speed im- 

 mensely exceeding these waterflows, and it is seen they must act 

 as accelerations in the quadrants coming to the moon's meridian, 

 and retardations in those leaving it. The separation and crowd- 

 ing of the arrows in the third earth-figure may, therefore, express 

 the water's rotary speed, exceeding the earth's in the nearest and 

 furthest quadrants, and falling short of it in those of moonrise 

 and moonset ; whence the new places of high and low water, 

 just contrary to those in the equilibriated earth, become plain. 

 For a child must see that, as in pouring out treacle the down- 

 ward acceleration makes the stream grow thinner, and in an up- 

 ward jet retardation makes it thicker, so here the sea, wherever 

 its rotation is being accelerated, must grow shallower (that is, 

 the tide be falling), and the contrary where its rotation is being 

 retarded. 



But if, fortified by the names of Laplace, Airy, and Abbott, 

 we grant this result to be correct, will it not follow that, seeing 

 an equilibriated earth would have (though no tides, and indeed 

 no moonrise or moonset) yet a permanent high water under the 

 moon, while the earth with her actual rotation tends (friction 

 apart) to have low water permanently under the moon, there 

 must be an intermediate state, a rate of rotation quicker than 

 monthly but slower than daily, that would cause no lunar high 

 or low water at all, and consequently no tidal currents nor fric- 

 tion ? And if so, of course there is also, substituting " sun " for 

 " moon," a rate of rotation (it may be greater or equal or less 

 than the above) which, though producing regular sunrise and 

 sunset, would have no solar tides. And is not the former rate, 

 or a mean between these two (which cannot very widely differ), 

 the final and permanent rate of rotation to which tidal friction is 

 tending to reduce, and must ultimately reduce, our globe ? If so 

 the length of day and night, which has passed its minimum (as 

 Mayer said) and is now on the increase 2 , must lengthen, at a rate 

 increasing to a maximum and then diminishing, till it perma- 

 nently settles to a duration calculably (but not greatly) shorter 

 than a month. And though this will give no tides, I conclude 

 that a slower rotation would produce tides^ and of such a kind that 

 their friction would accelerate instead of retarding the earth, and 

 give her that same final speed. 



It appears that, without supposing the remark to be in anywise 

 new, I happened in 1853 to make the first English mention that 

 tidal friction must increase the length of the day (in the article 

 " Steam-engine" of ' Tomlmson's Cyclopaedia of Useful Arts and 

 Manufactures '), and to suggest (what Delaunay is now consi- 

 2 Phil. Mag. June 1863, p. 42?. 



