OF ARTS AND SCIENCES : JANUARY 9, 1871. 305 



cases ; in each instance of this kind a separate physical description 

 will be indispensable, as the local circumstances are sometimes very 

 different. Tbe most simple case for the investigation of the laws of 

 tidal currents is afforded by observations made on shoals at a great dis- 

 tance from the coast. Thus observations on the shoals of the German 

 oceans, of the Sooloo Sea, and others, do not show the existence of any 

 noticeable rise of level. Let us suppose a shoal in the middle of the 

 ocean, the depth of the ocean to be 20,000 feet, and 20 feet on the 

 shoal, then the velocity of waters on the shoal could not exceed the 

 rate of the ocean motion more than one thousand times. In any case, 

 the velocity of the current on this shoal will not be great, as the ocean 

 motion is too slow ; besides, the velocity of tidal currents increases 

 gradually from nothing, and if the shoal is of small superficial dimen- 

 sions, then the resistance to the progress of tidal motion will be insig- 

 nificant, and observations will not show any rise of level. I will here 

 add an explanation why tides are not strong at the islands of the open 

 ocean, but attain great dimensions in bays and narrows along the coast 

 of the continent. In the former case, the lesser mass of the ocean 

 waters helps to communicate a progressive motion to the particles of 

 water ; whereas, in the latter case, all the mass of the ocean presses on 

 the coast of the continent, and the running waters being reflected from 

 the promontories and straight shore convey their vis viva to the waters 

 of the bays and narrows which indent the shore of the continent. 



I subjoin the following remarks to the conclusions made by me in 

 the first note : — 



1. The Astronomer- Royal, Mr. Airy, in his works on the tides, more 

 than once points to the inadequacy of all the theories of the tides (see 

 e. g. Airy, "Tides and Waves," Section II., No. 14) ; thus in the first 

 conclusion I explain the results given by Mr. Airy. 



2. The time and the magnitude of the greatest velocity of tidal 

 currents are opposed by me to the generally admitted rule of investi- 

 gating the laws of times and heights of high water. According to the 

 theory of tidal motion, the velocity of the current may be given by the 

 function of the disturbing forces, whereas the rise of level will be a 

 very complex function of currents, which only can be expressed by an 

 empirical formula, because many of the local circumstances cannot be 

 analytically stated. 



3. The law of the revolving direction of tidal currents (from E. 

 round by N. in north lat. and from E. round by S. in south lat.) is 



VOL. VIII. 39 



