the Displacement of Shore-lines. 493 



2. If we omit the portion between 7' and 8' of Leverrier's 

 cui"ve, Leverrier's and Stockwell's curves are in all essential 

 points identical also as regards the older part, although the 

 agreement is not so complete as for the last million of years. 

 The reason of this is that the calculations are less certain with 

 regard to the older periods ; when the number of years enters 

 as a factor in the formula, small errors in the values adopted 

 for the planets' masses will be enlarged in proportion to the 

 time, and the result becomes less certain. 



'6. A very remarkable consequence proceeds from these cal- 

 culations. The ciirve repeats itself aft ei' the lapse o/ 1,450,000 

 years, when it is calculated according to StockwelPs formulae. 

 In the period of 4^ million years for which McFarland has 

 calculated it, it repeats itself in this way with remarkable re- 

 gularity a little more than three times. In each of these cycles 

 there are 16 arcs of the curve. Thus the arcs which in the 

 accompanying plate (PL X.) are indicated by 1—16 correspond 

 with l'-16' and l'''-16'^ From calculations which he made 

 at my request, Mr. Geelmuyden has declared that the course 

 of the curve will probably be sufficiently correct to be adopted 

 with safety as the foundation lor geological considerations, and 

 that uncertainties in the curve caused by errors in the masses 

 employed by Stockwell will probably not be of any importance. 



4. The mean value of the eccentricity is least at the limits 

 of two cycles ; it rises in the first and sinks in the last half of 

 each cycle, and therefore attains its greatest value about the 

 middle of each cycle. Thus for the first and second of the 

 calculated cycles and their subdivisions it is as follows : — 



Cycle I. H-3,250,000— 2,720,000 years, 0-0304. 

 H-2,720,000— 2,150,000 years, 0-0332. 

 -f-2,150,000— 1,810,000 years, 0-0203. 

 Cycle II. H-1,81 0,000—1,250,000 years, 0-0247. 

 -hi, 250,000— 700,000 years, 0-0340. 

 ^ 700,000— 350,000 years, 0-0280. 

 Cycle III. ^ 350,000 to the present time, 0-0291. 

 Now as, according to our hypothesis, the sea-level under 

 high latitudes will rise and fall with the eccentricity, then it 

 must not only rise and fall once for each arc of the curve, but 

 the " mean sea-level " for longer periods must also rise and 

 fall with the mean value of the eccentricity, and such cycles 

 as cycles I. and II. must then correspond to two cycles in the 

 geological sequence of deposits. The limits between the 

 cycles of the curve must correspond to the periods of denu- 

 dation which divide the geological cycles, and the middle 

 must correspond to the periods of overflow. 



Phil. Mag. S. 5. Vol. 27. No. 169. June 1889. 2 L 



