1889.] THE DISPLACEMENT OF BEACH-LINES. 41 



calculation extends 3,250,000 years backwards, and 1,250,000 

 years forward from now. He has made his calculations with 

 shorter time-intervals than Croll (Croll 50,000 years intervals, 

 Mc. Farland 10,000 years) but the difference in the intervals 

 does not exert any particular influence in altering the form of 

 the curve. Mc. Farland has, in the same place, calculated the 

 curve, for the same period, by the more modern formulas of 

 Stod-tcell. The two curves show, upon the whole, a similar line 

 through the whole length of their course, yet, as regards the 

 first half, Leverrier's curve falls somewhat farther back. Stock- 

 well's formulas are considered to be more accurate than Le- 

 verrier's. 



Both curves have been published by Mc. Farland. If we 

 compare them with each other we obtain the following results: 



1. The curves, with a single slight variation, coincide from 

 the present day, for 1 million of years backwards. 



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

 curve, Leverrier's and Stockwell's curves coincide in all essential 

 respects, also for the still more remote period, although the 

 coincidence is not so perfect as it is in the last million of years. 

 This is clue to the fact that the formulas give less accurate 

 results for the more ancient epochs; as the number of years 

 is made use of as a factor in the formula, small errors in the 

 values taken for the masses of the planets will be increased in 

 relation to time, and the result be, consequently, less perfect. 



3. A very striking circumstance appears from those calcu- 

 lations. The curve repeats itself after the expiry of 1,450,000 years 

 when calculated according to Stockwell's formulas. In the period 

 °f 4y 2 million years, for which Mc. Farland has calculated it, 

 it repeats itself in this way, with striking regularity, a little 

 more than 3 times. In each of these cycles there are 16 arcs 

 of the curve. Thus the arcs which, in the accompanying table, 

 I bave denoted 1—16 correspond with V— 16' and 1"— 16". 



Mr. Geelmmjden the Astronomer has, as the result of 

 some calculations which he has made at my request, declared 

 that the general course of the curve is ljkely to be sufficiently 



