ON THE MOVEMENTS OF THE EARTn's CRUST. 351 



for a period of four millions of years ; tliree millions of years backward 

 and one million forward from the present time. The curve is also cal- 

 culated according to the same formula' by McFarland {Amer. Journ. Sci., 

 1880, [3], vol. XX, pp. 105-111). His calculation extends from ;i,2r)0,000 

 years backward, to 1,250,000 years forward in time.* He has calculated 

 with shorter intervals of time than CroU (Croll 50,000, McFarland 10,000 

 years), which however has had no particular influence in altering- the 

 form of the curves. McFarland has in the same place calculated the 

 curve for the same period of time from new formuhe of Stockwell's. 

 The two curves, taken in the gross, show a uniform course throughout 

 their length, but as regards the tirst half Leverrier's curve its thrown 

 somewhat backward. Stockwell's formulae are considered to be more 

 accurate than Leverrier's. 



Both curves are given by McFarland. If we compare them together 

 it appears — 



(1) The curv^es coincide with only a small essential difference from 

 the present day until one million years back. 



(2) If we omit the portion between 7' and 8' of Leverrier's curve, 

 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 calcula- 

 tions 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. 



(3) A very remarkable consequence proceeds from these calculations. 

 The curve repeats itself after the lapse of 1,450,000 years, when it is cal- 

 culated according to Stockwell's formuljB. In the period of 4,500,000 

 years for which McFarland has calculated it, it repeats itself in this 

 way with remarkable regularity 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 are indicated by 1 to 16 correspond with 1' 

 to 16' and 1" to ] 6". Mr. Geelmuyden, from calculations which he made 

 at my request, has declared that the course of the curve will probably 

 be sufficiently correct to be adopted with safety as the foundation for 

 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 (;ycle. 



* [On the scale sliown in the accompanying diagraiu, the interval of 2,000 years 

 would occui)y only ,/,n of an inch on the base line. The epoch of the table (IBfjO)— 

 marked "0" iu the third line of curves (cycle iii, just under tlie arc 4") — may there- 

 fore as well be assumed to be the present year. J 



