188 On the Apsidal Motion of a freely suspended Pendulum. 



As the last two terms of this expression are periodic, it is evident 

 that the progression of the apse during one complete vibration 

 of the pendulum is equal to 



2^'-; (13.) 



and that for any other period it is equal to 



3 area described by central radius vector 



4 (length of pendulum)^ 



(13.) 



Let N be the number of degrees described in one hour, then 



N = 



135 X 1800 



sT^ 



ah 



(14.) 



In this equation, g, /, a, b arc supposed to be expressed in feet. 

 The length of the pendulum used in our experiments was 35*4 

 feet; consequently, assuming gravity to be 32*19 feet, equation 

 (14.) will become for the pendulum used by us 



N = 58-86x«6; (15.) 



At the commencement of the experiments, « = 24 inches, ^= ; 

 at the end of first hour, « = 13 inches, ^ = *134 inch. 



The above figures are taken from ten experiments. Taking 

 the means of the semiaxes at the beginning and end of the hour, 

 and converting them into feet, we obtain fl6 = *009 square feet. 

 Hence 



N=0°-53. (16.) 



The progi*ession of the apse is consequently a little more than 

 half a degree in the first hour, and of course in the succeeding 

 hours should be considerably less in consequence of the small 

 value of the -product ab. 



The obseiTcd deviation from 12° per hour (due to the rotation 

 of the earth, at the latitude of Dublin,) in the ten experiments is 

 contained in the following table : — 



A comparison of the foregoing table with (16.) shows, that 

 although apsidal motion, of the kind here considered, accounts 



