642 MISCELLANEOUS PAPERS. 



with the balls ^,=5.651^0.017 aud without J,, =5.731 ±0.020. As al- 

 ready intimated the discrepancy is to be ascribed to the inaccuracy in 

 the determination of the weight of the pendulum, so, using the formulae 

 already given : 



A=/iA , /}=/},,-{ , from which J=— ^— ^ '-^—^ 



the reduced observations gave 



m,=4.6268± 0.0136 

 w,, = 1.9269 ±0.006 

 from which the mean density z^= 5.594 ±0.032. 



The probable error of the final result might have been reduced by in- 

 creasing the number of observations. Still it seemed better while test- 

 ing this new method not to accumulate too much material or more than 

 was needed to reach a reasonably accurate result. But since the ex- 

 periments here made point to the possibility of a better solution of 

 this problem, it is intended to carry the observations further, and by a 

 new determination of the constants to secure results indeiiendent of 

 their first determination. 



CONCLUSION. 



For the purpose of comparison, the previously-found values for the 

 mean density might properly be given here. 



Maskelyne found from local deflection at Schehallien, 4.713 ; Colonel 

 James, at Arthur's Seat, 5.14; Carlini and Airy received from pendu- 

 lum determinations 4.837 and 6.623, and in more recent times Menden- 

 hall and von Sterneck, 5.77. 



Cavendish (5.48), Reich (5.49, in the revision 5.58), Baily (5.66, after 

 correction by Corn a and Bailie, 5.55), Cornu and Bailie (5.56) used the 

 torsion balance, dually Joily (5.692), Poynting (5.69) utilizing the ordi- 

 nary balance. The result here found is considerably smaller than 

 those found by Jolly's method, aud slightly larger than the values 

 which the torsion balance gave, especially the corrected value of Baily. 

 1 think, however, that the correction here referred to as made by Cornu 

 and Bailie admits of criticism. As in the present case, Baily observed 

 in each position of the weights four stationary points. He also used 

 the time when the balance was stationary at its greatest elongation 

 for changing the weights, so that the last observation of each series 

 might at the same time be the first of the next series. With most of 

 his observations tlie difference between two consecutive elongations on 

 the one side did not agree with the corresponding difference on the other, 

 and furthermore this difference was always greater on the side where the 

 first reading was. Cornu aud Bailie concluded that this lack of symme- 

 try was owing to the presence of a constant error which was not 

 eliminated in the subsequent adjustments. However, it is not equally 

 npparent that the tendency of this error is to increase the final result. 

 According to their belief the irregularity referred to in the diminution 



