644 MISCELLANEOUS PAPERS. 



a fixed axis iu a closed box, if in addition to the conditional equations 

 which are to be fulfilled on the surface of the rod certain others are 

 introduced. In this way Stokes reduced Baily's experiments with the 

 rod-shaped seconds pendulum. In the foregoing case the pendulum- 

 rod was hollow, into which the air could enter unrestricted. This con- 

 dition complicated the problem ; however only a few changes in the 

 construction of the pendulum would be necessary iu order to render 

 Stokes's theory applicable. 



May the apparatus whose application to a special case is here shown, 

 prove itself useful in physical investigations iu other realms. 



In *' Publicationen des Astrophysikalischen Observatoriums," vol. 

 VI (the preceding part of this abstract), I have given a series of obser- 

 vations which I prosecuted with a peculiarly constructed i)endulum for 

 the purpose of determining the mean density of the earth. The dis- 

 cussion of these observations led to satisfactory results, but the exper- 

 iments justified the expectation that a greater accuracy might be 

 reached by an elimination of certain obstacles, partly of an accidental 

 nature, and especially by a more thorough protection against the intiu- 

 euce of temperature change. The results of the observations made 

 after the application of the contemplated improvements gratifle<l the 

 anticipations, since the probable error in the latter set of experiments 

 is only one-third of that obtained by the former. The axes of the cy- 

 linders, which were directed towards the center of the balls attached 

 to the pendulum, during the first experiments made an angle with the 

 plane of oscillation in order to secure a sufficient proximity of the balls 

 to the attracting masses. This state of affairs complicated the numeri- 

 cal computation of the situation of the pendulum with respect to the 

 masses, since besides the measurement of the separation of their sur- 

 faces from the middle point of the apparatus it was necessary to accu- 

 rately ascertain the difference of direction which the axes of the masses 

 made with the plane of oscillation. The supports were so changed that 

 the axes could be brought precisely into the plane of the pendulum. 

 This simplification made it possible to secure such a position as to allow 

 a more ready and accurate measurement of the distance of the masses 

 from the apparatus, and at the same time it served to keep it in that 

 position. On both sides of the pillar which supported the instrument 

 places were attached for the support of a contact lever rotating about 

 a vertical axis. One arm of this lever, terminating in a shari) point, 

 rested against the back of the attracting mass, while the otlier arm 

 swept over a short scale divided into millimeters, provided with a reg- 

 istering apparatus so that its position could be readily ascertained. 

 Since the lengths of the arms were as 1: 4, a change in the situation of 

 the cylinder could be estimated to a tenth of a millimeter without dif- 

 ficulty. In case of a contrary movement of the mass, the i)in of the 

 lever would keep, in contact with it through action of a pressure weight 



