298 EEPOET— 1893. 



even in the latest attempts there is still some slight discrepancy between 

 the positions of the image after successive to-and-fro movements of tbe 

 lever.' 



If the bottom of the lever be moved to the left, it is evident that the 

 screw advances and that the frame is tilted to the east. When this is 

 done the movement of the image is at first rapid, but in two or three 

 minutes becomes nearly insensible, and after five minutes no displace- 

 ment of the image can be perceived. In all the later and more satis- 

 factory trials the lever was moved every ten minutes, and in the intervals 

 the gas was turned down. It should be added that in the evenings when 

 these experiments were made the pendulum always indicates a movement 

 to the west. 



The range of motion of the bottom of the lever was regulated so as to 

 give a tilt of two seconds to the frame, and the corresponding lengths of 

 the scale in inches, as determined on May 24, were as follows : — 



+ 7-02 -6-65 +7-20 -6-95 +6-66 -6-96 

 -f6-90 -6-85 -I-6-83 -6-97 +6-94 -6-65 



A plus sign indicates a tilt to the west, and a minus sign a tilt to the 

 east. Thus the average of six tilts of two seconds to the west gives 

 6*92 ±'05 inches as the corresponding scale- value, and the average of six 

 similar tilts to the east gives 6-84±-04 inches. The difference between 

 these two values may no doubt be in part attributed to the westerly 

 tilting of the instrument. If, however, the mean of the scale-values of 

 successive pairs of tilts be taken, the effect of this westerly tilting will 

 be eliminated, if it may be supposed to be uniform throughout the 

 twenty minutes allowed for the to-and-fro movements of the lever and 

 for the subsequent readings. The average of these six means is 6-88±'03 

 inches. This value is probably the most accurate of the series, and a 

 tilt of one second will therefore be taken to correspond to 3 "44 inches of 

 the scale. 



The distance of the gas-jet from the pendulum being 10 feet, the 

 angle through which the mirror turns for an east or west tilt of one 



second is therefore ^ tan~^ _ -^ , or 49 minutes. 



Siuce the two parts of the silver wire which support the mirror 

 always lie in the vertical plane through their points of support, the angle 

 through which the mirror turns for a given east or west tilt is inde- 

 pendent of the distance between the mirror-hooks ; it depends only on 

 the horizontal and vertical distances between the two points of support 

 of the silver wire. If c be this horizontal distance, and d the angle 

 through which the mirror turns for an east or west tilt of one second, it 

 is evident that cd is constant. If x be the decrease in the value of c, due 

 to a given southerly tilt of the frame, and ? the corresponding increase in 

 the value of 0, then c=^xQjc. Hence, if the frame be tilted through one 

 second in a north and south line, the change in the value of is d^, and 

 the corresponding change in the scale- value above given is therefore ^^ih 

 of that value. It follows that, in order to make the error small, 6 should 

 be small ; that is, the scale should be a long way from the pendulum. 

 The original instrument used in the Cavendish Laboratory expei'iments 

 was free from this error. It would be possible to replace one of the fine 



' It is hoped that this discrepancy will disappear with another arrangement of 

 the lever which Mr. Darwin has designed. 



