524 



Major J. Herschel. 



wires the position of unstable equilibrium may be placed anywhere 

 from O =9O° to O =18O° ; and the nearer it is to 90°, i.e., the weaker 

 they are, the more sensitive will the instrument be at the position 

 0=90°. This suggests, I think, that the double wires should be 

 coarse and inelastic rather than the reverse. 



The ratio r : R is as nearly as I can judge by measurement 1 : 138, 



and (P+p) would be, at the equator, 3,725 grs. ; so that (P + p)_L = 



27 grs. very nearly. Now, 



2 r 1 



1-- . fl 



3 Pl 

 l + |.g + ...) gr , 



This is the force, exerted at a distance r='09 inch, which is requisite 

 to turn the single wire, of length 3 inches, through the angle sr, If 



^ betaken as above, equal to -, pi^=l^ grs., at '09 inch; and 

 Pi 9 

 /> 2 7r=2-f grs. nearly. 



We can now form some estimate of the effect of a small change of 



R 



weight. "We have seen that = 2/> 2 . — . BO. Substituting numerical 

 values, as above, we find <$p=138 x 4-f- x -^=591— nearly. 



7T 7T 



The collimator contains a scale, exactly Jth of an inch long, divided 

 into 30 parts. The focal distance being 8*5 inches, the angular value 

 of the scale is tan or 1° 41' ; and of each part, 3' 22 or 3-2V0 *" 

 approximately. Putting one of these parts equal to 2S0 (doubling on 

 account of the reflection) we find Sp=e^W=*092 gr., the change of 

 weight which will deflect the mirrors relatively one division. It follows 

 that the 30 divisions of the scale correspond to a change of weight of 

 about 2 '76 grs. 



But we must remember that this relation depends on an assumption, 

 viz., that px : p% : : 9 : 1. To provide for a more accurate estimate being 



hereafter obtainable, let ?f?=k. Then ~T' P^~T~~~T' § ?= 



3/9j 1 — k 1 — k 



7452 ^ — ; and in the case of the scale-division gp=l'16 - ^ grs., 

 1 — k 7r L — k 



or very nearly 35- — - for the whole scale. 



Let us now consider what may be expected as the actual conse- 

 quence of a change of gravity. The most practical evidence of this is 

 the effect on the rate of a pendulum. A pendulum which would beat 

 seconds at the equator would gain 225 seconds, or beats rather, at the 



