68 RECORD AND RESULTS OF 



bers of the remaining positions, we have to combine the mean of faces 1 and 3, or 

 86420.76 with face 2, or 86421.08, we find 86420.92, and adding the correction for 

 elevation we have the proportion g : (7i^(86421.14)^ : (86550.72)1 



Bearing of Preceding PLndulum Experiments on the Value for tlie Earths Com- 

 pression. — If there was no local disturbance in the force of gravity arising from 

 irregular distribution and various densities of masses in the vicinity of the station, 

 the observed number of vibrations at any two stations remote in latitude would 

 suffice to deduce the earth's compression, and in proportion as we increase the 

 nmnber of pendulum stations the deduced valiie for the compression will gain in 

 reliability, it being improbable that the local disturbances shoiild all tend the same 

 way. From two stations only we can obtain but a first approximation, thus from 

 our observations 



let Ni :=r^ observed number of vibrations in a mean solar day in latitude ^^ 

 iV"„= " » " " " " ^-u 



N = number of vibrations in the same interval at the equator 

 n = a function ot the earth's ellipticity 

 then the relation iVo^ = iV^ (1 + m sin ^<po) furnishes the two equations 

 (86421.14)2 = N'- (1 +n sin^ 42° 22' 51".5) 

 (86550.72)^= i^^' (1 +Msm" 78 17 39 ) 

 and solving these, we find for the Hayes pendulum iV= 86304.26 and w= 0.005965. 

 We have further by Clairaut's theorem 



5 1 a — b 1 1 



— c whence c = hence c = — — - 



2x289 h 372 



a value very much smaller than that arising from the assemblage of the best pendu- 

 lum results (2-1-5°, Baily in Vol. VII, Mem. Roy. Ast. Soc), but if combined with 

 them would tend to diminish the value of c, and bring it nearer to that found from 

 the geodetic measures (2^3^ Lt. Col. James, Account of the Ordnance Trigonome- 

 trical Survey of Great Britain and Ireland, London, 1858). Values as small as 

 that found above have, however, been observed before, see " an account of experi- 

 ments for determining the variation in the length of the seconds pendulum at the 

 principal stations of the trigonometrical survey of Great Britain. By Cap. H. 

 Kater." Phil. Trans. Roy. Soc, 1819, Part 3, p. 423 ; also " Figure of the Earth," 

 by G. B. Airy, Ast. Roy., Encyclopfedia Metropolitana, 1830, p. 230. According to 

 Baily's formula F= (7441625711 +.38286335 sin" L^we should have nearly 112 

 vibrations more at Port Foulke than at Cambridge, whereas by direct observation 

 we have 131 nearly.^ 



Respecting the horizontality of the siipporting plates of the Flayes' pendulum, 

 the record at either station makes no mention, but as a deviation can easily be 

 detected, I do not apprehend any source of error on this account. A special 



* The maximum increase in the number of vibrations (in a clay) of the seconds pendulum is about 

 half the number of seconds in the maximum defiectiou of tiic plumbline (Cg,pt, Clarke in Lt. Col. 

 James' Ordnance Survey, pp. 590 and 594). 



