of the Pendulum made by Capt. Kater, M. Biot, 6fc. 13 



with great precision. The radius of the equator, though not 

 perfectly exact, may be depended upon as being known to 

 within a few hundred feet of the truth. By making use of 

 those of the best authority we arrived at formula (9), page 164, 



_j 2091957 6 y. , 



or, ^"2^20919576-1-1856062635 3 «* ^' 



in which z, the length of the seconds pendulum at the equator, 

 and y, the excess of the seconds pendulum at the pole above 

 that at the equator, are the only unknown quantities. 



As the equator is accessible in many points, we may shortly 

 expect to have z well determined ; though it will not be easy, 

 perhaps impossible, ever to obtain y by actual experiment. 



We have used this care in detailing the manner in which 

 we obtained the general formula, and selected the values of the 

 quantities employed, that it might be apparent what confi- 

 dence results derived from it deserved. This was the more ne- 

 cessary, as we have shown, page 169, that the ellipticity derived 

 from the measurement of arcs, and that determined from the 

 observations by the pendulum, were in mean latitudes, as well 

 as extreme latitudes, though in a less degree, directly opposed 

 to each other, upon the assumption that the arc of the meri- 

 dian is a portion of a regular ellipse*. 



As we discussed the experiments of Kater, Biot, &c., sepa- 

 rately in our last communication, we have, in order to throw 

 some light, if possible, upon this anomaly, here combined 

 them along with others which we have since obtained, making 

 as nearly as possible a regular series of them from the equator 

 towards the north pole, retaining one only, that at Rio Janeiro, 

 in the southern hemisphere, as being near the equator, and 

 haviii"- without it, proportionally to the others, rather too few 

 near that circle. 



Pursuing the same method as formerly, we obtain 



1. 39-01951— 2 — 0-0000884 j/ = <?i 



2. 39-02339— -—0-0511335^=^.^ 



3. 39-04115— s-0-1347996j/ = .?3 



4. 39-04602_2:_0-1517026j/=^4 



5. 39-09419— s- 0-39034 17.?/ = <?i 



6. 39-11319— j;_ 0-49323 70 .?/ = «'« 



7. 39-11300 — c— 0-49721 72 j/=6't 



8. 39-11809— z-0-5136117i/=^8 



9. 39-1 2928 -c-0-5667720.y=<rB 

 10. 39-13770- = r-0-6045723y = «',o 

 1 1. 39-13929-2-0-6127966 j/=f,, 



' At page IfiO, line 2ij, of my last conitnunictition, between -j.|^ and 

 iwl, the worils " gur* an cUii'tidli/ " should have been inserted. 



12. 



