of the Pendulum made by Capt. Kater, iVf. Biot, Sfc. IB 



Substituting the proper values for sin^ A, we obtain the 

 length of pendulum by computation to be compared with that 

 from experiment. 



Places. Latitude. 



Galapagos 



Madras 



San Bias 



Rio .Janeiro 



Fornientera 



Figeac 



Bordeaux 



Clermont 



Paris 



Dunkirk 



London 



Arbnry-Hill 



Clifton 



Leith 



Portsoy 



L^nst 



Hare Isle 



Melville Isle 



Length of PenduUnnj 

 by Expe- by (^alcu- 



riment. 



32 

 13 4 



21 32 



22 55 

 38 39 

 44 36 



44 50 



45 46 

 48 50 

 51 2 

 !51 31 

 !52 12 

 53 27 

 55 58 

 57 40 

 60 2(> 

 70 2(i 

 74 47 



19N. 

 9 



24 

 22S. 

 56N. 

 45 

 26 

 48 

 14 

 10 

 8 

 55 

 45 

 39 



59 I 

 27 

 17 

 12 



lation. 



A, 



01951 39 

 02339 39 

 04]]5|39 

 04602'39 

 09419'39 

 113]9i39' 



11300 

 11809 

 12928 

 13770 

 13929 39- 

 1 425039- 

 14600;39- 

 15549 39- 

 16159 39- 

 17162 39- 

 19840 3!)- 

 20700 39-: 



•011672 

 •022344! 

 •0;;9836| 

 •043370; 

 •093262' 

 •114774' 

 115606 

 119034J 

 130148 

 13805l! 

 139770! 

 142238' 

 146620 

 155271 

 160970 

 170830 

 197284! 

 2063251 



-0-007838,?, 

 -0-001046^2 

 -0-001314^3 



- 0-002650 c, 

 -0-000928^5 



' + 0-001584^6 

 + 0-002606 (?T 

 -1-0-000944 eg 

 + 0-000868 e 3 

 + 0-000351 e\o 

 + 0-000480 e-„ 



- 0-000262 e,o 

 + 0-000620^1 

 -0-000219 eHJ 



- 0-000620 eii 

 -0-000790 e, J 

 -0-001116e,- 



- 0-000675 e J 



+ 0-006792 

 - 0-000268 

 -0-001336 

 + 0-001722 

 + 0-002512 

 + 0-001022 

 -0-001662 

 -0-000076 

 -0-000317 

 + 0-000129 

 0-000742 

 + 0-000882 

 -0000839 

 -0-000401 

 -0-0001701 

 !- 0-000326 i 

 + 0-000441 i 



The numbers in column A , are the differences between the 

 results from experiment and calculation by the formula, the 

 sign — shoAving that the calculated lengths are less than those 

 by experiment, and + that they are greater. The mmibers 

 in column Aj are obtained by subtracting those in A suc- 

 cessively from each other, retaining the algebraic sians. 



On duly considering the (juantities in A,, it appears that 

 the first five aie negative ; the next eight, with the exception 

 of that at Arbury-Hill, arc positive; and again, the last five 

 are negative. 



With the regularity of these signs I was forcibly struck ; 

 and after a little reflection sti'ongly sivspected that it was 

 owing to some peculiarity in the form of the earth, more 

 especially as these api)arently show some connexion with 

 what I formerly observed with regard to the ellipticity derived 

 from the measurement of arcs in the corresponding latitudes. 

 — If the figure of the earth is not that of a regular ellipsoid, 

 what modification must it receive in order to satisfy these 

 conditions ? 



It is evident, .since tlic length of the pendulum by experi- 

 ment exceeds that derived from comjjutalion on the elliptical 

 hypolhcsis at CJalajiagos, Madras, San Bias, Hio Janeiro, 

 and r'ormentera, that the gravitating force is greater at these 



places 



