397 



Testigates a formula geometrically, to express the ellipticity in terras 

 of such difference ; and thus by accurate observations of Foucault's 

 pendulum in different parts of the earth, he conceives the ellipticity 

 might be determined. 



As an instance, he cites Foucault's result for the latitude of Paris ; 

 which differs by a small amount from the formula, and which he 

 considers accordingly to express the ellipticity, though he does not 

 calculate it. 



2. " On the Extension of the value of the Base of Napier's Loga- 

 rithms ; of the Napierian Logarithms of 2, 3, 5, and 10 ; and of the 

 Modulus of Briggs's, or the Common System of Logarithms ; all to 

 205 places of decimals." By William Shanks, Esq. Communicated 

 by Gr. B. Airy, Esq., Astronomer Royal, F.R.S. &c. Received 

 January 21, 1854. 



The author, after referring to the value of tt to 527 decimals com- 

 puted by him and printed in the ' Proceedings,' for January 20, 1853, 

 states that he has very recently extended and computed the values which 

 form the subject of this communication to 205 places of decimals ; 

 and as very great care has been taken to exclude error, it is presumed 

 there exist reasonable grounds for pronounciDg them quite accurate. 

 At the same time it should be distinctly understood, that no direct 

 check or ;;roo/ has yet been applied to the values in question. He states 

 that the formulae employed in finding these logarithms, are investi- 

 gated by Mr. J. R. Young, in his ' Elementary Essay on the Com- 

 putation of Logarithms,' pp. 13 and 14, and he considers that no 

 better formulae than these have yet been published for readily com- 

 puting, to a great extent, the Napierian logarithms of 2, 3, 5, 7, &c. 



Subjoined are the values referred to : — 



Base of Napier's Logarithms 



2-7182818 

 7757247 

 3035354 

 3919320 

 033429s 

 6323382 



•6931471 



8075500 



2754439 

 8226310 

 5101002 

 3980048 



i"0986i22 

 4647490 

 1626456 

 4230252 

 0906550 

 0000626 



2845904 

 0936999 



7594571 

 0305992 

 2605956 

 9880748 



5235360 



5957496 

 3821785 

 1817413 



3073813 

 2070767 



2874713 

 6967627 

 2516642 

 5966290 

 2328627 

 3049394 



Napierian Logarithm of 2 



8055994 5309417 



1343602 5525412 



2266635 5206804 



4298719 4582110 



4259177 643432] 



7339123 6947695 



2321214 



0679523 

 5602137 

 0448886 



7424545 

 8281006 



Napierian Logarithm of 3 = 



8866810 9691395 2452369 



5578227 4945173 4693570 



2261348 7915959 6453630 



7148232 3776931 0688498 



5814573 8582278 9682167 



IIIII54 1362298 9315024 



5266249 

 7240766 

 7427466 

 4357290 

 9434907 

 92+ &c. 



5817656 

 5S47083 

 0371911 

 1731607 

 3493150 

 80+ &c. 



2252570 

 0667031 



4663543 



5615669 



2037498 



24-f&e. 



