tein|K'rat(ire coirectmns l>v hwiiiginjj tin» |>cnilii!iiin8 ut diflVrent toniiiei-iitiini«, 

 otlitT tiling rt'mnining tlic sume. Want of tiim- fli<l not onuble iik to iiiidiTtuko 

 Biicli 11 series of ex|MTiraents anil the conmionly acoj-pted oH'fticient of cximiMon 

 for linifs";, .O(.t00187 |>er degree eentigrade, was ussiiined ; »hicli we tliiiik will U» 

 sufficiently accurate for our |>rcfent |>ur|>o«e. A thennoineter wa« linng near the 

 j>endiiliiti) and the Headings weix- tak^n at the iKnrinning and end i«f each ex|>i'ri- 

 ment. The mean of the two rejidings is given in tlie Hth eohnnn under the 

 lieading " Mean Teniperatun'." The tenifXM-ature was fäensiiily constant during 

 any one ex|>eriment. In making; out the corn-clion 2r>'' ('. was taken as the tem- 

 perature of refi'rence as it hapjiened to l<" ahout midway J>etween tlie extreme 

 tenijieratiires. The correction is 



II 



t , iT — -j:.! 



where t is tin- time of a viliralimi uncorrected, n the eoeffieient of <-x|i,tiii>ion 



(.WlKJiST), and T tl hsiMvcil mi-iiti tcniji'Taf inc. 'I'Kis («iro-rtioii i» L'ivi-ii in 



the 10th cohunn. 



Tlie correction for the chronometer rate has \teeu compnteil from the daily 

 rate ohtained hy transit observations. The daily rate got from transit observa- 

 tions on two successive nights is of course no more than the mean nitc during the 

 day. In making out this correction we have however supiHPi«e<l the rate to be 

 uniform throughout each day, for, although this may introduce a slight error 

 into the individual results, yet in the mean of a numlier of exi>eriment.« continue«! 

 during a whole day the error thus intriHluied will eventually be very small. 



The further correctionw for the statical buoyancy and the viscous resistanc«! 

 of the air will apjiear in the form r/'<,* where c is some constant de|>^'nding 

 iijxm the form of |>cndulum, /< the density of the air ilivided by that of thi- |>«'n- 

 dulum. and t the time of vibration after the other corrections have l>een a|>|iiied. 

 Using the suffixes t and s to denote /' and f at Tokio and SipiKiro ni«|>ectively, 

 the ratio of the values of tiie acceleration due to gravity at the two hnMlities 

 when thus corrected will become 



neglecting higher ])Owers fif small quantities. Now taking the density of braw 

 to be 8.47 the temperatiire of the air 2^> C and the baromettic (pressure 7ß.O era. 



;, = .(X)ü>4<» 

 c has l)een computed by Poissfin to be ^ f in the case of a sphere attacheil to it thin 

 r<"Ml. In the present ciuse. the pen<lulum consistwl of « very oblate ellipsoid 

 attached to a bar as aliwidy descril<e<l. and vibrate«! in the plane of it* longer axis, 

 60 that we may safely a-osuine c to have Iwen something not far from the above. 

 Further, since the Viarometric reiulings were sensibly the same during lioth the 



• BeMel.— Bcrl. AkuH. 182«. 



t Airy, Treatixo on Soiiiid. Art. Sii. 



