30 
ME. J. E. H. GOBDON ON THE DETEEMINATION OE 
The Kew formula of correction is 
Eeal time of vibration = (observed time) ' ' ' * (^9) 
where s is the daily rate in seconds, being -j- when clock gains, ( — ) when it loses. 
On April 29, at 4 p.m. the clock was 7 minutes 5 seconds slow*; on May 3, at 4 p.m. 
the clock was 9 minutes 30 seconds slow. Giving a rate of 
s= — 36-25; 
viz. it lost 36|- seconds per day.; 
By interpolation from the Kew Tables we have 
' 1 - 8 Aoo)= 1 - 00W225 
To obtain the times of vibration at 40 o, 3 we have 
Log (vibration time at 40 o, 3) 2 =2 log (observed time)— log (l+S'o)- . (30) 
Also the torsion causes an apparent increase of magnetic force, and therefore decreases 
the time of vibration, whence 
Log (vibration time corrected for torsion) 2 =2 log (observed time)— log ^1+g-^. (31) 
Also 
Log (vibration time corrected for clock error) = log (observed time)-}- log ^1+^— . (32) 
Combining these three formulse, we have for the true time of vibration corrected for 
temperature, torsion, and clock — 
Log (true vibration time) 2 =2 ^log (observed time)-}- log — gg^oo)) 
-log(l+ ft )-log(l+£) (33) 
We have the following values for the corrected vibration times : — 
At Kew. 
Set. 
Log of observed 
time of vibration. 
LogCl+So). 
Ue ( 1+ e)- 
Log of square of 
true time of 
vibration. 
1 . 
0-5667909 
0 0008894 
0-0002647 
1-1324277 
2. 
0-5666496 
0 0010057 
0-0002909 
1-1320026 
3. 
0-5666260 
0-0009971 
0-0002909 
1-1319649 
4. 
0-5664375 
0-0000000 
0-0002996 
1-1325754 
5. 
0-5665318 
0-0001557 
0-0002996 
1-1326083 
I_ 6 - 1 
0-5665435 
0-0002253 
0-0002996 
1-1325621 
* These observations were taken by the Dorking clock-maker. 
