156 
REV. F. FALLOWS’S OBSERVATIONS WITH AN INVARIABLE 
to be a standard instrument in an observatory ; that it should be swung at all 
seasons of the year ; that it would be proper to forward it on authorized occa- 
sions to the various fixed observatories now situated in the northern and 
southern hemispheres ; that the instrument should return again to the same 
stations as before, and the observations be renewed ; that, finally, after each 
circuit it should undergo a strict examination at the spot where it was first 
tried, in order that it might proceed again as before. Should any harm take 
place from improper packing or accidental circumstances, the evil would be 
soon discovered, and the instrument repaired. The pendulum is of a very 
delicate construction, and consequently it is the more necessary that it should 
be as often as possible compared at those points where it has previously been 
used. 
Formulae used in computing the Observations. 
a — greater, and b the lesser arc observed at the beginning and end of each 
set of coincidences. 
t = mean of the thermometers immediately adjacent to the pendulum. 
1 1 = height of the barometer. 
t = height of the attached thermometer. 
It must be remarked that the sidereal day is reduced to a mean solar day for 
comparison in London. 
Log (reduct, for arc) = 9.55132 + log(a+&) -{-log (a — b) — log {log a— -log 6} 
Reduct, for temp. — (t — 62°) X 0.421. 
Log (reduct. for vacuum) = 9.31083 + log H. i 
- {log (1 +*002083 . t — 53°) + log (1 +’6ooT.r - 53° }J 
The specific gravity of the pendulum is assumed ... 8.6 Sabine. 
The expansion for 1° of the pendulum 0.421 — 
The temperature assumed as the standard for spec. grav. = 53° — 
The temperature assumed as the standard for pendulum = 62° — 
Specific gravity of the air (water =1) —j-y — 
