REDUCTION OF PENDULUM OBSERVATIONS. 
BY 
Erasmus Darwin Preston. 
[Read before the Society by permission of the Superintendent of the U. S. 
Coast and Geodetic Survey, May 25, 1889.] 
Every physical investigation involves certain determina¬ 
ble quantities. The accuracy attainable in the measurement 
of these quantities depends on various external conditions, 
to a certain extent beyond our control, but which, from the 
very fact that they bear on some one final result, have a 
certain degree of correlation. If from reciprocally imposed 
relations between the quantities sought and the data bear¬ 
ing on the solution of the problem the accuracy of the result 
is limited, all auxiliary quantities should be determined 
with especial reference to this degree of accuracy. In the 
process of finding chronometer corrections from star observa¬ 
tions the refinement in the determination of any one of the 
auxiliary quantities— i. e., in the correction for aberration, 
level, azimuth, and collimation—should not be pushed be¬ 
yond that possible in the final result. When a time-piece, 
from the nature of its mechanism, cannot be expected to 
indicate true time—that is, to run uniformly with an error 
less than one-tenth of a second—the application of the correc¬ 
tion for diurnal aberration becomes superfluous. This same 
principle, namely, that the strength of any investigation in 
physics is the strength of its weakest part, is everywhere 
applicable, and it is proposed in the present paper to examine 
recent work with the pendulum with reference to the degree 
of accuracy attainable or desirable in the determination of 
the corrections usually applied to the observed period of 
oscillation. 
13-Bull. Phil. Soe., Wash., Vol. II. 
(115) 
