124 
PRESTON. 
considered the greatest enemy to accuracy in work of this 
kind, there still remain unexplained differences even where 
the temperature is all that can be desired. The changes in 
the atmospheric effect, whether depending on buoyancy or 
the viscosity of the air, need not be particularly examined, 
because for any one station the conditions do not vary 
enough to change the time of oscillation by nearly so much 
as those produced either by temperature or by the time-piece. 
Peirce’s treatment of the atmospheric corrections is briefly 
this: From observations at varying pressures an empirical 
formula is deduced for the times of oscillation at a given 
temperature. This formula contains a constant term with 
two others depending on the pressure and the square root of 
the pressure. The coefficients are then reduced to make 
them applicable to one absolute atmosphere and to one 
absolute unit of temperature, on the supposition that the 
second term varies directly as the pressure and inversely as 
the temperature, while the third term varies directly as the 
square root of the pressure and inversely as the eighth root 
of the temperature. By one absolute atmosphere is meant 
one million centimeter gramme second units.* * The absolute 
zero of temperature is taken to be at 273° centigrade below 
the freezing point. For pendulums No. 3 and No. 4 the 
following formulae are given by Professor Peirce: 
No. 3: 
T. = * + '0003107 f + -0000349 
t Yt 
T u = y 4- '0008821 j + -0001047 
No. 4: 
T„ = x + -0003315 y + -0000428 
d t v* 
T„ = y 4- -0009905 f + -0001247 8 l ^| 
cm. 
* This corresponds to 74.986 barometric pressure at Paris. See Report 
. . Coast Survey . . lor 1876. 4°, Washington, 1879. Appendix 15, 
pp. 265-266. 
