256 The Proposed Pendulum Operations for India. [No. 4, 
longer pendulum will have lost two oscillations on the shorter one. 
Hence all that is requisite in practice, is to observe as accurately as 
possible the intervals between the successive coincidences ; the number 
of vibrations made by the clock pendulum is determined by observ- 
ations of the sun or stars, and then the number made by the detached 
pendulum is computed by simple proportion.* 
The first pendulum observations of which any account is preserved 
are those made by Picard at Paris and Uranienburg (Tycho Brahe’s 
observatory) and those by Richer at Cayenne in 1672. These last 
observations are said to have attracted Newton’s attention, as they 
proved the variation in the length of the seconds pendulum in different 
latitudes, and it is generally stated that Richer made the discovery by 
accident. But it appears from Picard’s address to the French academy 
in 1671, that a variation had been already observed, and it is probable 
that Richer’s mission was undertaken partly with a view to throw 
light on the subject. Picard stated that “‘ from observations made at 
London, Paris and Bologna, it would seem as if the seconds pendulum 
required to be shortened in approaching the equator, but that on the 
other hand, he is not sufficiently convinced of the accuracy of those 
measurements, because, at the Hague, the length of the seconds 
pendulum was found to be quite the same as at Paris, notwithstand- — 
ing the difference of latitude.” + 
Near the end of the 18th century, Borda made his celebrated expe- 
riments for determining the length of the seconds pendulum at Paris. 
His apparatus, which is named after him, consisted of a spherical ball of 
platinum attached by grease to a brass cap which had been truly ground, 
so as to fit it perfectly. The object of this attachment was to enable 
the observer to turn the ball round in the cap at pleasure, so as to 
destroy the effects of unequal density in different parts of it. A. fine 
wire carrying the cap was fastened to the lower end of a small 
cylinder, passing through the knife edge, which carried on its upper 
end a small moveable weight, by adjusting which the knife edge 
and cylinder could be made to vibrate independently in the same 
* If r = daily rate of the clock and I the mean interval of the coincidences, 
then the number of oscillations made by the pendulum in a day = n 
I—2 ‘ 
n = — (86400 + 7) the lower sign is to be ussd when the 
IT 
clock is losing. 
7 Cosmos Vol. LV. page 25, Sabine’s translation, 

