Viewing page 332 of 504

This transcription has been completed. Contact us with corrections.

[[upper left corner]]141)[[/upper left corner]]

oscillation of the pendulum [[insertion]] may be had [[/insertion]] by M. [[superscript]] r [[/superscript]] Emerson's Fluxions, 1. [[superscript]] st [[/superscript]] Edit. page 230, or  2. [[superscript]] d [[/superscript]] Edit. p. 319. Or by his Mechanics, 1. [[superscript]] st [[/superscript]] Edit. p.87. Then measure this distance of the centers of suspension and oscillation; lay it upon a good plain surface (provided for that purpose) which done, and a line drawn in a right direction therefrom, the length whereof is known from above, or from the Newtonian principles of gravitation, &c. which length divided into Feet, Inches and parts, and you will have a universal measure. [[underscore]] R. Waddington.[[/underscore]]

     It may, perhaps, be worth while to collect all the observations & experiments, made upon the vibration & length of pendulums in different latitudes & climates, in order to ascertain what may be attributed to the effect of heat & cold; and what from the different [[insertion]] powers of gravities arising from different figures [[/insertion]] [[strikethrough]] figure [[/strikethrough]] of the Earth, which, [[insertion]] (figure) [[/insertion]]  it is said, they [[insertion]] (Pendulums) [[/insertion]] have so much verified. But we ought also for this purpose, to be furnished with the states of the theremometer during the time of the observations, which is a thing rarely to be met with. However I shall reserve the rest of this page and the following for such as I shall meet with in the course of my reading.

From the most accurate observation of Jupiters Satellites, by M. [[underscore]]Couplet [[/underscore]] the Son, Abbot [[underscore]] Bignon[[/underscore]], president of the royal academy of Sciences at [[underscore]] Paris [[/underscore]], made at [[underscore]] Lisbon [[/underscore]] & by M.[[underscore]]Cassini [[/underscore]] made at the observatory at [[underscore] ]Paris[[/underscore]]. May 7. 1698. the Difference of Meridians was 0 [[superscript]] H [[/superscript]]..51 [[superscript]] m [[/superscript]]..51[[superscript]] s [[/superscript]]=12°..57'..45", whereby [[underscore]] Lisbon [[/underscore]] is more easterly than [[underscore]] Paris[[/underscore]]. Supposing Long. of [[underscore]] Paris [[/underscore]] 21°. only, that of Lisbon will be 8°..2'.15".  The former gentleman M. [[underscore]] Couplet [[/underscore]], Observed the greatest & least Altitude of the Polar star in the end of [[underscore]] December [[/underscore]] 1697 & thence deduces the apparent Alt. thereof or Latitude of [[underscore]] Lisbon [[/underscore]] 38°.45'.25".  -- Before he left [[underscore]] Paris[[/underscore]], he regulated his clock, beating seconds, at the Observatory in [[underscore]] July[[/underscore]] & beginning of [[underscore]] August [[/underscore]] 1697. which continued to go with the mean motion a considerable time that he might be assured of the just length of his pendulum. He left it in this state, & set it agoing at [[underscore]]Lisbon [[/underscore]] the [[underscore]] Nov. [[/underscore]] following & found it lost 2'..13" in 24 Hours, & [[strikethrough]] required [[/strikethrough]] the pendulum required to be 2½ lines shorter at [[underscore]] Lisbon[[/underscore]] than at [[underscore]] Paris [[/underscore]].

This same gentleman, in [[underscore]] March[[/underscore]] 1698 by the same methods, settled the Lat. of [[underscore]] Paraiba[[/underscore]] [[insertion]] in Brazil, [[/insertion]] to be 6°..58'..18" South. Then he put his pendulum into the same state as when he left [[underscore]] Paris[[/underscore]], & found it lost of mean motion 4'..12" in 24 hours, & required to be shorter at [[underscore]] Paraiba[[/underscore]] than at [[underscore]] Paris [[/underscore]] by 3 2/3 lines.  He then put it into the same state as when he used it at [[underscore]] Lisbon, [[/underscore]] which then lost 2'..5" in 24 hours at [[underscore]] Paraiba[[/underscore]].  The length of his [[underscore]] pendulum[[/underscore]] at [[underscore]]Paris [[/underscore]], was 3 feet 8 lines ½; At [[underscore]] Paraiba[[/underscore]] 3 feet 4 lines 5/6; & at [[underscore]] Lisbon[[/underscore]] 3 feet 6 Lines, when it vibrated seconds.  

Memoir 4, of the Royal Academy of Sciences at [[underscore] Paris [[/underscore]], abridged by [[underscore]] Martin[[/underscore]] & [[underscore]]Chambers [[/underscore]] Vol. I. p. 230 to 234. 

M. [[underscore]] de la Caille[[/underscore]], from the result of many trials, in 1751 & 1752, found the length of a simple pendulum, at 33°.55' of South Latitude, to be 3 feet 8,07 lines of the [[underscore]]Chatelet [[/underscore]] of [[underscore]] Paris [[/underscore]]. Gents Mag. for Nov. 1755. p. 512.

Peruse Newtoni Principia lib. 3 Prop. 20. p. 382.

M. [[underscore]]Richer [[/underscore]], having regulated his pendulum-clock at [[underscore]] Paris [[/underscore]] [[insertion]] to the mean motion of the Sun; [[/insertion]] went to [[underscore]] Cayene [[/underscore]] in 1672 to make Astronomical Observations, and there found it lost every day 2 minutes and 28 Seconds. This island is not above 5 degrees distant from the equator. He reported this experiment in France, and it became the object of the attention, and disquisition of all the Philosophers and mathematicians.
[[left indent]] "They immediately saw, that in consequence of this experiment, the pressure of gravity was less at [[underscore]] Cayene[[/underscore]] than at [[underscore]] Paris [[/underscore]]"-------- For though "in warm climates, it is true, the rod of the pendulum lengthens, as all rods of metal do, consequently its oscillations are retarded; for the longer the rod is, supposing an equality in other respects, the slower are its oscillations; but we know pretty exactly, how much heat lengthens pendulums; and, consequently, how much it retards their motion