Full resolution (JPEG) - On this page / på denna sida - Pages ...
<< prev. page << föreg. sida << >> nästa sida >> next page >>
Below is the raw OCR text
from the above scanned image.
Do you see an error? Proofread the page now!
Här nedan syns maskintolkade texten från faksimilbilden ovan.
Ser du något fel? Korrekturläs sidan nu!
This page has never been proofread. / Denna sida har aldrig korrekturlästs.
240 JOURNEY OF MAUPERTUIS.
figure was fufceptible of a proof rather fingular in thefe operations, depending on the
natural qualities of polygons. The fum of the angles of an heptagon on a level is goo”:
the fum of our heptagon upon a curved furface ought to exceed this a little, and we
found it goo® 1’ 37”, according to our obfervations of fixteen angles. Towards the
middle of the figure we formed a bafe, the largeft perhaps that ever was meafured, and
the moft even ; fince it was on the furface of the river that it was to be meafured, when
it fhould be frozen. ‘The extent of this bafe fecured to us an exactitude in meafuring
the heptagon, and its pofition left no room to apprehend that there could be any errors
of moment, from the {mall number of triangles in the mid{t of which it was placed.
Indeed the length of the arc of the meridian which we were meafuring was very con-
venient for the certainty of our work. If there be an advantage in meafuring large
arcs, inafmuch that the errors which may arife in computing the amplitude are not
greater for large than {mall arches, and that diffufed amid {mall ones, they make a more
confiderable total of error than amid larger ones: on the other’hand, the miftakes
which may be made in the triangles may have confequences dangerous in proportion to
the diftance to be meafured, and the number of the triangles. 1f the number be great,
and the conveniency of a bafe for frequent proofs be wanting, thefe laft errors may
form a very diverging feries, and more than counterbalance the advantages derivable
from large arcs. I had read to the academy before my departure a memoir on this
fubject, in which I determined the moft advantageous length to be meafured for a cer-
tainty of exactitude ; this length depends on the precifion with which the horizontal
angles are obferved, compared with that which the inftrument may give, with which the
diftance of the ftars from the zenith is taken; and applying the reflections which I made
to our work, it will be found that a longer or fhorter arc than ours would not have
afforded fo much certainty of its meafure.
For obferving the angles between our fignals, we ufed a quadrant of two feet radius,
with a micrometer attached, which being verified round the horizon, always gave the
fum of the angles very nigh by four proofs: its centre was always placed in the centre
of the fignals, every one took and wrote his obfervations feparately ; and afterwards we
adopted the mean of all the obfervations, which differed very little one from another.
On every mountain we took efpecial care to obferve the elevation or depreffion of the
objects chofen for taking the angles, and the reduétion of the angles to the level of the
horizon we eftablifhed on thefe heights.
This firft part of our work, which might have been impoflible, being thus happily
terminated, we gathered frefh {pirits to go through the reft, which fimply required
labour.
In a fucceflion of triangles joined one to another by common fides, the angles of
which are known, one fide being afcertained, it is eafy to find the remainder : we were
fure of pofleffing the exact diftance from the fteeple of the church of Torneo, which
terminated our heptagon towards the fouth, to the fignal of Kittis which was its northern
extremity, as foon as the length of our bafe fhould be known; and the meafurement of
this we poftponed till winter, when we fhould not want either for time or ice.
We then turned to another part of our work, to determine the amplitude of the are
of the meridian comprehended between Kittis and Torneo, the meafurement of which
we looked upon as complete. I have.already {tated what this was which we had to de-
termine. It was neceflary to obferve how much higher or lower the fame ftar when on
the meridian appeared at Torneo than at Kittis, or what is the fame, how much this ftar
on crofling the meridian was more near or diftant from the zenith of Torneo than of
Kittis. This difference between the two clevations, or the two diftances from the zenith,
Was
<< prev. page << föreg. sida << >> nästa sida >> next page >>
