Sector (astronomy) – Wikipedia

Didactic representation of the Father Picard sector (1671).

The sector is an ancient angular measurement instrument whose use range is a few degrees. Astronomical instrument, it is mainly used in the field in geodesy at XVII ^{It is} And XVIII ^{It is} centuries to precisely measure the zenithale distance of stars.

It is one of the two instruments used by Jean Picard, with the quarter circle, to measure a degree of land latitude ^{[ first ]} and by the Cassini – among others – to establish the map of France known as “Cassini map ^{[ N 1 ]} ». It will be replaced, later, by the repeating circle, more precise and easier instrument of exploitation.

On the sidelines of its use in geodesy, the sector can be adapted on an equatorial frame in observatories; It is then the “equatorial sector”.

Originally, this instrument is akin to the quarter of a mobile circle. It is, in a way, an adaptation of the latter to very precise angular measures. The sector is different from the quarter circle by:

• its much larger radius;
• its limb graduated on only a few degrees and distributed symmetrically with respect to the swivel central amount ^{[ 2 ]} .

Indeed the accuracy of the results requires that:

1. the resolution of the instrument, linked to the size of its radius, is the best possible ^{[ 3 ]} : for example, an error of ten seconds of degree on an angle of one degree generates an error of 111.11 km on the land circumference ^{[ 4 ]} .
2. The measured zenithale distances do not exceed a few degrees because of the refraction: null in the zenith, it progresses in an inconsistent way, as soon as one moves away from the vertical.

Difference in latitude γ between 2 points A and B.

In geodesy, to XVII ^{It is} And XVIII ^{It is} centuries, the “measure of the earth” goes through the determination of a degree of meridian.

Knowing the length of a meridian arch and the angle that underlies it (difference in latitude), you can simply deduce the length of a degree of meridian.

Either to measure the difference in latitude γ, between two points A And B of the surface of the earth (see figure):

The zenithale distance of a star is measured in the meridian’s plan. Let α are A a β one B These angles. The difference in latitude will be γ = β – α (angles in degrees).

Knowing the arc AB , we deduce the length of a degree of meridian X = arc AB / C.

Picard sector: Return verification.

The first to use a sector is Father Picard on his meridian in 1669. His “great instrument”, as he calls him ^{[ 5 ]} 10 feet of radius (3.25 m). His lead is protected: “Lead or perpendicle was locked up in a white iron cannon which put it entirely covered with the wind, besides that one has always observed in a closed place whose roof was broken expressly ^{[ N 2 ]} ». Its limb is graduated on 18 ° and is divided by transversals from 20 to 20 seconds; The resolution is evaluated at 3 “by Picard ^{[ 6 ]} .
The abbot uses the sector to measure zenithale distances on his meridian in three places: Malvoisine, Sourdon and Amiens. Its results are respectively: 9 ° 59’45 “; 8 ° 47’8”; 8 ° 36’10 “. These values ​​are the means of a large number of observations whose variation never exceeds 5” ^{[ N 3 ]} .

Cassini I then Cassini II establish the meridian who crosses France from north to south via the Paris Observatory. After the death of Jean-Dominique in 1712, she was completed in 1718 by her son Jacques. The latter employs two different sectors in the field: in the south, an instrument ^{[ 7 ]} – always without name – 10 feet of radius whose limb, graduated on 26 °, is in copper; to the north, an instrument identical to that of Picard ^{[ 8 ]} , whose limbe is 12 °, divided by transversals from 20 to 20 seconds “from which we easily distinguished a quarter or the fifth”, which goes in the direction of the resolution of 3 “given by Picard.
Jacques Cassini will measure, with these two instruments, zenithal distances in Collioure and the observatory on the one hand, and, in Dunkirk and the Observatory on the other hand. Its angles, which are averages of an unrecognized set of surveys are expressed at the half-second; In the south, as in the north, he takes care to refer to five different stars, the extent of the variation of stars in the north east of 41 “, but he chooses only as only reference, without arguing ^{[ 9 ]} …

• 

  Cassini sector, Refinition by reversal (the telescope is in AE).

In Great Britain, following Robert Hooke, Graham designs a new sector, more robust and more precise ^{[ ten ]} , around 1712. He built one of this type, in 1725, for Molyneux, British astronomer, then another for Bradley, in 1727, “with which this great astronomer discovered abberation and nuitation. »Maupertuis, in 1735, commanded one for the measure of the earth in Lapland ^{[ 3 ]} .
Maupertuis devotes a whole chapter to the instrument: “Description of the sector with which we determined the amplitude of the Arcs of the Meridian, both in Lapponia and France ^{[ 11 ]} . “It is a sector of 9 feet of radius, whose seat” has the figure of a truncated pyramid … twelve feet high “; The telescope measures more than eight feet. The limmbe is eleven degrees divided from 7.5 in 7.5 minutes. The measurement takes place through a micrometer with a graduated drum in seconds. Its resolution, according to the statements, is around 2/10 of a second but the variability of a measurement on 8 test values ​​reaches 2.6 “.
In Lapland, the Maupertuis team will measure the amplitude of the meridian arch between the extreme point of triangulation north of the polar circle and Tornea starting point in the south. Observations will focus on two stars located less than 3 ° from Zenith. In Kittis, the variation between five surveys on the first star will be less than 3 “, and wrongly, it will be a second, always out of five surveys. The statements on the second star, to validate the previous values, will keep a maximum of 3.5 ” ^{[ twelfth ]} .

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  Graham sector, used by Maupertuis.

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  Plate of the encyclopedia dedicated to the Graham sector.

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  The micrometer in the Graham sector used by Maupertuis.

In 1739, at the Ecuador, Condamine and Bouguer employ different sectors, inspired by that of Graham for Bradley, with some modifications (each had his). The Condamine instrument is composed of a large vertical radius of twelve feet, suspended by a spherical joint to a beam of the local observatory. Its limb, placed horizontally at the bottom of the department, made seven to eight degrees of amplitude. It is divided in a special way, and a micrometer allows you to read better than the half second ^{[ 13 ]} .
Observations will be made at the ends of the Arc de Méridien in Tarqui and in Coachesqui, but also in Quito. Several suites of independent observations are made, on three stars very close to the Zenith. They will validate the choice of a single star for the final results. Novelty is also the fact of observing simultaneously, at the same nights and at the same hours, at the two ends of the meridian ^{[ 14 ]} . The dispersion of the averages of the two observers is around 2 “to 3” ^{[ 15 ]} .

In 1740, La Caille, Maraldi and Cassini de Thury (Cassini III) checked “on the entire extent of the kingdom by new observations” The meridian of the Royal Observatory of Paris ^{[ 16 ]} . They employ a sector ordered in Langlois, in 1738, similar, in broad outline, that of Father Picard. Its radius is six feet, the telescope is slightly larger and it has an ordinary micrometer ^{[ 17 ]} . Its lead wire has at its end a copper ball which dips in a bowl filled with water to amortize the oscillations; A lamp and a magnifying glass complete the equipment to facilitate the location of the wire. The limb has an extent of 52 ° 1/3 and is divided from 10 ‘in 10’. The resolution given by the micrometer is of the order of a few sixties of seconds ^{[ 18 ] , [ N 4 ]} .
Astronomers take zenithal distances in the following five places: Dunkirk, Paris, Bourges, Rodez, Perpignan.
The number of statements for each station is very important; For example, in Dunkirk, 57 measurements are made on six different stars. The measures are qualified as very accurate, exact, passable … The results are expressed in degrees, minutes, seconds and thirds (1 third = 1/60 of a second); Nevertheless, the dispersion remains important, of the order of 3 “on the exact and very exact measures. But, the large number of surveys reduces the uncertainty over the means of the results; ultimately, from the means of results on the three The most significant stars, the extent of the dispersion is 3 “on the celestial arc between Dunkirk and Paris ^{[ 19 ]} .

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  Sector used in 1739 to verify the meridian of the Paris Observatory.

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  A measure in the sector: the hob with the bezel, Cassini with the clock.

Finally, in 1768, in North America, Charles Mason and Jeremiah Dixon, measure an arc of 1 °. They use “an excellent sector of John Bird , of a new design. And, towards the end of the century, Ramsden, then Troughton renew the principle of its construction ^{[ 20 ]} . It was also at that time that on the meridian of France, Delambre and Méchain, will replace the sector (and the quarter circle) with the new instrument that is the rehearsal circle.

This sector is a particular sector designed by Graham for observatories. “It is used to easily take the differences in right ascent and declination of two stars, when they are too large to be observed with a motionless telescope. It is an adaptation of the sector on an equatorial frame. He also bears the name of astronomical sector of Graham ^{[ 3 ]} .

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: document used as a source for writing this article.

• Father Picard, Earth measurement , Paris, 1671 ( read online )
• Jacques Cassini, Of the greatness and the figure of the earth , vol.  2, Paris, coll. “History of the Royal Academy of Sciences”, 1718 ( read online ) .
• Jean-Jacques Levallois , Measure the earth: 300 years of French geodesy , Paris, A.F.T., 1988 , 389 p. (ISBN  2-907586-00-9 ) .
• Cassini de Thury, The meridian of the Royal Observatory of Paris , vol.  2, Paris, coll. “History of the Royal Academy of Sciences”, 1740 ( read online ) .
• Maurice Daumas , Scientific instruments at XVII ^{It is} And XVIII ^{It is} centuries , Paris, P.U.F., 1953 .

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