coulomb- first memoir on electricity and magnetism (1785).pdf

8/13/2019 Coulomb- First Memoir on Electricity and Magnetism (1785).pdf

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Charles-Augustin Coulomb

First Memoir on Electricity and Magnetism

Charles-Augustin Coulomb, Construction et usage d'une balance lectrique, fonde surla proprit qu'ont les fils de mtal, d'avoir une force de raction de torsion

proportionnelle l'angle de torsion,Histoire de l'Acadmie [royale] des sciences avec

les mmoires de mathmatiques et de physique, partie "Mmoires" [178], 1788, p

!"#-!77

$ranslated b% &ouis & ucciarelli, (meritus )rofessor of (ngineering and $echnolog%

*tudies +$., $, /000 +revised and notes added b% Christine londel and ertrand

olff, /01/.

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Construction and use of an electric alance based on the propert% that filaments of

metal produce a reactive force in torsion proportional to the angle of t3ist222222222

!perimental determination o# the la$ accordin% to $hich the elements o# &odies,

electri#ied $ith the same ind o# !lectricity, are mutually repelled(

n a memoir presented to the Academ%, in 1784, have determined frome5periments the la3s governing the torsional resistance of a filament of metal and

have found that this force is proportional to the angle of torsion, to the fourth po3er of

the diameter of the suspended filament and inversel% proportional to its length - allmultiplied b% a constant coefficient 3hich depends on the nature of the metal and is

easil% determined b% e5periment

have sho3n in the same emoir that b% means of this force of torsion, it 3as

possible to precisel% measure e5tremel% small forces as, for e5ample, one ten

thousandths of a grain1 n the same emoir described a first application of this

theor%, see6ing to evaluate the constant force attributed to adhesion in the formula for

the surface friction of a solid bod% moving through a fluid

$oda%, set before the e%es of the Academ%, an electric balance constructedaccording to the same principles t measures 3ith the greatest precision the state and

the electric force of a bod%, ho3ever 3ea6 the degree of electricit%

)onstruction o# the *alance +l( -.../

hile practice has taught me that, in order to e5ecute several electric

e5periments in a convenient 3a%, it is necessar% to correct some defaults in the first

1 1 grain 0,0! g


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balance of this 6ind that put to use, still, as this has been up until no3 the onl% one

3hich have emplo%ed, am going to give its description, noting ho3 its form and

dimensions can and ought to be changed according to the nature of the e5perimentsone plans to carr% out $he first figurepresents the balance in perspective 9ere are thedetails

:n a c%linder of glassA*)0, of 1/ ;pouces/< in diameter and 1/ ;pouces< high,

3e place a plate of glass of 1 ;pouces< in diameter, 3hich covers the 3hole vessel of

glass $his cover is pierced 3ith t3o holes of appro5imatel% /0 ;lignes< in diameter,

one in the middle, at#, on 3hich is elevated a tube of glass of /4 ;pouces< in height

$his tube is cemented over the hole#, 3ith the cement used in electric apparel= at the

highest e5tremit% of the tube at h, is placed a torsion micrometer the details of 3hich

are sho3n in#i%ure $he top, n2 1, bears a 6nob &, the pointer io, and the clasp of

suspension, q( $his piece goes into the hole 3 of part n2 )art n2 is formed of a

circle a& divided on its edge into "0 degrees, and of a copper tube > ?3hich fits into

the tubeH, n2 4, sealed at the interior at its highest e5tremit% of the tube or of the

glass stem#h of#i%ure 1 $he clasp q +#i%ure , n2 1. has appro5imatel% the shape of

the e5tremit% of a solid mechanical pencil clamp ;porte5crayon


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until, 6eeping in vie3 the vertical filament 3hich suspends the needle and the center

of the ball, the needle a% is directed to3ards the first division of the circle9 then

introduce through the hole m the other ball t suspended b% the filament m6 t such thatit touches the ball a and that, in 6eeping in vie3 the center of the filament of

suspension and the ball t, one encounters the first division o of the circle9 $he

balance is no3 in a state read% for all operations 3e go on to give as an e5ample, themeans b% 3hich 3e are able to determine the fundamental la3 according to 3hich

electrified bodies repel themselves

:he #undamental la$ o# !lectricity(

:he repulsive #orce o# t$o small %lo&es electri#ied $ith the same ind o# electricity, is

inversely proportional to the square o# the distance &et$een the centers o# the t$o

%lo&es(

$ 9 ( ( B ) ( ( D $

:ne electrifies,#i%( ;, a small conductor, 3hich is nothing but a pin 3ith a largehead, 3hich is isolated b% forcing its point into the end of a rod of *panish 3a5 :ne

introduces this pin into the hole m, bringing it in contact 3ith the ball t, ;3hich is< in

contact 3ith the ball a( n retracting the pin the t3o balls find themselves electrified

3ith the same 6ind of electricit% and the% repel themselves mutuall% to a distance that

one measures in vie3ing, +6eeping in line. the filament of suspension and the center of

the ball a, the division corresponding to the circle9( $urning then the pointer of themicrometer in the directionpno, one torques the filament of suspension lp, and one

produces a force proportional to the angle of torsion, 3hich tends to ma6e the ball aapproach the ball t :ne observes, b% this means, the distance to 3hich different

angles of torsion bring the ball abac6 to3ards the ball t and in comparing the forces

of torsion 3ith the corresponding distances of the t3o balls, one determines the la3 of

repulsion

3ill onl% present here, some tests 3hich are eas% to repeat and 3hich 3ill

immediatel% reveal the la3 of repulsion


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!plication and results o# this eperiment(

efore the balls are electrified, %et touching, the center of the ball a, fi5ed to the

needle, is at a distance equal to the diameter of the balls from the point 3here the

torsion of the filament of suspension is null t is necessar% to be 3arned that the

filament of silver l, /8 ;pouces< long, 3hich forms the suspension is so fine that the3eight of one pied4of length is but 1E1" of a grain n calculating the force required to

t3ist this filament, in acting at the point a elongated some four ;pouces< from thefilament l or from the center of suspension, have found, using the formulas derived

in a emoire on the la3s of the force of torsion of filaments of metal, printed in the

volume of the Academie for 1784, that to torque this filament "0 degrees, requires at

point a, in acting 3ith the lever a of four ;pouces< of length, a force of 1E40 of a

grain $hus as the forces of torsion are, as proved in the emoire, proportional to the

angles of torsion, the least repulsive force bet3een the t3o balls, displaces them

sensibl% one from the other

e find in our first test, 3here the pointer of the micrometer is at the point o,

that the balls are displaced " degrees, 3hich produces in the same time a force of

torsion of

"F 1E400 of a grain

in the second test, the distance of the balls is 18 degrees, but as one has torqued the

micrometer 1/" degrees, it results that at the distance of 18 degrees, the repulsive

force is 144 degrees= thus at half of the first distance, the repulsion of the balls is

quadrupled

n the third test, 3here 3e have t3isted the filament of suspension !"7 degrees,the t3o balls find themselves no further apart than 8 and one half degrees $he total

torsion, is consequentl%, !7" degrees, quadruple the one of the second test, and it is

onl% off b% one half a degree that the distance of the t3o balls in this third test 3as

reduced to half of the distance it 3as in the second t results thus from these three

tests, that the repulsive action of the t3o balls electrified 3ith the same 6ind of

electricit% e5ert on upon the other 3as the inverse ratio of the square of the distances

emar

n repeating the preceding tests, 3e 3ill observe that in ma6ing use of a filamentof silver, as thin as the one 3e have emplo%ed +3hich onl% requires a torsional force of

appro5imatel% /4 thousands of a grain to t3ist it through an angle of ! degrees. that

ho3ever calm be the air, and 3hatever precautions that one can ta6e, 3e could not

ans3er for the natural position of the needle 3hen the torsion is @ero, to 3ithin / or

degrees $hus, in order to have a first test to compare 3ith the follo3ing ones, it

requires, after having electrified the t3o balls, to torque the filament of suspension

some 0 to 40 degrees, this 3hich 3ill give a force of torsion strong enough so that the

4 1 pied /,! cm


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/ or degrees of uncertaint% in the initial position of the needle, 3hen the torsion is

@ero, does not produce an% sensible error in the results t is necessar% furthermore to

be 3arned that the filament of silver, 3hich used in this test, is so fine that it brea6s3ith the least disturbance have found in the follo3ing that it 3ould be more useful to

emplo% in these tests a filament of suspension of nearl% double the diameter, although

its fle5ibilit% to torsion be 14 to 1! times smaller than that of the first t is necessar% tota6e care, before ma6ing use of this filament of silver, over the course of t3o or three

da%s, to tension it b% a 3eight 3hich is appro5imatel% half this that might brea6 it t is

necessar% still %et to 3arn the reader, that in using this last filament of silver, never totorque it be%ond 00 degrees because in e5ceeding this degree of torsion it begins to

strain-harden and reacts, as 3e have proven in the emoir alread% cited, printed in

1784, 3ith a force smaller than the one corresponding to the torsion angle

=econd >emar

$he electricit% of the t3o balls diminishes some3hat over the duration of the

e5periment noticed that, the da% 3here have made the preceding tests, the

electrifiedballs, finding themselves repulsed to 0 degrees one from the other, underan angle of torsion of !0 degrees, the% come bac6 to3ard each other about one degreein three minutes ut as have onl% used t3o minutes to ma6e the three preceding

tests, one can, in these tests, neglect the error 3hich results from the loss of electricit%

f one desires greater precision, as 3hen the air is humid, and the electricit% dissipates

rapidl%, one ought, b% a preliminar% observation, determine the la3 of diminution of

the electric action of the t3o balls in each minute, and then, on the basis of this

preliminar% observation, use it to correct the results of tests that one 3ishes to ma6ethat da%

:hird >emar

$he distance of the t3o balls, 3hen the% are displaced one from the other b%

their reciprocal repulsive action, is not precisel% measured b% the angle the% ma6e, but

b% the cord of the arc 3hich Goins their centers n the same 3a% that the lever at

3hose e5tremities acts the action, is not measured b% the mean of the length of theneedle, or b% the radius, but b% the sine of the half of the angle formed b% the distance

of the t3o balls $hese t3o quantities, of 3hich one is smaller than the arc anddiminishes consequentl% the distance measured b% this arc, 3hile the other reduces the

lever arm, compensating themselves in some 3a% and in the tests of this sort 3ith

3hich 3e are concerned, one can 3ithout sensible error, hold to the evaluation that 3e

have given, if the distance of the t3o balls does not e5ceed /! to 0 degrees in the

other cases, one must ma6e the rigorous calculation

emar

As e5perience has sho3n, in a 3ell closed chamber, one can determine 3ith the


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firstfilament of silver, to 3ithin / or degrees, the position of the needle, 3hen thetorsion is null, this 3hich gives, after the calculation of the forces of torsion,

proportional to the angle of torsion, a force more or less of a 40 thousandth of a grain,the 3ea6est degree of electricit% 3ill be measurable easil% 3ith this balance Hor this

operation, one ma6es pass,#i% , across a cor6 of *panish 3a5, a small filament of

copper cd, terminating at cb% a crochet and in d, b% a small ball of gilded pith, and 3eput the cor6A in the trough m of the balance,#i% 1, in such a 3a% that the center of the

ball d, vie3ed b% the string of suspension, reta6es to point o of the circle9( n

approaching then an electrified bod% of the crochet o, ho3ever 3ea6 be the electricit%of this bod%, the ball a separates from the ball d, giving the sign of the electricit% and

the distance of the t3o balls as a measure of the force, according to the principle of

the inverse ratio of the square of the distances

ut ought to 3arn %ou that, since these first tests, have had different small

electrometers made according to the same principles of the force of torsion, using a

filament of sil6 for the suspension, such as it leaves the cocoon, or a thread of thesheep of Angora :ne of these electrometers 3hich has almost the same shape as the

electric balance, described in this emoir, is much smaller t is onl% ! to " ;pouces

coulomb- first memoir on electricity and magnetism (1785).pdf

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