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On Small Differences in Sensation

By Charles Sanders Peirce & Joseph Jastrow (1885)

Classics in the History of Psychology An internet resource developed by Christopher D. Green ,ISSN 149!"#1"

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On Small Differences in Sensation

By Charles Sanders Peirce & Joseph Jastrow (1885)

'irst p%lished in Memoirs of the of Sciences, 3, #"!8"Presented

Posted Jan !!"

*ditor+s note, -han.s to Joseph / $ansdell o0 0or proidin2 3e with an electronic ersion o0 this tet !cd2!

-he physiolo2ical psycholo2ists ass%3e that two nere ecitations ali.e in %ality will onlyprod%ce distin2%ishale sensations proided they di00er in intensity y an a3o%nt 2reater than a

0ied ratio -he least perceptile di00erence o0 the ecitations diided y hal0 their s%3 is whatthey call the #nterschiedssch$elle 'echner16 2ies an eperi3ent to proe the 0act ass%3ed7na3ely, e 0inds that two ery di3 li2hts placed nearly in line with the ed2e o0 an opa%e odyshow %t one shadow o0 the ed2e It will e 0o%nd7 howeer7 that this pheno3enon is not aclearly 3ar.ed one7 %nless the li2hts are nearly in ran2e I0 the eperi3ent is per0or3ed withlateral shi0tin2 o0 one o0 the li2hts7 and with a .nowled2e o0 the e00ects o0 a telescope %pon theappearance o0 terrestrial oects at ni2ht7 it will e 0o%nd ery 0ar 0ro3 concl%sie

-he conception o0 the psycholo2ists is certainly a di00ic%lt one to sei:e ;ccordin2 to their owndoctrine7 in which the osered 0acts see3 0%lly to ear the3 o%t7 the intensity o0 the sensationincreases contin%o%sly with the ecitation7 so that the least increase o0 the latter 3%st prod%cea correspondin2 increase o0 the 0or3er ;nd7 indeed7 the hypothesis that a contin%o%s increase

o0 the ecitation wo%ld e acco3panied y s%ccessie discrete incre3ents o0 the sensation72rat%ito%s as it wo%ld e7 wo%ld not e s%00icient to acco%nt 0or a constant#nterschiedssch$elle <e are there0ore 0orced to concl%de that i0 there e s%ch apheno3enon7 it has its ori2in7 not in the 0ac%lty o0 sensation7 %t in that o0 co3parin2



sensations In short7 i0 the pheno3enon were estalished7 we sho%ld e 0orced to say that therewas a least perceptile di00erence o0 sensation !! a di00erence which7 tho%2h eistin2 insensation7 co%ld not e ro%2ht into conscio%sness y any e00ort o0 attention B%t the errors o0 o%r %d23ents in co3parin2 o%r sensations see3 s%00iciently acco%nted 0or y the slow anddo%tless co3plicated process y which the i3pression is coneyed 0ro3 the periphery to therain= 0or this 3%st e liale to 3ore or less accidental deran2e3ent at eery step o0 itspro2ress ;ccordin2ly we 0ind that the 0re%encies o0 errors o0 di00erent 3a2nit%des 0ollow the

proaility c%re7 which is the law o0 an e00ect ro%2ht ao%t y the s%3 o0 an in0inite n%3er o0 in0initesi3al ca%ses -his theory7 howeer7 does not ad3it o0 an #nterschiedssch$elle >n thecontrary7 it leads to the 3ethod o0 least s%ares7 accordin2 to which the 3%ltiplication o0 oserations will inde0initely red%ce the error o0 their 3ean7 so that i0 o0 two ecitations onewere eer so little the 3ore intense7 in the lon2 r%n it wo%ld e %d2ed to e the 3ore intensethe 3aority o0 ti3es It is tr%e that the astrono3ers the3seles hae not %s%ally s%pposed thatthis wo%ld e the case7 eca%se (apart 0ro3 constant errors7 which hae no releancy to thepresent %estion) they hae s%pposed this etre3e res%lt to e contrary to co33on sense B%tit has see3ed to %s that the 3ost satis0actory co%rse wo%ld e to s%ect the %estion to thetest o0 direct eperi3ent I0 there e a least perceptile di00erence7 then when two ecitationsdi00erin2 y less than this are presented to %s7 and we are as.ed to %d2e which is the 2reater7we o%2ht to answer wron2 as o0ten as ri2ht in the lon2 r%n <hereas7 i0 the theory o0 least

s%ares is correct7 we not p #?6 only o%2ht to answer ri2ht o0tener than wron27 %t we o%2ht todo so in a predictale ratio o0 cases6

<e hae eperi3ented with the press%re sense7 oserin2 the proportion o0 errors a3on2 %d23ents as to which is the 2reater o0 two press%res7 when it is .nown that the two are twostated press%res7 and the %estion presented 0or the decision o0 the oserer is7 which iswhich@ 'ro3 the proaility7 th%s ascertained7 o0 co33ittin2 an error o0 a 2ien 3a2nit%de7 theproale error o0 a %d23ent can e calc%lated accordin2 to the 3athe3atical theory o0 errorsI07 now7 we 0ind that when the ratio o0 the two press%res is s3aller than a certain ratio7 theerroneo%s %d23ents n%3er one!hal0 o0 the whole7 while the 3athe3atical theory re%iresthe3 to e sensily 0ewer7 then this theory is plainly disproed7 and the 3ai3%3 ratio at whichthis pheno3enon is osered the so!called #nterschiedssch$elle I07 on the other hand7 the

al%es otained 0or the proale error are the sa3e 0or errors aryin2 0ro3 three ti3es to one!0o%rth o0 the proale error (the s3allest 0or which it is easy to collect s%00icient oserations)7then the theory o0 the 3ethod o0 least s%ares is shown to hold 2ood within those li3its7 thepres%3ption will e that it etends still 0%rther7 and it is possile that it holds 0or the s3allestdi00erences o0 ecitation B%t7 0%rther7 i0 this law is shown to hold 2ood 0or di00erence so sli2htthat the oserer is not conscio%s o0 ein2 ale to discri3inate etween the sensations at all7all reason 0or eliein2 in an #nterschiedssch$elle is destroyed -he 3athe3atical theory hasthe adanta2e o0 yieldin2 conceptions o0 2reater de0initeness than that o0 the physiolo2ists7 andwill th%s tend to i3proe 3ethods o0 oseration /oreoer7 it a00ords a ready 3ethod 0or deter3inin2 the sensiility or 0ineness o0 perception and allows o0 a co3parison o0 oneoserer+s res%lts with the res%lts o0 others= 0or7 .nowin2 the n%3er o0 errors in a certainn%3er o0 eperi3ents7 and acceptin2 the concl%sions o0 this paper7 the calc%lated ratio to the

total ecitation o0 that ariation o0 ecitation7 in %d2in2 which we sho%ld err one ti3e o%t o0 0o%r73eas%res the sensiility Incidentally o%r eperi3ents will a00ord additional in0or3ation %pon theal%e o0 the nor3al aera2e sensiility 0or the press%re sense7 which they see3 to 3a.e a 0iner sense than it has hitherto een elieed to e B%t in this re2ard two thin2s hae to e noted,(1) >%r al%e relates to the proale error or the al%e 0or the point at which an error isco33itted hal0 the ti3e= () in o%r eperi3ents there were two opport%nities 0or %d2in27 0or theinitial wei2ht was either 0irst increased and then di3inished7 or ice ersa7 the s%ect hain2 tosay which o0 these two do%le chan2es was 3ade It wo%ld see3 at 0irst l%sh that the al%eth%s otained o%2ht to e 3%ltiplied y A(1414) to 2et the error o0 a sin2le %d23ent et thiswo%ld hardly e correct7 eca%se the %d23ent7 in point o0 0act7 depended al3ost ecl%siely onthe sensation o0 increase o0 press%re7 the decrease ein2 0elt ery 3%ch less -he ratio A(1414) wo%ld there0ore e too 2reat7 and 1 wo%ld perhaps e ao%t correct -he adanta2e

o0 hain2 two chan2es in one eperi3ent consists in this, I0 only one chan2e were e3ployed7then so3e o0 the eperi3ents wo%ld hae an increase o0 ecitation only and the others adecrease only= and since the 0or3er wo%ld yield a 0ar 2reater a3o%nt o0 sensation than thelatter7 the nat%re o0 the res%lts wo%ld e 2reatly co3plicated= %t when each eperi3ent



e3races a p ##6do%le chan2e this di00erence in the a3o%nt o0 sensation ca%sed y anincrease and decrease o0 press%re a00ects eery eperi3ent ali.e7 and the liaility to error isconstant"6

-hro%2ho%t o%r oserations we noted the de2ree o0 con0idence with which the oserer 2aehis %d23ent %pon a scale o0 0o%r de2rees7 as 0ollows,

denoted asence o0 any pre0erence 0or one answer oer its opposite7 so that it see3ednonsensical to answer at all1 denoted a distinct leanin2 to one alternatie denoted so3e little con0idence o0 ein2 ri2ht" denoted as stron2 a con0idence as one wo%ld hae ao%t s%ch sensations

<e do not 3ean to say that when :ero was the recorded con0idence7 there was asol%tely nosensation o0 pre0erence 0or the answer 2ien <e only 3ean that there was no sensation thatthe oserer noticed when attendin2 to his 0eelin2s o0 this sort as closely as he conenientlyco%ld7 na3ely7 closely eno%2h to 3ar. the3 on this scale -he scale o0 con0idence 0l%ct%atedconsideraly -h%s7 when /r Jastrow passed 0ro3 eperi3ents %pon di00erences o0 wei2ht o0 ?7 "7 and 15 on the tho%sand to di00erences o0 7 17 and 5 on the tho%sand7 altho%2h theacc%racy o0 his %d23ents was decidedly i3proed7 his con0idence 0ell o00 ery 2reatly7 owin2 tohis no lon2er hain2 the sensation prod%ced y a di00erence o0 ? present to his 3e3ory -heesti3ations o0 con0idence were also ro%2h7 and 3i2ht e i3proed in 0%t%re wor. -he aera2e3ar.s see3 to con0or3 to the 0or3%la!!

m D c lo2 ( pE1! p)

where m denotes the de2ree o0 con0idence on the scale7 p denotes the proaility o0 theanswer ein2 ri2ht7 and c is a constant which 3ay e called the inde o0 con0idence

-o show that this 0or3%la approi3ates to the tr%th7 we co3pare it with the aera2e 3ar.s

assi2ned to esti3ates o0 di00erences 0or which 3ore than a h%ndred eperi3ents were 3ade/r Jastrow+s eperi3ents are separated into 2ro%ps7 which will e eplained elow



p #86-he %d23ents en%nciated with any 2ien de2ree o0 con0idence were 3ore li.ely to e ri2ht with2reater di00erences than with s3aller di00erences -o show this7 we 2ie the 0re%ency o0 the

di00erent 3ar.s in /r Jastrow+s second7 third7 and 0o%rth 2ro%ps46

%ditor&s note' (he table immediately belo$ is misplaced $ithin footnote ) in the ori*inal publication. +cd*+6



-he apparat%s %sed was an adaptation o0 a FF post!o00ice scale= %pon the end o0 the ea3 o0

which was 0ied a s%are enlar2e3ent (ao%t one!hal0 inch s%are)7 with a 0lat top7 whichsered to coney the press%re to the 0in2er in a 3anner to e presently descried -his wasti2htly coered with an India!r%er cap7 to preent sensations o0 cold7 etc7 0ro3 contact withthe 3etal ; .ilo2ra3 placed in the pan o0 the alance ro%2ht a press%re o0 one!0o%rth o0 itswei2ht %pon the 0in2er -he di00erential press%re was prod%ced y lowerin2 %pon the pan o0 thealance a s3aller pan into which the proper wei2hts co%ld e 0ir3ly 0ied= this little pan had itsotto3 o0 cor.7 and was placed %pon a piece o0 0lannel which constantly re3ained in the pan o0 the alance It was li0ted o00 and on y 3eans o0 a 0ine India!r%er thread7 which was so 3%chstretched y the wei2ht as certainly to aoid any noise or ar 0ro3 the 3o3ent%3 o0 thedescendin2 pan ; s%00icient wei2ht co%ld also e h%n2 on the ea3 o0 the alance7 so as tota.e o00 the entire press%re 0ro3 the 0in2er at the end o0 each eperi3ent -his wei2ht co%ld eapplied or re3oed y 3eans o0 a ca3 actin2 %pon a leer= and its earin2s %pon the ea3

were 2%arded y India!r%er It was 0o%nd that the %se o0 this arran2e3ent7 which re3oed allannoyin2 irre2%larities o0 sensation connected with the re3oal and replace3ent o0 the 2reater (initial) press%re7 rendered the res%lts 3ore %ni0or3 and di3inished the proale error It alsoshortened the ti3e necessary 0or per0or3in2 the eperi3ents7 so that a series o0 5eperi3ents was concl%ded e0ore the e00ects o0 0ati2%e were noticeale It 3ay e 3entionedthat certain ca%ses tended to the constant decrease o0 the proale error as the eperi3entswent on7 these 3ainly ein2 an increased s.ill on the part o0 the operator and an ed%cation o0 the sensiility o0 the s%ect -he 0in2er was s%pported in s%ch a way as to e li2htly %t 0ir3lyheld in position7 all the 3%scles o0 the ar3 ein2 relaed= and the India!r%er top o0 the rassenlar2e3ent at the end o0 the ea3 o0 the alance was neer act%ally separated 0ro3 the0in2er -he proectin2 ar3 o0 a 0ilter!stand (the hei2ht o0 which co%ld e ad%sted) with so3eattach3ents not necessary to detail7 2ently preented the 0in2er 0ro3 3oin2 %pwards %nder

the press%re eerted y the wei2ht in the pan In the case o0 /r Peirce as s%ect (it 3ay enoted that /r Peirce is le0t!handed7 while /r Jastrow is stron2ly ri2ht!handed) the tip o0 0ore0in2er7 and in the case o0 /r Jastrow o0 the 3iddle 0in2er7 o0 the le0t hand were %sed Inaddition7 a screen sered to preent the s%ect 0ro3 hain2 any indications whateer o0 the3oe3ents o0 the operator It is hardly necessary to say that we were 0%lly on 2%ard a2ainst%nconscio%sly receied indications

-he oserations were cond%cted in the 0ollowin2 3anner, ;t each sittin2 three di00erentialwei2hts were e3ployed ;t 0irst we always e2an and ended with the heaiest7 %t at a later period the plan was to e2in on alternate days with the li2htest and heaiest <hen we e2anwith the heaiest 5 oserations 56 were 3ade with that= then 5 with the 3iddle one7 andthen 5 with the li2htest= this constit%ted one!hal0 o0 the sittin2 It was co3pleted y three 3ore

sets o0 57 the order o0 the wei2hts ein2 reersed <hen we e2an with the li2htest theheaiest was %sed 0or the third and 0o%rth sets In this way 15 eperi3ents on each o0 %s wereta.en at one sittin2 o0 two ho%rs



; pac. o0 5 cards were ta.en7 1 red and 1" lac.7 or ice ersa7 so that in the 5eperi3ents 3ade at one sittin2 with a 2ien di00erential wei2ht7 5 red and 5 lac. cardssho%ld e %sed -hese cards were c%t eactly s%are and their corners were distin2%ished yholes p%nched in the3 so as to indicate the scale o0 n%3ers (7 17 7 ") %sed to desi2nate thede2ree o0 con0idence o0 the %d23ent -he ac.s o0 these cards were distin2%ished 0ro3 their 0aces -hey were7 in 0act7 3ade o0 ordinary playin2!cards ;t the e2innin2 o0 a set o0 57 thepac. was well sh%00led7 and7 the operator and s%ect hain2 ta.en their places7 the operator

was 2oerned y the color p 86 o0 the s%ccessie cards in choosin2 whether he sho%ld 0irstdi3inish the wei2ht and then increase it7 or ice ersa I0 the wei2ht was to e 0irst increasedand then di3inished the operator ro%2ht the press%re eerted y the .ilo2ra3 alone %pon the0in2er o0 the s%ect y 3eans o0 the leer and ca3 3entioned aoe7 and when the s%ectsaid Fchan2eF he 2ently lowered the di00erential wei2ht7 restin2 in the s3all pan7 %pon the pano0 the alance -he s%ect7 hain2 appreciated the sensation7 a2ain said Fchan2e7F where%ponthe operator re3oed the di00erential wei2ht I07 on the other hand7 the color o0 the card directedthe wei2ht to e 0irst di3inished and then increased7 the operator had the di00erential wei2htalready on the pan o0 the alance e0ore the press%re was ro%2ht to ear on the 0in2er7 and3ade the reerse chan2es at the co33and o0 the s%ect -he s%ect then stated his %d23ent and also his de2ree o0 con0idence7 where%pon the total press%re was at oncere3oed y the ca37 and the card that had een %sed to direct the chan2e was placed 0ace

down or 0ace %p accordin2 as the answer was ri2ht or wron27 and with corner indicatin2 thede2ree o0 con0idence in a deter3inate position By 3eans o0 these tri0lin2 deices the i3portantoect o0 rapidity was sec%red7 and any possile psycholo2ical 2%essin2 o0 what chan2e theoperator was li.ely to select was aoided ; sli2ht disadanta2e in this 3ode o0 proceedin2arises 0ro3 the lon2 r%ns o0 one partic%lar .ind o0 chan2e7 which wo%ld occasionally eprod%ced y chance and wo%ld tend to con0%se the 3ind o0 the s%ect B%t it see3s clear thatthis disadanta2e was less than that which wo%ld hae een occasioned y his .nowin2 thatthere wo%ld e no s%ch lon2 r%ns i0 any 3eans had een ta.en to preent the3 ;t the end o0 each set the res%lts were o0 co%rse entered into a oo.?6

-he 0ollowin2 tales show the res%lts o0 the oserations 0or each day,

-he n%3ers in the col%3ns show the n%3er o0 errors in 0i0ty eperi3ents <ith the aera2e

n%3er o0 errors in a set o0 0i0ty we co3pare the theoretical al%e o0 this aera2e as calc%latedy the 3ethod o0 least s%ares -he n%3er 51 th%s otained in this case est satis0ies the3ean n%3er o0 errors -he n%3ers a00ied with a si2n denote7 in the %pper row the osered(a posteriori ) proale error o0 the 3ean al%e as 2ien7 in the lower row the calc%lated (a



priori ) proale error -he last two lines 2ie the aera2e con0idence osered and calc%latedwith each ariation o0 the ratios o0 press%re It will e seen that the correspondence etweenthe real and theoretical n%3ers is close7 and closest when the n%3er o0 sets is lar2e -heproale errors also closely correspond7 the osered ein27 as is nat%ral7 sli2htly lar2er thanthe calc%lated proale errorsp 816

-he 0ollowin2 is a si3ilar tale 0or /r Jastrow as s%ect,It wo%ld oio%sly e %n0air toco3pare these n%3ers with any set o0 theoretical n%3ers7 since the proale error is on thedecrease thro%2ho%t7 owin2 to e00ects o0 practice7 etc 'or ario%s reasons we can coneniently2ro%p these eperi3ents into 0o%r 2ro%ps -he 0irst will incl%de the eperi3ents 0ro3 Gece3er 1 to Jan%ary 7 incl%sie= the second 0ro3 Jan%ary 4 to 'er%ary 47 incl%sie= the third0ro3 /arch 4 to /arch 57 incl%sie= the 0o%rth 0ro3 /arch " to the end o0 the wor. -he3ean res%lts 0or the di00erent 2ro%ps are ehiited in the 0ollowin2 tales,p 86



-he tales show that the n%3ers o0 errors 0ollow7 as 0ar as we can coneniently trace the37the n%3ers assi2ned y the proaility c%re7#6 and there0ore destroy all pres%3ption in 0aor o0 an #nterschiedssch$elle -he introd%ction and retention o0 this 0alse notion can only con0%setho%2ht7 while the conception o0 the 3athe3atician 3%st eercise a 0aorale in0l%ence on



psycholo2ical eperi3entation86

-he %antity which we hae called the de2ree o0 con0idence was proaly the secondarysensation o0 a di00erence etween the pri3ary sensations co3pared -he eidence o0 o%r eperi3ents p 8"6 see3s clearly to e that this sensation has no Sch$elle7 and anishes onlywhen the di00erence to which it re0ers anishes ;t the sa3e ti3e we 0o%nd the s%ect o0tenoerloo.ed this ele3ent o0 his 0ield o0 sensation7 altho%2h his attention was directed with a

certain stren2th toward it7 so that he 3ar.ed his con0idence as :ero -his happened in caseswhere the %d23ents were so 3%ch a00ected y the di00erence o0 press%res as to e correctthree ti3es o%t o0 0ie -he 2eneral 0act has hi2hly i3portant practical earin2s7 since it 2iesnew reason 0or eliein2 that we 2ather what is passin2 in one another+s 3inds in lar2e3eas%re 0ro3 sensations so 0aint that we are not 0airly aware o0 hain2 the37 and can 2ie noacco%nt o0 how we reach o%r concl%sions ao%t s%ch 3atters -he insi2ht o0 0e3ales as well ascertain FtelepathicF pheno3ena 3ay e eplained in this way S%ch 0aint sensations o%2ht to e0%lly st%died y the psycholo2ist and assid%o%sly c%ltiated y eery 3an

otes

16 *le3ente der Psychophysi.7 I7 p 4

6 -he r%le 0or 0indin2 this ratio is as 0ollows, Giide the lo2arith3 o0 the ratio o0 ecitations y

the proale error and 3%ltiply the %otient y 4## Call this prod%ct t *nter it in the tale o0 the inte2ral Ht7 2ien in 3ost wor.s on proailities= Ht is the proportion o0 cases in which theerror will e less than the di00erence etween the 2ien ecitations In all these cases7 o0 co%rse7 we shall answer correctly7 and also y chance in one!hal0 o0 the re3ainin2 cases -heproportion o0 erroneo%s answers is there0ore (1!Ht)E In the 0ollowin2 tale the 0irst col%3n2ies the %otient o0 the lo2arith3 o0 the ratio o0 ecitation7 diided y the proale error7 andthe second col%3n shows the proportion o0 erroneo%s %d23ents,-o 2%ess the correct card o%to0 a pac. o0 0i0ty!two once in eleen ti3es it wo%ld e necessary to hae a sensation a3o%ntin2to "# o0 the proale error -his wo%ld e a sensation o0 which we sho%ld proaly neer eco3e aware7 as will appear elow

"6 -he n%3er o0 errors7 when an increase o0 wei2ht was 0ollowed y a decrease7 was sli2htlyless than when the 0irst chan2e was a decrease o0 press%re



46 -he res%lt o0 o%r oserations on the con0idence connected with the %d23ents is as 0ollows,

In 1715 eperi3ents (s%ect7 /r Peirce) !! ariations 157 "7 and ? 2ra3s !! there occ%rredcon0idence o0 "7 "5 ti3es (" per cent)= o0 7 1 ti3es (9 per cent)= o0 17 8 ti3es (5 per cent)= o0 7 #? ti3es (?" per cent) In these eperi3ents there were "" (9 per cent) errorsco33itted7 o0 which 1 (" per cent) was 3ade in connection with a con0idence "= 1 (" per cent) with a con0idence = 51 (15 per cent) with a con0idence 1= # (81 per cent) with acon0idence 'ro3 which we 0ind that in connection with a con0idence o0 " there occ%rred 1error in "5 cases (" per cent)= with a con0idence o0 7 1 errors in 1 cases (1 per cent)=with a con0idence o0 17 51 errors in 8 cases (18 per cent)= with a con0idence o0 7 # errorsin #? cases ("8 per cent)

In 179#5 eperi3ents (s%ect7 /r Jastrow) !! ariations 157 "7 and ? 2ra3s !! there occ%rredcon0idence o0 "7 ? ti3es (" per cent)= o0 7 19? ti3es (1 per cent)= o0 17 594 ti3es (" per cent)= o0 7 171" ti3es (5# per cent) In these eperi3ents there were 451 (" per cent)errors co33itted7 o0 which (4 per cent) were 3ade in connection with a con0idence o0 "= 1(" per cent) with a con0idence o0 = 9# ( per cent) with a con0idence o0 1= "4 (#5 per cent)with a con0idence o0 ;2ain7 in connection with a con0idence o0 "7 errors occ%rred twice in ?cases (" per cent)= with a con0idence o0 7 1 ti3es in 19? cases (? per cent)= with acon0idence o0 17 9# ti3es in 54 cases (1? per cent)= with a con0idence o0 7 "4 ti3es in 171"cases (" per cent)

In 17?#5 eperi3ents (s%ect7 /r Jastrow) !! ariations 57 17 and 2ra3s !! there occ%rredcon0idences o0 "7 none= o0 7 none= o0 17 115 ti3es (# per cent)= o0 7 175? ti3es (9" per cent) In these eperi3ents there were 5"8 (" per cent) errors co33itted7 o0 which 1? (" per cent) occ%rred in connection with a con0idence o0 1= 5 (9# per cent) with a con0idence o0

;2ain7 in connection with a con0idence o0 17 errors occ%rred 1? ti3es in 115 cases (14 per cent)= with a con0idence o0 7 5 ti3es in 175? cases ("4 per cent)

56 ;t 0irst a short pa%se was 3ade in the set o0 57 at the option o0 the s%ect= later this wasdispensed with

?6 In the eperi3ents o0 Gece3er7 188"7 and Jan%ary7 18847 the 3ethod as aoe descriedwas not 0%lly per0ected7 the 3ost i3portant 0a%lt ein2 that the total wei2ht instead o0 ein2re3oed and replaced y a 3echanical deice7 was ta.en o00 y the operator pressin2 with his0in2er %pon the ea3 o0 the alance



#6 In the tales o0 the third and 0o%rth 2ro%ps7 there is a 3ar.eddier2ence etween the a prioriand a posteriori proale error7 0or theaera2e n%3er o0 errors in 57 3a.in2 the oseredproale error toos3all -his can only e partly acco%nted 0or y the 0act that thes%ect0or3ed the %nconscio%s hait o0 retainin2 the n%3er o0 each.ind o0 eperi3ent in a set andanswerin2 accordin2 to that .nowled2eIn point o0 0act the pl%s errors and 3in%s errorsseparately do notehiit the sin2%lar %ni0or3ity o0 their s%3s7 0or which we are %ite%nale toacco%nt -h%s in the 0o%rth 2ro%p we hae,86 -he concl%sions o0 this paper are stren2thenedy the res%lts o0 a series o0 eperi3ents on the color sense7 3ade with the %se o0 a photo3eter y /r Jastrow -he oect was to deter3ine the n%3er o0 errors o0 a 2ien 3a2nit%de7 andco3pare the n%3ers th%s ascertained with the theoretical n%3ers 2ien y the proailityc%re ; tho%sand eperi3ents were 3ade Giidin2 the 3a2nit%de o0 the errors 0ro3 to thelar2est error7 3ade into 5 parts7 the n%3er o0 errors7 as osered and calc%lated7 that occ%r ineach part are as 0ollows, -hese n%3ers wo%ld e in closer accordance i0 the proale error were the sa3e thro%2ho%t7 as it is not owin2 to the e00ects o0 practice7 etc /oreoer7 theeperi3ents were 3ade on di00erent colors !! " on white and 1 each on yellow7 l%e7 doe7pin.7 2reen7 oran2e7 and rown -hese eperi3ents were not contin%o%s

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