The American journal of psychology
Hall, G. Stanley (Granville Stanley), 1844-1924 | Titchener, Edward Bradford, 1867-1927 | Dallenbach, Karl M., 1887-1971, ed | Bentley, Madison, 1870-1955, ed | Boring, Edwin Garrigues, 1886-1968, ed | Washburn, Margaret Floy, 1871-1939, ed
Dermographism. < ^Dermographism, or skin writing, is said to be dependent on two causes : an irritable nervous system and some toxic agent. Both of these conditions become causes whicdi may act either on the peripheral vaso-motor nerves, or on the vaso-motor centre, and so influence directly the circulation." The foregoing is about what the physicians say of this. But it is very easy to obtain upon perfectly h^thy subjects. In order to test this, after having found it true for myself, I asked a class of ten men to write, with moderately blunt pieces of cork, on their lower arms the word bloody and then slightly rub the arm. This was done, and the word in each case came out in flaming red letters after a pause of a few seconds. In some cases, there was left a welt where the cork passed over the skin, after the increase of the blood had died away, although the writing with the cork was done very lightly and gave no sensations of scratch- ing. 368 DBE8BLAB. The studies here described were made daring the present academic year at Clark University, under the immediate direction of President Hall, to whom I wish here publicly to express my grateful acknowledgments for the many sugges- tions receiv^ during the progress of the work. Likewise to Assistant Prof. Sanford, who has been ever ready to render any assistance, my thanks are due. To all those also who have so generously lent their services as subjects for experi* mentation, I acknowledge my indebtedness, and especially to Mrs. Dresslar, without whose cooperation some of the work would have been imi>088ible. ON THE DIFFERENCE SENSIBILITY FOR THE VALUATION OF SPACE DISTANCES WITH THE HELP OF ARM MOVEMENTS. 1 A. £. 8B08W0BTB, B. A. Hon. Fellow In Pqrohology, Clark UntTortitj. The experimente which form the basis of this paper, were com- menced in the institute for experimental psychology here under Professor Wundt. in the summer semester of 1892, and continued during the following two semesters. The object was to determine the fineness of the space-sense as shown by the difference sensi* bility for movements of the arm in vertical curections upwards and downwards, at different heights, standards and rates of movement. The influence of the leaving of the end points determined or un- determined is also considered. The experiments consider other- wise different asymmetrical influences of the body on the valuations and certain phenomena which result from the loading of the moved members with weights. Either the two arms together or only one were moved as far as possible without bending of the elbow and hand- joints. There are two chief parts to the experimente. The first comprises such as were made oy drawine simple curves upon a vertically standing table or on the wall with a soft lead penciL These are described as the pencil experimente. They are one- handed or two-handed, according as the movements belonging to a single experiment were made with only one arm or with the two arms. In both cases the direction of the arms was forwards, par- allel to the median and at riffht aneles to the side plane of the body. The second part compr&es such one-handed experimente as were made by what is here described as the angle method. For this purpose a verticidly standing upwards and downwards movable table was used. On one side of this, the side adjacent to the arm, a half circle was described, whose radius was 68 cm. and at eveiy one-fourth degree of it a hole was bored through. By this means movements of different extents in angles could be marked off by the placing of plugs in ate holes. The observer sat on a chair, and the centre of uie circle could be made to correspond to the centre of tlie arm's motion by shifting of the table up and dowi^. ' TransUtion tn part of the origliuU m written In Geraum. iprinir and lummer of 1808. See Wnndt, OrundMU-Mh Ed. VoL I. p. 420. Revue FKOatoph. Deo. 1808, p. 068. To aU of thoee who acted m OMenren* I am Indebted for their patience, namely, Qeh. Prof. Wundt, Dr. KtUpe, Dr. Kirechmaan, Dr. Oohn, Mr. Kleeow, Mr. Boetoety, Mr. Child, Mr. Boiren and Mr. Hicka, aa well m to the flnt mentioned fbr the oooTenlenoet of hit laboratorj. 370 8E6SWOBTH : I.. Experiments by Means of the Pencil Method. The method of relative valuaUon and the method of relative differ- ence senHbUity. When one investigates the difference sensibility for motion sen- sations, he can either leave the extent of the normal distances in any series or g^up of experiments determined, or he can aUow the observer to fix the extent himself. In the experiments of Fnllerton and Oattel^ both methods are used. In the latter case the psycho- physical methods of the average errorjthe mean valuation and the right and wrong cases can be used. Where, however, the normal extentBj as also the compared extents, are fixed, the method of just perceptible change, the method of mean valuation and the method of right and wrong cases can be used. The fixing of the normal and compared extents brings about groups of other sensa- tions, which complicate the judging of the pure motion sensations. These are contact, pressure and resistance sensations. Hence it is desirable to have ihe movements made without contact, pressure or resistance through the fixing of the extents. If, also, only the normal extents are fixed, the pressure contact and resistance at the end can make these of no use as standards for the compared extents. If one investigates the pure motion sensations, then one must, if possible, make the movements without fixing the end points. This can only take place if one makes use of shadows, photography, mirrors, or some other such optical apparatus. My first group of experiments made by the pencil method give impure motion sensations in so far as contact sensations are felt with these. Their calculation, however, is similar to such as can be made without contact. In all such movements, where the making of the standard curves equal to one another in anv single series is dependent on the observer, there exists a variation or the indi- vidual from the average normal length. The influence of this variation upon the average differences between normal and com- pared extents where one uses the method of average error,* is considered in another place.* Between the smaUest and largest normal extents in any single series, one can further reckon out whether the individual differences upon increase of their respective normal extents increase or decrease. If we call such of the indi- vidual differences between the normal and compared extents, where the latter are greater than the former, plus; where they are smaller, minus; and where they are equal to, eaual,— then the indi- vidual differences in any series can either be all plus and equal, aU minus and equal, or also there can be all plus, minus and equal differences. The difference sensibility where the normal extents increased, would increase or decrease respectively with increase and decrease in the individual differences in proportion to the increase in their normal extents. > Pages 876, 875, par. 12, 881, 891d. -t- — » ON THE DIFFEBENOE SENSIBILITY. 371 difference sensibility with the variations in the normal curves, where all the indivianal differences are plus, minns or both plus and minns, is reckoned, I call the method of relative difference sensibility. The reckoning of the difference sensibility by this method is verv similar to the reckoning used in the method of relative valuation. If we let the individual differences in a series be all plus, all minus, or both plus and minus, then the valuation (judging) will increase where the compared extents increase with increase in their normal extents. This will be shown by the abso- lute increase of the individual differences with increase in their respective normal extents. Inversely, the valuation will decrease where the compared extents decrease with the increase in their normal distances. This will be shown by the absolute decrease in the individual differences with increase in their respective normal distances. The method by which this valuation within the varia- tions of the normal extents in a series is reckoned out, I caU the method of relative valuation. The estimation of this valuation is similar to the estimation of the difference sensibility by the method of relative sensibility, where the individual differences are either all plus or all minus. As it is the simplest, I give at first the reck- oning out of the method of relative valuatdfon. Description of the Reckoning Out of the Method of Relative Valuation, We let mi mt, mt,etc mz be the simple digits 1, 2, 8, etc X, of which mi represents the greatest normal ex- tent, mt the one in the same series which is just smaller than mi. and so on up to m^ — x, which represents the smallest normal extent. We let further Ux, nz-.i, Uz-s, etc Ut. Ut. Ui, be the same digits x, x — 1, x — 2 . . . . 8, 2, 1, of which, however. Uz = X represents the smallest difference between any individual normal einent and its compared extent in the same series, Uz-i = X— 1, that which is somewhat greater than nz up to ni = 1, which represents the greatest difference between any normal extent and its compared extent in the series. We add, then, each m value to its respective n value, so that the m value, which represents any indivianal normal extent, is added to its respective n value, whicn represents the simple difference between this normal extent and its compared extent, r, o, s, etc g are the sums of such individual values as m^ + Uz. etc mz + Ui, accord- ing as the valuation takes place. In every series there exists x such values, d, e, etc. . . . f are the variations of these values from (mB-Hl)=(ni + l). q represents the average of these variations. If m^ mt, etc mx are added respectively to nx. nz-i, etc ni,then will d, e, etc f each be like null and the average variation q will also be like null. If they are added together inversely, namely mi to Ui, mt to Ut. etc mz to Uz, then the average variation will be Q. This Q gives us the q greatest possible average variations "q" X *" gives us a value which shows whether the differences between the normal and com- pared extents increase or decrease with the increase in their normal extents, i. 6., whether the valuation increases or decreases q with increase in the normal extents. If -q- X *^ is equal to 100, i. «., q = Q, then in comparison with the valuation of the smallest compared extent, a gradual increase of the compared extent with reference to its normal extent would be shown with increase of 372 BB08WOBTH : q this last in the same series. If -q- X *^ is equal to 0, t. e,, q=^ (P^ «.... *..U. .^ ^ ».. ^ .^™. « ^ X -.. equal to 50, then there would be shown on the averase for the series neither such a deorease nor such an increase. If the value of q -j^ X *^ lay between 0 and 60, then there would be more or less of a decrease; if between 50 and 100, more or less of an increase. DasoftoMon of the Reckoning Out of the Method of BelaHve Difference amieibUUy. If all the individual differences between the normal and compared extents are plus, then the difference sensibility, where the value obtained by the method of relative valuation is 0, increases with increase in the normal extents; where 100, decreases; where 50, it neither increases nor decreases on the average; where it is between 0 and 50, it more or less increases, and where oetween 50 and 100. it more or less decreases. If the individual differences are both plus and minus, or equal and minus, then it is necessary to reckon out the value obtained by the method of relative valuation for the dif- ferent normal extents which show plus or plus and equal differences between the normal and comparea extents, and likewise for the different normal extents which show minus or minus and equal dif- ferences. The reckoning out of this latter will, however, be differ- ent from the reckoning in the case of the method of relative valu- ation only in so far as one allows n. « x to represent the difference, which is nearest the value null, Uz— 1 » x — 1, that which is some- what smaller, and Ui -^l, the minus difference, which is most q unequal to the simple difference null. The values of q, Q, and-Q X ^ are now reckoned out, and also the mean of the two values, namely, that obtained from the normal extents which give plus differences and that obtained from those which give minus. If this value is null, then the difference sensibility srMually increases with increase in the normal extents; if it is 100 it gradually decreases; if it is 60, then it neither increases nor decreases on the average; if it is between 0 and 50 it increases more or less, and if between 60 and 100 it decreases more or less. It is here to be remarked that when we speak of the normal ex- tents in any single series, from the standpoint of difference sensi- bility, we have to do with an absolute increase or deorease in the series and not with a relative. Only when we compare this increase and decrease in one series with the same in another can we speak of a relative difference sensibility. If one wished to estimate the relative difference sensibility for each series alone, then instead of using the individual differences to reckon out Uie n values, he must use Uiese divided by their respective individual differences. This, however, has little value. In the same wav, we can only speak about an absolute increase or decrease in the valuation, unless we use, in reckoning out the n values in the method of relacive valuation, in- stead of the individual differences, these divided bv their respective normal extents. This has also, however, insufficient value. We can, however, speak about a relative valuation or a relative differ- ence sensibility In connection with the values obtained bv these methods, in so far as in the case of the first method one takes the valuation where the normal extent is smallest, as normal valuation fdr the series, and in the case of the other, the diffierence sensibility ON THB DIFFEBBNOS SENSIBILITY. 373 M shown, where the individoal differenoe is nYill. or nearest above or below null, as the normal difference sensibility in each series. The values obtained by these methods are denendent on this normal valuation and on this normal differenoe sensioili^, and to some ex- tent show a relative valuation and a relative difference sensibility. From these considerations we obtain four methods which show con- nections between the individual series and the increase in the normal extents, as well as the increase or decrease connected with this in the increase and decrease in the valuation and in the differ- ence sensibility, namely, the two which we have above completely described, the method of relative valuation and the method of relative difference sensibility, and two others which correspond to these, and which give values for the increase and decrease in the relative valuation and the relative difference sensibility in the individual series, instead of the absolute valuation and the absolute difference sensibility, in the individual normal extents. These two latter methods we do not consider further. The reckoning out of the method of relative valuation and of the method of relative difference sensibility is accompanied by certain difficulties which can be overcome only through carefullv choosing the number of experiments and the digits. In the first place, if there is more than a single normal extent, of the same value, one must take the mean of these and also of their respective differences and reckon out the results in the ordinary way with this reduced number of experiments in the series. The same can also be done where there is more than a single simple difference in the same series of the same value. In the second place the average value " q >' might be the seat of an error in that the individual parts of y (mx + 1) work contrary to one another. A table (Part ll) with an instance where this occurs is given below, where 2.40 is » q » Q. Pabt I. Pabt n. -H N = sum V (m, + 1) NL M N MH-N V(m,-|-1) d e etc. etc. f 20.50 — .50 8 1 4 21.50 —1.50 1 2 8 21.25 —2.00 2 8 5 18.25 —8.75 4 4 8 17.50 —4.00 5 5 10 2 8 1 2 4 5|r + etc. + g 5[d + e + etc.-t>f mx-fl q 5| 12 2.40 But it is easy to see that it should be smaller. This error is not frequent and it woidd serve no present purpose to reckon it out, in so far as no wholly exact value Is sought, but only a relative one. The method of relative valuation and the method of relative dif - 374 SE6SWOBTH : ferenoe sensibility will be used as an aid in the reckoning oat of the difference sensibuitv in the experiments made by means of the Senoil method, and is represented by the symbols M. R. V. and I. D. S. The One-Handed Movements. i. A General Consideration of the First ExpeHimenta. I have reckoned out these enerimente all together, without tak- ing into consideration the length of the curves. The results show that out of a total number of experiments of 1008, 1} per cent, were overvalued, i per cent, were valued correctlv, and 181 per cent, were undervalued. Each of the sixty- six series was at nrst treated separately. The average differences of the experiments, where over, under and equal valuations took place, alone with the average variation of these, were reckonea out for £n the experiments. These were then grouped into combinations of six and seven series in a group. These groups were then calculated all together. The average of the whole of the averages of the normal and compared curves, of their differences, of their variations, of the experiments of the sixty-six series, was then reckoned out. In each of the sixtv-six series there were overvalued experiments, and in fifty-one of them. there were experiments where undervaluations took place. The number of experiments, where correct valuations took place, was so small that we shall not take them into consideration here. The lengths of the normal curves varied between 10 and 60 cm. The average of aU the normal curves, where an overvaluation took place, is 22.31 cm. The same, where an undervaluation took place, is 20.62 cm. The average of tne differences of the former is 6.48 cm., of the latter, 3.53 cm. When both the normal and compared curves are added together, the average obtained in the first place was 25.96 cm., and in the second, 26.93 cm. In this way one obtains an average difference in valuation of .97 cm. The average of all of the average normal curves of each series, without consideration of the over and undervaluation, is 23.59 cm. The arithmetical average of all the average differences was 2.75 cm. overvaluation, an average differ- ence sensibility of about ^, It is seen, then, tnat both according to the number of enerimente, and also to the average differences, a significant overvaluation had taken place. A review of the series shows that nineteen series had an average normal curve of ^between 10 and 15 cm., twenty of between 20 and 30 cm., fifteen of between 30 and 40 cm^ four of between 40 and 50 cm. ana two of between 50 and 60 cm. llie average of the average variations of fifty-one series, where an overvaluation took place, was 2.37 cm. For thirty- seven series, where an undervaluation took place, it was 1.00 cm. As this was small in such a general consideration, I have not ti^en it into account. It is desirable now to find out what sort of influences the upwards and downwards direction of the motions, the changes in the normal lengths and in the height of the starting points, as well as special differences in the observers and in the methooiB of experimenting, could show. In the case of the first fifteen series the height of the starting point was not taken, and we do not consider these further. Instead of a lead pencil being used« also a small brush ^th lamp black mixture was used. Of tne remaining fifty-one series, thirty were made in the upwards direction* and twenty-one in the- >8eeUtleII.p.407. ON THE DIFFERENCE SENSIBILITY. 375 downwards.* The accompanying tables^ show the heights of the starting points from the lowest, which is marked with minus, to the highest, which is marked with plus. The horizontal starting point, which could be only roughly estimated, is marked with zero. In considering this first group of experiments it is important to remark that they were aU made more with respect to the conven- ience of the observer than to any previously determined plan of experimenting. The beats of the metronome, which regulated the rate of movement as well as the length of the curves, show also to some extent the disposition of the observer apart from the exact- ness of his judging. Very quick time and very slow time was dis- agreeable. A look at the diagrams* shows also that the averaee lengths of the normal curves for the series varied more under the horizontal point in the case of the upwards movements, but in the case of the downwards movements more over the horizontal point. Not only also are the limits for the average normal lengths greater in these directions, but the number of series is also greater in the case of upwards movements under the horizontal point and in the case of downwards movements above the same. Apart from series 20 of the upwards movements and series 17 of the downwards, a certain attempt was made to make aU the normal curves in eacn series as much as possible equal to one another. There was nothing binding in this, however, as it was thought that it could possibly disturb the power of valuing correctly between the normal and compared curves. Still a certain indirect valuation in this respect was pres- ent in each series. Each new normal curve was more or less of an attempt to reproduce the former. In so far, such a valuation was implicated. The variation of the normal curves gives a value for this. In the case of the upwards motions, the changes in the variations follow the changes in the lengths of the average normal lengths, with few exceptions. In the case of the downwards mouons this is also very often the case. This shows that the difPer- ence sensibility is dependent on the length of the normal curves. In many cases also, the normal curves were made of the same length as the just previously described compared curves. In sucn cases the compared curves were made smaller than their normal curves. These two pairs of curves appear, then, to form a separate basis of valuanon. The above described average values of all the series can be considered as a sum of such valuations, of which the average differences show the exact- ness of the valuation. As the average overvaluation of the experiments of all the 66 series, where overvaluation took place, is 5.48 cm., the corresponoing average undervaluation 3.53 cm., and the average overvaluation in aSl the e:n>eriments was 2.75 cm., we see that the difference sensibilitv would amount to about ^. -H23.59 cm. is the average normal length of aUthe experiments; ^I'.ll x t = ^o = difference sensibility. In general, the curves show no very exact changes caused by changes in the lengths of the normal curves and in the starting points. The larger normal curves show in the case of the upwards movements, where the stfi^rting points were, — 30 and --60 cm. larger average differences than do the smaller normal curves. In the case of the downwards movements, the average differences show the opposite results, so that the smaller normal curves are more overvalued than the larger. It is easy to see that on account of the changes in the average normal lengths and in their variations, the ixmuence of the changes in the starting points in these experunents can not be >8eetAbleLp.40«. * See original. 376 SEGSWOBTH : very exactly determined. Where also the variations of the average normal curves and the changes of the starting points do not vary much, the variations of the averaee differences are too great to, fl:ive exact results. In order to finaout the influence of the start- ing points, I have made the two-handed experiments, which are given below (B), and I have also made other additional one-handed experiments to determine the influence of the extent of the normal curves. I give in addition certain remarks on the individual series. By the method of relative valuation above described, I have reckoned out in the individual series the tendencies towards under and over- valuation. From this it appears that in the case of upwards motions, where the starting points are very low or very mgh, an undervaluation takes place more and more with the increase in the length of the normal curves. Under and at the horizontal point, however, more of an overvaluation takes place. These over- valuations and undervaluations are not very much dependent either on the changes in the average normal lengths nor on the changes in the variations of the individual normal curves from their average normal lengths. In the case of the downwards motions with low starting points, a distinct undervaluation of a similar kind takes place, and is also present where the starting points are taken qmte high. Only when the starting points are very high is* an overvaluation met with. 2. CongideraUon of the Individual Seriea, a. Series 11 and 12 of the upwards motions and series 8 of the downwards were made while the observer was seated. They show no special deviations from the other series. Among the later experi- ments are some which show more particularly differences between the standing and sitting posture. 6. With and without the beatins of the metronome. Series 16, 24, 26 and 5 of the upwards moaons were carried out with no accompanying beating of the metronome. It is to be remarked that the variation of the normal curves in each case is very small. The angle method experiments to be described later will show the more important influence of the rate of movement upon the relative valuation. In general it appears that the observer without the beating of the metronome, chooses the most convenient rate of movement for the starting point and length of movement. The metronome's beating has less influence on the variation of the normal lengths with such as are accustomed to see the regular motions of machines, or to make regular motions themselves. In these oases the two groups of sensauons, the normal and the com- pared, are more or less localized in the organs of motion. The motions are automatically made. Where this \b not the case the metronome exercises a greater and more distinct influence upon the variation in the normal curves. Along with this the two groups of motion sensations can be considered more as sensaUons of tne willing impulse, which are localized in the glottis and in the breathing apparatus. As the metronome tends to make these motions also automatic, however, these sensations are not so im- portant (as materials in investigating) as in either case where one makes movements of unusual length and height. c. Influence of the lengths of the radii. The irregularity of manv of the average differences which are dependent neither upon the aifferences in the variations of the normal curves, nor upon the differences in the heights, can be very well ascribed to the bending ON THB DIFFE&ENOE BEN8IBIIJTY. 377 of the arm. It is desirable, therefore, to find out what relation the radii of the normal carves bear to tiie radii of the compared ones. The curves were more or less bent towards the extremities. The measuring of the radii, then, was confined to the normal arcs in the middle of the curves. A large wooden compass was used to meas- ure these directly. Where the radii of tne normal curves are smaller than those of the compared, the differences are marked with plus, where larger with minus. In the case of the upwards motions, it appears that the normal radii are smaller where the starting points are very high and very low than where the points lie between these extremes. It is meant that the variations in the lengths of the normal radii and the average differences between those of the normal and compared, show the value of this meas- uring. Where one variation is relatively small, so is the other, where large, likewise. From this it follows that there existed regular fiuctuations in the bending of the arm. The bendhig of the arm alternates more or less in each series, and the average differ- ences of the radii show, then, how the valuations of the movements are influenced through this. If we consider now more particularlv series 2. 5, 6, 7 and 9 of the upwards movements, which have starting poinui very nearly idike. we find that by increasing the height of the starting point as well as bv lengthening the average lengths of the normal curves, the lengths of the average radii of these increase. If we consider, however, only the dumges of the lengths of the average differences of the radii in connection with the changes in the average differences of the curves, then we find that they stand in a directly inverse relation to one another. The exception in series 6 can be very easily ascribed to the greatness of the variation. In series 1, 6, 6 and 11 of the downwards motions, the lengths of the average normal radii increase with the heightening of the starting points. The first three series were made under the hori- zontal point and can be considered by themselves. The average differences of the normal and compared curves stand in a direcUy inverse relation to the average differences of t^eir radii. Apart from the starting point the increase in the average lengths of the curves is aocompimied by a decrease in the average diUferences of the normal and compared curves, and by an increase in the average differences of the radii themselves. In the case of both upwards and downwards movements, then, it results that an increase in the average differences of the normal and compared curves is accompanied oy a decrease in the lengths of the differences of their radii. The greater normal curves are, however, more overvalued in the former case than in the latter. d. What relation do the curves bear to their corresponding angles and perpendiculars ? I have drawn diagrams', which givo the average values for the above described series. For series 2. 5,. 6. 7 and 9 of the upwards motions, the average of the heights of the starting points was —62.10 cm. The average of the average normal curves is 26.87 cm.; of the compared 34.10 cm.: of the average radii of the first 56.72 cm., of the last 61.96 cm. In the case of the down- wards movements, tne average of the heights of the starting points for series 1, 6 and 6 was —42.87 cm. The average of the average normal curves is 16.96 cm.: of the average compared! 17.66 cm.; of the radii of the first 64.19 cm., of tlie last 66.6 cm. From these values I have reckoned out the correspon^ng angles and the perpendiculars to the horisontal pUme lying hereon the extrradfies of the curves. Dr. J. Loeb^ has shown >ArDlilTfardSeco.Flij.4.M.ii.d.Th.TOBPAO««r. Bd.46,LB. 1; Bd.tt,&10T. 378 BEOBWOBTH : that where the starting points lie onder the horizontal plane, motions made at right aneles to this plane show great devia- tions between the normal and compared distances, and this Inst so mnch the more that the starting points are distant from the norizontal plane. If the observer had described such straight lines without changing the angles of movement, the above perpendicu- lars would snow my results to agree with those of ix>eb's. My experiments show, however, that m order to mi^e lines of equal greatness, the angles at the shoulder should be taken as the stajid- ard and not the perpendiculars. In both cases, whetiber one makes movements with the arm held straight out in the form of curves or with the elbow joint bent in the form of straight lines, it is to be assumed that the mass of sensations are so nearly equal to one another that they do not need separate consideration. There exists a probabilify for this in so far as the contact and holding of the elbow joint when the arm is fully stretched out. compensate for the other kinds of stimuli which arise through tne bending of the elbow joints and the muscles. How far the sensations due to the moving muscles and to the so-called will-impulse are to be taken as the basis for the valuation, will be explained later. The chief point to be noted here is that the angle at the shoulder joint (or joints) is to be taken as Uie basis for the valuation of the dis- tance moved. The above described changes in the perpendiculars bear a similar relation to their corresponding angles at tne shoulder in the case of the upwards movements to what 8.12 cm. and 26.42 cm. bear to 26° 56' and 81° 84', and in the case of downwards move- ments to what 9.25 cm. and 5.72 cm. bear to 15° 58' and 17° 48'. These two aocompanvinff diagrams* give us examples as to how these perpendiculfurs stand to their curves or angles at the shoulder. This relanon changes with the starting points. In the horizontal plane both stand in a very close relation to one another. High above and low below, the greatest deviation between the two occurs. Loeb used the two arms in his experiments. The normal arm had always the horizontal plane as starting point, while the starting point for the other arm was varied. 3. The Later One-Handed Experiments of the Winter Semester^ 1892-3. As above mentioned I have made further experiments with spe- cial respect to the changes in the averagre differences which anse through changes in the lengths of the normal curves and in the heighSs of the starting points. The latter I have considered more especially in the two-handed experiments to be described later. The experiments we consider here, consisting of ninety- nine series, were all one-handed. In twenty-nine series the starting points were changed. In all the ninefy-nine series an attempt was made as much as possible to keep the variation of the normal curves for each series small. The number of experiments for each series was ten. The observers were Mr. Ohiid, '^ C, " and the experi- menter himself, '* S. " The former was seated, while the latter remained standing and acted as his own experimenter. The hori- zontal plane for the former was 102.5 cm. above the floor, and for the latter 180 cm. above the same. The number of series made by the first was nine in the upwards direction and eleven in the down- wards; by the last, forty -five in the former and thirty- four in the latter. The beating of the metronome was. with the exception of eleven series, by observer S., where it made 180 beats in the minute, and five others where it made 120, kept at sixty beats to the minute. ^Seetheorigliua. ON THE DIFFERENCE SENSIBILITY. 379 (1.) ObBerver C— The series by observer C. were made, with two exceptions, in order to find out the changes in the average differ- ences caosed by change in the lengths of the averas^e normal curves. In general the average differences were not nearly as larg^ as in the earlier experiments. The variation in the normal carves follow in their relative values the changes in the lengths of the average normal cnrves. Where the latter decrease, so do the for- mer. With the same decrease the average differences in the case of the downwards motions also decrease, and inversely in each individual series the increase in the individual differences is accom- panied by an increase in the lengths of the normal curves. Upwards movements. The accompanying tables* show the two groups of series of upwards mouons by observer 0. Series 4, group n., had, besides the starting point in the horizontal f»lane for the normal curves, a different one for the compared, t is, then, left out of consideration here. The question presents itself here, '^ How does the relative and absolute difference sensi- bility decrease or increase with the increase in the lengths of the normal curves?" The variations of the normal curves and the differences of the normal and compared curves can only be considered as absolute spatial changes, which serve as a basis for an absolute difference sensibility. With the increase in the nor- mal curves they also increase. Hence the absolute difference sensibility decreases. The M. R. V. shows that where the individual differences in each series are considered, each increase in the nor- mal curves, where these are greatest, is accompanied by a decrease in the individual differences; where they are smallest bv an increase, however. The average differences show that with increase in the average normal curves the average differenoes increase in group II., and inversely in group I. decrease. Were the average differences not reckoned out, one could estimate the differ- ence sensibility to a certain extent bv the method of relative dif- ference sensibility. The figures obtained by this method show that in group I. the difference sensibility increases with the increase in the individuaJ normal curves, and this just in proportion as the individual normal curves decrease. In group IT., however, it decreases, and just in proportion as the normal curves increase. Downwards movements. Two groups of experiments were also made by observer 0 in the downwards direction. The M. R. V. shows a constant increase of the absolute values of the individual differences in the series with the decrease in the normal curves, and this the more the average normal curves increase. The average differences in the two groups are themselves different. In series 1-4, group n., they are greater than in series 1-8, group I. The dif- ference sensibility is then inversely greater with the latter. In both groups the increase in the lengths of the average normal curves appears to cause neither an increase nor a decrease in their averase differences. They do not allow of a judgment in regard to the ab- solute difference sensibility. In both groups the norm al variations decrease also with decrease in the average normal curves. As above mentioned there is ffround here for concluding that the abso- lute difference sensibility decreases with the decrease in the lengths of the average normal curves. Changes in the starting points. The two remaining series of downwards movements of observer 0. show with increase of the starting points a greater decrease of the compared curves in rela- tion to their normal. The absolute difference sensibility was great- >8eetiieorigliua. 380 8E6SWOBTH : er above than below, because the differences in both oases were greater. This agrees with what was said in regard to the other downwards movements. (2.) Observer fif.— Upwards movements. The sixgronps of upwards movements of observer S. were made under different conoitions. 