348 



SCIENCE. 



[Vol. XIV. No. 355 



tions as dancing, scanning, and even the fluctuations of sensation. 

 For example : a star just visible to the eye fades away and re- 

 appears. The intervals of this attention v^rave have been measured, 

 and, according to one observer, are from 2.5 to 3 seconds for sen- 

 sations of electrical shock, 3 to 3.4 seconds for light sensations, 

 and 3.5 to 4 seconds for sensations of hearing ; or 24 to 20, 20 to 

 18, and 17 to 15 fluctuations per minute, — a rate strikingly similar 

 to the rate of breathing. It would be interesting to find whether 

 these sensation " waves " vary essentially in persons with abnor- 

 mally high or low respiration rates. Again, the relation of the 

 rate of scanning to pulse and respiration may be tested. One sub- 

 ject, when his pulse tells 77 per minute, reads 113 feet per minute, 

 but, with a pulse of 83, reads 140. Individual differences in pulse 

 and respiration may affect the normal rate of reading. One sub- 

 ject, with a pulse of 86 and a respiration of 26 per minute, makes 55 

 double steps, and reads 126 trochaic feet, in a minute ; while an- 

 other, with a pulse of 66 and a respiration of 22, makes 51 steps 

 and reads 120 feet in the same time. Verse-reading in schools 

 might be similarly tested. In a preliminary test a pupil with a 

 pulse of 85 read 107 feet per minute, another with a pulse of 98 

 read 129. 



In one case Professor Leumann made a distinct test, measuring 

 the pulse at frequent intervals, and also the rate of scannings as the 

 subject was reading. Comparing the rates before an intermission 

 with those after, he finds an almost exact correspondence of scan- 

 ning rapidity with pulse rate. When 40.1 feet are read per minute, 

 the pulse is 85-§- ; when 38.8 feet are read, the pulse is 82!-. 



It is noteworthy, too, that a large range of association times varies 

 between .7 and .8 of a second, — the period of a normal pulse-beat. 

 In reproducing time intervals, the period reproduced with least 

 error is also this same period. These, however, are mere sugges- 

 tions. The outcome of the paper is to accentuate the importance 

 of noting these physiological conditions when studying psychic 

 phenomena, and particularly when making time measurements of 

 them. 



Distance and Size. — One of the most vexed questions of 

 psychological optics relates to the inference of distance when the 

 size of an object is known, or the inference of size when the dis- 

 tance is known. Psychologists are agreed that the process is not 

 immediately given in sensation, but the result of experience. The 

 young infant reaches for things entirely beyond its grasp. Under 

 ordinary circumstances, our inferences of size, though uncon- 

 sciously performed, are extremely complicated. The estimation of 

 half a dozen different kinds of perspective, together with what real 

 knowledge we have of the sizes of the objects in question, enters 

 into the result. To study the question scientifically, we must 

 arrange the observation so as to exclude all but a single variable. 

 When this can be done, as, for example, in the gradual removal of 

 an object from the eye, under proper conditions, the general as- 

 sumption has been that the result depends on the size of the retinal 

 image, or by the angle made at the centre of the eye by the extreme 

 contours of the object. In the last number of the Philosophische 

 Studien (vol. v. No. 4), Dr. Gotz Martins describes a few experi- 

 ments that lead him to question the correctness of this view. At 

 a constant distance of 50 centimetres from the eye of the observer 

 he placed a rod 20, 50, or 100 centimetres long. At a much greater 

 distance (either 2^ or 5i metres) he had a variety of rods, differing 

 from one another slightly in length only. Both were viewed 

 against a continuous and uniform brown background, and the 

 problem of the observer was to judge when the distant rod seemed 

 equal in size to the near one. Even here the fact that we are ac- 

 customed to interpret the far in terms of the near, and pay atten- 

 tion only to estimating the actual size of the object, makes it diffi- 

 cult to separate judgment and impression ; to answer, not whether, 

 if the distant rod were brought side by side with the near one, it 

 would be equal to it in length, but whether the retinal impressions 

 of the two as they are seem the same. After a little practice, this 

 can be done, though the result does not point to a definite length, 

 but to a narrow range of lengths any one of which seems equal to 

 the near rod. Taking the average values, one observer, with 5.25 

 metres between the two rods, judges the distant rods of 21.67 

 centimetres, of 57.62 centimetres, and of 106.62 centimetres to be 



equal to near rods of 20, 50, and 100 centimetres : at 2.50 metres 

 between the rods, the former lengths become 20.62 centimetres, 

 53.87 centimetres, and 107.75 centimetres. Similar results for Dr. 

 Martius are 21.92 centimetres, 59 centimetres, no centimetres^ 

 and 21.62 centimetres, 56.62 centimetres, and 109.25 centimetres.. 

 What these figures show, apart from the facts that such observa- 

 tions are possible and that the result varies with the individual, is 

 that a distant object, to seem equal to a near one, increases in size 

 with the distance, but increases very slowly ; much slower, that is, 

 than the visual angle decreases. It is probable, too, at the same 

 difference of distance, the ratio between near and distant objects of 

 various sizes remains constant. The result requires further corrobo- 

 ration and extension, but, even as it is, is important in rendering 

 improbable the usual view of the matter. 



Sensibility to Tone Intervals. — The ear has been calledi 

 the mathematical sense, because the perception of musical interval 

 involves the nicest appreciation of definite numerical relations be- 

 tween the vibration rates of the tones forming the interval. The 

 very slight deviations from a true interval recognized as such by- 

 skilled musicians, which Helmholtz has satisfactorily explained as 

 due to the relations of the overtones of the two tones, shows us. 

 that the interval sensibility must be very fine. The accurate de- 

 termination of this sensibility for the various intervals has been, 

 attempted by a few methods, but with results individually different, 

 and containing sources of error. The whole topic has been rigor- 

 ously re-investigated by Iwan Schischmanow in the psychological 

 laboratory at Leipzig {Philosophische Sttidien, v. No. 4). The 

 method consisted in adjusting a movable weight on a tuning-fork 

 until (i) it just formed a certain interval with a constant fork, (2) 

 it just appreciably diverged from it above, and (3) just appreciably 

 diverged from it below. The results are then grouped, and aa 

 average formed, expressing in fractions of a vibration per second the 

 difference between the vibration rate of the true interval and the 

 tone just distinguishable as not a true interval. For two observers,, 

 S and K, of whom S is a good amateur musician and K is not 

 musical, the results thus expressed were as follows : for the octave 

 whose ratio is 2 : i, S 0.220, K 0.356 ; the fifth (ratio 3 : 2>, S 0.332,. 

 K 0.374 : the fourth (ratio 4 : 3), S 0.419, K 0.403 ; the third (ratio. 

 5 : 4), S 0.485, K 0.559 ; major sixth (ratio 5 : 3), S 0.502, K 0.506; 

 the second (ratio 9: 8), S 0.548, K 0.716 ; minor third (ratio 6 : 5), S 

 0.607, K 0.640 ; minor sixth (ratio 8 : 5), S 0.672, K 0.740 ; minoir 

 seventh (ratio 9 : 5), S 0.678, K 0.763 ; major seventh (ratio 1 5 : 8)„ S 

 0.861, K 0.902. A comparison of these with former results leadis 

 to the conclusion that practise and individual traits contribute \<t) 

 the result, but that in general the oider of delicacy of the various 

 intervals as shown by S, especially the order of the four '■' besJ '* 

 and the " worst " perceived intervals, may be taken as fairly mot-^ 

 mal. This order corresponds nearly with that elaborated by Hellna,- 

 holtz on the basis of relative consonance of overtones, but it shows; 

 that perceptions of intervals are possible without such an aid'., 1\». 

 numbers show, too, the great accuracy of the sense of musical in^ 

 terval. Another result is that the sensibility for the lowering of an 

 interval is finer than for an increase of the interval, though it must 

 be noted that the variable tone in these experiments was. alwa;^s 

 lower than the constant tone. 



ELECTRICAL NEWS. 



Siemens's Five-Lead System. 



The municipal authorities of Konigsberg, in Prussia, in GonjjujJia> 

 tion with the representatives of the citizens, resolved this spuing: lay 

 carry out, at their own expense, an electric central station foa the: 

 town, which was calculated for a supply of 30,000 i6-candle glow-- 

 lamps, though arrangements are to be made at first for 8,0.00 

 lamps. The entire installation, as it is now about to be executed,, 

 merits the attention of the entire electro-technical world, and' of alll 

 persons interested. A correspondent of the London Eltctr.itali 

 Review, therefore, briefly gives the chief points which wiili be- 

 brought forward in executing the installation. The current willl be,- 

 supplied from four groups of slow-speed dynamos,, arranged! i«i 

 series, and connected directly with the steam-engine. Betwsan.! 

 these dynamos and the conducting net there is placed a, bsttoig ?if 



