I20 



SCIENCE. 



[VuL. XI. No 266 



somewhat different from what Jastrow would make us believe. In 

 the first class of sensations there are two reasons for the existence 

 of a threshold. — a physiological and a psychological. As a bal- 

 ance has a certain limit of accuracy beyond which it does not show 

 differences of weight of two bodies, so our organs of sensation are 

 not able to show differences between stimuli varying only to a very 

 small extent. This is the physiological threshold. But, besides, 

 the advocate of the threshold theory says it is necessary that the 

 sensations should differ to a certain degree, else they cannot be dis- 

 tinguished. He does not say, however, as Jastrow assumes, that 

 the magnitude of this least perceptible difference is the same at 

 -any moment. On the contrary, it depends on the state of mind of 

 the person, and varies just as Jastrow's sensibility varies, every 

 moment having its own threshold, the average of which is the aver- 

 age threshold of the observer. 



The theory of the threshold may be summed up in the following 

 remarks : — 



Two sensations are given, the difference of which is to be judged 

 upon. The judgment can have various characteristics. Either a 

 certain phenomenon is observed which has no immediate connec- 

 tion with the sensations to be compared (for instance, the line divid- 

 ing two fields of various colors is observed), or the sensations are 

 separate in space and time. In this case the conception of the 

 former is compared with the latter sensation. In the former case 

 the physiological threshold is the main consideration, and for this 

 reason it may be omitted in these brief remarks. 



In the latter case let the sensations S^ and S« be given, which are 

 produced by the stimuli i^ and s.^. Let S^ be the first to be ob- 

 served. In making the comparison, Sj will not be correctly re- 

 membered ; but the probability that another and similar sensation, 

 S:^, which would correspond to the stimulus i^, is produced, will be 

 PV= f{s^,si, C) ds, 



the constant depending upon the conditions of the experiment. 



Experiments show that fKincreases when the difference between 

 s^ and .Tj; decreases. Further experiments show that when the two 

 stimuli s^ and s„ differ but slightly, in a great number of cases the 

 ■observer will judge 8-^ = 5^. According to the theory of prob- 

 ability, U' is only very small as compared to all other possible re- 



productions. Therefore the only possible explanation of the fact 

 that the judgment S^ = S2 is comparatively frequent, is, that not 

 only in those instances when ihe conception S^ is reproduced are 

 both judged to be identical, but that sensations varying only slight- 

 ly from S^ cannot be distinguished from it ; and the task of psycho- 

 physic methods is to find the limits of these variations. Mathe- 

 matically the number of observations in which both sensations are 

 considered the same is expressed by the following formula : — 



f^i = / f{s,s„C)ds. 



(Ji and (5 are the upper and lower thresholds respectively. This 

 ■explanation agrees exactly with the observed fact, that slightly dif- 

 ferent stimuli cannot be distinguished; and Jastrow's objections 

 are founded on a misconception of the mathematical basis of the 

 theory. No advocate of the threshold theory assumes, as Jastrow 

 supposes, that below the threshold the probability of a greater error 

 is the same as that of a smaller error. 



In another passage of his critique, Jastrow rejects the use of 

 doubtful cases in the theory of right and wrong cases. It seems to 

 me that his objections cannot be accepted. The fact is, that in a 

 number of cases doubtful answers must be given. In his paper he 

 says, and rightly, that the confidence is increasing with the differ- 

 ence of the sensations. Now, the answer ' doubtful ' is nothing else 

 than an expression of the degree of confidence ; and, according to 

 the above formula, the proper way to include these answers, in the 

 theory is to assume a second threshold which shows the limit of 

 doubtful cases, and this has been successfully done. 



It will easily be seen that variations of a sensation such as as- 

 sumed by the theory outlined above always occur, and that they 

 must prevail in all psycho-physic experiments except in the first 

 class. 



Dr. Jastrow's suggestion to measure the sensibility by psycho- 

 physic methods is a good one. It has been successfully applied for 

 measuring various degrees of attention, and the writer fully agrees 

 with Dr. Jastrow's opinion that this is the most promising field of 

 psycho-physic research. Dr. Franz Bo.\S. 



New York, March i. 



American and Foreign Microscopes. 



My attention having been called to the ' Complaint ' in Scuiice 

 for Dec. 2, 1887, and the following articles on microscopes, the 

 facts did not seem to me fully presented therein. I immediately 

 addressed the following questions to more than twenty of the lead- 

 ing colleges of the country, the Department of .A-griculture, Geolog- 

 ical Survey, and Microscopical Society of Washington, D.C., and 

 Messrs. WoUe and Smith, two of the oldest microscopists in the 

 country. The results are herewith presented, with my own ideas 

 on the subject. 



The questions were, I. How many microscopes of American 

 make have you ? [659.] 2. How many of foreign make ? [434.] 

 3. How many without a joint ? [309.] 4. Do your students 

 work standing, or sitting ? 5. Is the instrument used in an in- 

 clined position to any extent ? 



The figures in brackets give the sums total of the replies. Penn- 

 sylvania University reports 100 American, 3 foreign ; Michigan, 

 120 American, 30 foreign. Of the foreign instruments, 108 belong 

 to Harvard, and 135 to Bryn Mawr, Johns Hopkins, and Massachu- 

 setts Institute of Technology. About 40 jointed instruments are 

 reported used in the upright position ; more than two-thirds of the 

 whole number are used inclined. To No. 4, the answer " Sitting," 

 is almost universal; "Standing or sitting," a few. The following 

 extracts from the replies are pertinent : — 



" I prefer to work it upright, and teach my students so, but they 

 will incline it whenever possible." 



"When long at work, I prefer a vertical tube; but I find for 

 young students the inclined position and the rack and pinion ex- 

 tremely desirable." 



" Only by unfortunates. Of course, the joint is a convenience, 

 but is not, in my opinion, essential." — Harvard College, in 

 answer to No. 5. 



" The instruments are used almost exclusively in the upright po- 

 sition, the tables being low enough to permit of such use with ease." 



— University of Nebraska. 



" Mostly foreign instruments, generally inclined, prefer inclined ; 

 would use it inclined if I could" [of upright instruments]. — GEO- 

 LOGICAL Survey. 



" The latest purchases are American, which are now preferred." 



— Albany. 



" Personally, I believe the best instruments are made in this 

 country." — University of Michigan. 



" In my laboratory (physiology and hygiene), we use forty. I 

 bought the first in 1876, foreign because then cheaper. In four 

 years they were all worthless. We then bought American : they 

 have stood more rough usage, and had fewer repairs necessary, 

 than any others. My work is especially trying on account of the 

 frequency with which acids must be used." 



" I believe the eye is more nearly in its normal and best position 

 when the microscope is inclined." — PRINCETON. 



" My constant companion at my table is Zentmayer's army micro- 

 scope. Have used it twelve or more years, always inclined, or very 

 rarely vertical." — F. Wolle. 



" Twenty-five years ago I got Powell and Lealand's stands. I 

 seldom use their objectives. For long years I have preferred Amer- 

 ican objectives. I have recently seen letters from purchasers of 

 Zeiss apochromatics, confessing that Spencer's most recent glasses 

 fully hold their own, and at less prices." — H. L. Smith. 



" The facility to incline when needed is indispensable." — J. G. 

 Hunt. 



In 1862 I saw much of Dr. Hunt, then unsurpassed as a histolo- 

 gist. He used a Beck best, inclined, in continuous daily work. His 

 experience assisted in the construction of the American Centennial 

 instrument, which he has since used. This is an instance of an 

 elaborate tool employed in actual, original, and long-continued 

 work. After this came the Beck International, costing seventeen 



