December 29, 1893 



SCIENCE. 



53 



SCIENCE: 



Published by N. D. C. HODGES, 874 Broadway, New York. 



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VARIATION IN SPORES OF CORN SMUT. 



BY A. S. HITCHCOCK, MANHATTAN, KAS. 



A DIAGNOSTIC character among cryptogamic plants is 

 the size of the spores. Since the size varies it has been 

 customary in descriptive works to give the spore meas- 

 urements between the limits of observed variation. 

 These limits show the actual variation, or nearly so, 

 only when a large number of observations are made. It 

 is well known that in many cases of original descrip- 

 tions the measurements are founded upon too small a 

 number of spores. But suppose the limit of variation 

 is known, it is still desirable to know the usual size. 

 There are only a few individuals that approach either 

 extreme, and the greater number will lie near the aver- 

 age. 



A curve might be constructed to show the variation 

 of a given species by laying off abscissas representing 

 equal differences in a given dimension and erecting 

 ordinates whose lengths shall represent the number of 

 spores having the corresponding dimension. If this 

 curve descends rapidly from the maximum and afterwards 

 gTaduall)^ approaches the axis, it becomes more neces- 

 sary to know the usual limits than the extremes, since 

 spores lying near the extremes are proportionately more 

 infrequent than where the curve approaches the axis of 

 X more abruptly. The curve will probably always 

 show two points of inflexion, and these two points will 

 represent the usual limits. 



In testing the matter by applying it to the measure- 

 ment of corn smut spores I arrived at a somewhat un- 

 expected result. Spores from several different sources 

 were thoroughly mixed and samples froin various parts 

 of the mixture mounted in water. In taking the meas- 

 urements, all the spores passing within convenient 

 range of the micrometer were measured until about 

 fifty observations were made. The results are in divis- 

 ions of the eye-piece micrometer, each of which repre- 

 sents 3.85 //. The 500 spores measured may be ar- 

 ranged as follows : 



Diameter 1.7 1.8 i.g 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.g 3.0 3.1 



Number 3 2 18 67 92 8g 66 41 38 28 21 20 10 4 i 



Since it is rather difficult to estimate correctly i/io of 

 a division on the micrometer, it will be well to unite 

 the results in pairs. We shall then have: 



Divisions 1.7 i-Q 2.1 23 2.5 2.7 2.9 3.1 



Number 5 85 181 107 66 41 14 i 



If the curve is constructed for this set of measure- 



ments, we find that it is not symmetrical around the 

 axis of Y. It is much steeper on one side than the 

 other. The arithmetical mean does not represent the 

 average diameter. The result shows that the curve is 

 not that of the curve of probabiUty which follows the 

 law of variation in the physical world, but, in this par- 

 ticular case, follows the law governing biological varia- 

 tion. This difference between the laws of variation in 

 the physical and living worlds has been nicely shown 

 by Dr. C. S. Minot.^ He shows that biological curves 

 rise rapidly to their maximum and then fall on the other 

 side much more gradually. 



It will also be seen that over 50 percent of the spores 

 fall between 2.0 and 2.2, and that nearly 80 per cent 

 fall between 2.0 and 2.5 inclusive. 



A similar series of observations was made upon 300 

 pollen grains of Acuida tuherculata, but owing to the un- 

 even surface there was more difficulty in making accu- 

 rate measurements. 



Divisions s.o 5 5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 g.5 lo.o 



Number 4 10 47 67 g6 5.5 g 5 3 3 i 



The observer should be careful to measure all the 

 spores in a given field, otherwise there is a tendency to 

 pick out the very large and the very small ones, thus 

 giving these too great a representation. 



ON THE MEASUREMENT OF HALLUCINA- 

 TIONS. 



BY E. W. SCRIPTURE AND C. E. SEASHORE, NEW HAVEN, CONN. 



In an article on "Tests on School Children," by E. 

 W. Scripture, in the Educational Review, 1893, V. 61, a 

 test on suggestion was proposed, in which a wire was 

 sometimes heated at a given signal and sometimes not. 

 The observer, not knowing the facts of the case, was 

 required to tell when the wire felt hot. When the 

 wire was not heated, but the observer believed it to be 

 heated, the time required for the hallucination to arise 

 was measured. 



This crude idea has been taken up on a larger scale 

 this year, and measurements have been made on sev- 

 eral persons in several ways. The work so far has been 

 considered to be the preliminary or qualitative stage of 

 the investigation. Before proceeding to the careful 

 and laborious technical work necessary for exact meas- 

 urements, which must necessarily take a great deal of 

 time, we wish to secure priority rights as the first to 

 measure hallucinations. In the first place, as the sug- 

 gestion calling out the hallucination is a sensation or a 

 compound of sensations, we can measure the intensity 

 of the stimulus in the usual ways. In the second place, 

 by finding that stimulus whose sensation is not percep- 

 tibly different from the hallucination, we measure the 

 intensity of the hallucination. In the third place, by 

 reacting to the hallucination we record the time required 

 for it to appear; in more accurate work the reaction- 

 time is to be subtracted from the total time, but as the 

 hallucination-time in the cases already investigated 

 ranges from seven to thirty seconds it was of no ac- 

 count. Our work has hitherto been confined to the 

 weak hallucinations of sane people. We find very great 

 differences, corresponding to classes of society and to 

 training in scientific judgment. With abnormal per- 

 sons we shall expect much shorter hallucination-time 

 and much greater intensity. 



'.Vi:. A. A. A. S., XXXIX,, p. 271. 



