802 



SCIENCE. 



[N. S. Vol. XXII. No. 572. 



first marked uneasiness on the part of the 

 insect under treatment. In some cases this , 

 effect is immediate. 



It is to be also noted in this particular that 

 in the case of many specimens the first notice- 

 able effect was an attempt on the part of the 

 insect to clean its antennae. The striking in- 

 dividual variations, in other words, the revival 

 of many subjects after apparent death, show 

 the necessity of extreme thoroughness in field 

 and greenhouse, that is, a long enough ex- 

 posure to insure carrying the insect beyond 

 all possibility of recovery. 



One hour's exposure to one part liquid CS^ 

 to 12,000 parts of atmosphere is apparently 

 sufficient to kill aphids, but in making sug- 

 gestions for practical application, I should 

 certainly urge an hour and a half's exposure 

 to that strength as being more sure, especially 

 with crude CSj. Ants appear generally to 

 succumb to one hour's exposure to one part 

 liquid CSj to 12,000 parts of atmosphere, the 

 same as aphids, and yet in actual practise, 

 to insure the best results, they should be sub- 

 jected to a longer treatment. Aphids show 

 immediately the effect of exposure, and some 

 were on their backs from two to four minutes 

 after treatment, and yet recovered after an 

 exposure of three fourths of an hour to one 

 part liquid OS. to 12,000 parts of atmosphere. 

 Tribolium confusum was observed particularly 

 to clean the antennae immediately upon ex- 

 posure. 



The remarkable vitality of the Aphidae 

 (insects that we commonly regard as ex- 

 tremely delicate) is to be noted in connection 

 with this work. Further, in a few cases we 

 found that some of the insects which recovered 

 such treatment died later, say within twenty- 

 four hours, although the bottles in which they 

 were confined were left open, only slightly 

 plugged with absorbent cotton. This ' ap- 

 parent death' is very deceiving. To all ap- 

 pearances these insects were absolutely dead, 

 perfectly motionless, and in many cases we 

 entered them on the record as dead, although 

 we had to change that record several minutes 

 later, when a wing, a leg or an antenna would 

 be seen to move. Frequently only a slight 



movement of the mouth parts, all other ap- 

 pendages being quiescent, would indicate that 

 the insect treated was still alive. 



F. L. Washburn. 

 Minnesota Experiment Station, 

 St. Anthony, Minn. 



a note on the calculation of certain 

 probable errors. 



The purpose of this note is to call the at- 

 tention of workers in biometry to a point 

 which serves to lessen somewhat the labor of 

 computation in the frequently arising cases 

 when one wishes to test whether a given fre- 

 quency distribution obeys the normal law. 

 Though sufficiently obvious, the point seems 

 not to have been noticed. 



In determining whether a given distribu- 

 tion of frequency follows the normal or Gauss- 

 ian law it has been shown by Pearson^ that 

 the important constants are 



theskewness = |^g-^— g, 



and the ' modal divergence,' 



d ^= skewness X ? • 



All these constants should equal zero within 

 the limits of the error due to random sampling 

 if the distribution be truly normal. 



The probable errors concerned are (for the 

 normal distribution), when iV = the total 

 number of individuals. 



Probable error of skewness = .67449 A/^^ < (i) 

 Probable error of i/^= .67449 -J- . (ii) 



Probable error of 



Probable error of 



/3,=:.67449a/-. (iii) 



d = . 67449 



V4-'^-(^^^ 



It is at once clear that the values of ex- 

 pressions (i), (ii) and (iii) stand in the re- 

 lation to each other of 



1:2:4. 



"■ Biometrika, Vol. 4, pp. 169-212. 



