FEEDING PAEAMECIUM KNOWN BACTERIA 153 



An entirely different picture is presented by the combination of 

 A' or B' with C. In the combination A'C, a mixture was ob- 

 tained which proved to be the most satisfactory of all the possible 

 combinations of these three bacteria. The average division rate 

 for the entire time, 131 days, was 1,793. During that time the 

 percentage of high divisions was 40.3 — a higher mark than was 

 reached by the other combinations. The percentage of low 

 divisions, 33.7, is somewhat higher than some of the others, but 

 this is more than compensated for by the exceedingly low death 

 rate of 3.3 per cent. We have here a very striking example of 

 the stimulation of the metabolism of Paramecium when fed with 

 a mixture of a bacterium in itself incapable of maintaining a 

 high rate of metabolism in Paramecium with one which, when 

 fed alone, failed utterly to support life. That this increase in 

 the metabolic rate is of real significance is shown by computing 

 the probable error of the constants of the two uncorrelated series, 

 C and A'C, according to the formula V(Ex)2 + (Eg)-. 



Here, Ei and E2 represent the probable errors in the mean 

 division rates of C and A'C, respectively, when computed ac- 

 cording to Peter's formula for the probable error (Huntington, 

 '18), namely: 



0.08453 , 



E = == (Vi + Vo + V3 + Vn) 



nVn-1 



It is well known in biometry that if the probable error of the 

 difference in the constants of two uncorrelated series is contained 

 more than three times in the numerical value representing the 

 difference in the means under the two experimental conditions, 

 the results are of statistical significance. For such a quotient I 

 have used the expression 'significance factor,' a term suggested by 

 Doctor Obreshkove. It is evident that the greater this factor, 

 the greater the value of the numerical data. In the case of C and 

 A'C, the difference in the mean division rates is 0.760. The 

 probable error of the mean rate of division for C is 0.0462; that 

 for A'C is 0.0624. Applying the formula, V(Ei)2 + (E2)', 

 the probable error of the difference in the constants of these two 

 series, C and A'C, is 0.775. This is contained in the difference 



