The Flight of Nocturnal Lepidoptera S3 



correlated. Thus "r ^" is the correlation of catch with temperature, 

 etc The "total" coefficients show the relationships between two fac- 

 tors, in the presence of all others, and it is necessary to treat this 

 mathematically in order to eliminate the effects of the other factors 

 leaving a "partial" correlation coefficient which gives the correlation 

 between the first and second factors, the others being eliminated. The 

 notation for the partial coefficients is similar to that for the total co- 

 efficients, except that the two factors correlated are given first in the 

 subscript, followed by a period, then by the factors eliminated. Thus 

 ,'rct. p" is the correlation beteen catch and temperature, pressure 

 being eliminated, and "rct.ph" the correlation between catch and tem- 

 perature, both other factors being eliminated. 



Coefficients such as the last are obtained in two steps, one factor 

 being eliminated at a time by the application of a formula of the fol- 

 lowing form : 



ret (rch X rtb) 



(l-rch2)l'2 (l-rth2)l/2 



which gives the coefficients of the "first order." The remaining factor 

 is then eliminated from each coefficient by the similar formula : 



ret. h (rep. h X rtp. h) 



ret. hp = (Yule, 6, p. 238) 



(1 -rep. h2) 1/2 (1- rtp. h2)l 2 



As correlation makes the assumption that the relation between 

 the variables correlated is a straight line, it becomes necessary to divide 

 the data on the basis of humidity in such a way that the humidity 

 curve becomes two approximately straight lines. This is done by di- 

 viding the data at the optimum, making one set of correlations with 

 the data below 54 per cent relative humidity, and another set with those 

 above 50 per cent, including the optimum in both sets. 



