42 BULLETIN 1339, U. S. DEPARTMENT OF AGRICULTURE 



From values found in Table 2 are derived the following values of 

 the correlations specified, used in calculating the value of the unknown 

 factors influencing change of colony weight during the spring period: 



Diurnal 



r . T = .7529 r T .rv= .5717 r TV .Bv = .7855 



r a .Tv= .5967 r T .s = —.1551 r T v.s = .7327 



To. h = -.3806 t t .bv= .3899 rir. j»= -.7584 



r a .Ev= .4229 r T .s = .5798 r fl . s =-.6420 



r .s = .6124 r^. H =-.7113 r H v. 8 = .6780 



Nocturnal 



r L . T = .1754 v t .tv= — .0739 7>».ff =—.5655 



r £ . r „ = -.3439 r T . H = -.0043 r™..Ht> = ,4493 



ri.H = -.1264 7>. s „=-.3373 /•*.*„ = -.6819 

 r L .Rv= —.0654 



Solving, we find the values of the path coefficients to be — 



a = .6898, Z> = .0630, c=-.3217, d=-.2075, e=.1004 



By knowing the values of the path coefficients, the value of o 2 can 

 be determined from the following formula: 



PotTot + JparvToTv + PgbTqb + PqbvTqbv + pasTas = 1 — O 2 



and is found to be — 



o 2 =. 34705 



the degree of determination of unknown factors for the spring 

 period. 



In determining the value of the unknown factors influencing 

 nocturnal loss during the spring, only four variables were used, 

 namely, nocturnal average temperature, temperature variation, noc- 

 turnal average relative humidity, and variation of relative humidity. 



The values of the path coefficients were obtained by solving the 

 following simultaneous equations: 



Tlt = Qj ~\~ OT'tvt ~f~ CTffr ~r CLTbvt 



ThTv = (LTttv ~r t CTbtv ~r (LThvtv 



r L H =ar T H +br T vn +c + dr B vB 



Vlhv — (LVtbv + OTtvhv ~f~ CTbbv ~f~ u, 



and are — 



a=.07329 0= -.58681 c= -.57172 d= -.16688 



The values of the unknown factors are determined by substituting 

 the known values and solving the equation — 



PltTlt + PltvTltv + PlbTlb +PlrvTlbv = 1 — 2 



whence — 



o 2 =-.70268 



