iRh'r.ari..iRmi.s /.v i.o.inr.n rp.i.r.riio.xr. cinccits 5r.o 



ii is rt'tiiriU'<l to llii- sending t-iul from llii' first irrc^iil.irit\- (assumc<l 

 1(1 Ik- \iT\- iK-ar ilu- si'iidinjj i-iul) 



«i = rjo (14) 



a sfcoiul ciirreiU 



i, = /lVi/a (15) 



is returned from the IrreKuIarity located al a distance of one loading 

 section away from the sending end, since the current is reduced by 

 the factor .4 in going to the irregularity and again in returning. 

 SimilarK', a current 



i„ = .42(— 'V„/„ (16) 



i-> returned from the wth irregularity. 



The tirst current will return to the sending end with a certain 

 phase angle Oi with respect to the initial current, the second with a 

 phase angle H., etc. Kach returned current ma%- be resolved into 

 two components, one in phase with tiie initial current and one in 

 quadrature. 



The in-phase components of the currents are then: 



i\' =/o''i cos 9i from the first irregularity. (17) 



ii =IurtA- cos 82 from the second irregularity. (18) 



/V = /or 3-4* cos 03 from the third irregularity. (19) 



iV = /oN/l^'"~" cos e„ from the «th irregularity. (20) 



and the quadrature components are: 



ii"=/ori sin 61 from the first irregularity. (21) 



i«" =IoriA' sin 83 from the second irregularity. (22) 



«3"=/orj-4* sin 83 from the third irregularity. (23) 



in" = lornA^'-"'^^ sin 8„ frotii the nth irregularity. (24) 



Now the deviations of the inductance (and capacity) resemble the 

 errors of measurement discussed in nvdny text books dealing with the 

 precision of measurement, consequently, they can be studied and 

 their effects combined by the same mathematical law. 



Kxamination of measurements of the inductance of large numbers 

 of loading coils and the capacities of the pairs and phantoms in many 

 reels of cable ha\e shown that the most reasonable assumption is 

 that the deviations of inductance and capacity follow the "normal" 

 law of the distribution of errors. 



The deviation at each irregularity is not known but it is possible 

 to derive from the measurements of the inductance of large numbers 

 of loading coils (and the capacity of man>- lengths of cable) representa- 



