166 The Ohio Journal of Science [Vol. XVIII, No. 5, 



That over the other half has to do with the receiver. Accordingly 

 we can take 

 rt2y\ 



A = 4" 



2- 



cos — ox = — ^ sm 7 cos 7 and A- = — ^ . 



X 2x 4:Tr 



t' 



4 ' n 



Call ° ° = C. Then our expression for E becomes 



E = C X* sin- 



7COS^7[-^7^^cos-^7^''+|('-,''-7)|(^-7)(2cos27+l) 



+3 sin 7 COS''' 7 (1 + sin- 7) —5 sin^ 7 cos 7+4 sin 7 cos 7. > I . 



Now Abraham's theory for the transmission of electric 

 waves along a pair of parallel wires does not take into account 

 the necessary bending of the wires leading up to the plates. 

 For obvious reasons the ideal case shown in Figure 3 cannot be 

 realized unless one has a rather large distance between the 

 Lecher wires, which means a long bridge and larger phase- 

 changes due to the bridge length. Blake and Sheard have 

 shown that there are two factors, which they called 6 (y) and 

 0(7/) controlling the relation between the edge-on distance 

 between the plates and the tone intensity. The former rep- 

 resents the electrostatic leakage to plates of the same circuit, 

 the latter the phase-changes due to that portion of the wires at 

 right angles to their main length. They have shown that these 

 two factors act in opposite directions and the preceding paper 

 confirms this. Abraham's theory does not consider either of 

 these factors. We have m.ade no attempt to determine the 

 nature of either of these functions of y, (though the exper- 

 imental data of Blake and Jackson are probably sufificient to 

 determine both). They have determined, however, the opti- 

 mum value of y for each frequency, that is, the value of y at 

 which the tone intensity is a maximum. Obviously, this 

 optimum value of y is that value at which these two factors 

 nullify each other. 



If then we compare the tone-intensities for the various 

 optimum values of y they should agree with the simple theory 

 of Abraham that neglects the two factors mentioned above. In 

 making the theoretical calculations, however, some circum- 

 spection must be used. For instance, theory and experiment 

 should not be expected to agree except at or near those values 



