280 PROCEEDINGS OF THE AMERICAN ACADEMY. 



particular values of Zi, L^ aud the coefficient of coupling of the two 

 circuits, and is not general so far as the scales are concerned. The 

 shape of the curves is general, however, and, it is hoped, may prove 

 explanatory of the relations of the many variables. 



The curves resembling hyperbolas are each for a constant primary 

 capacity plotted with main current, /», as abscissae, and fundamental 

 wave length of the primary discharge frequency as ordinates. The 

 lower curve, marked " secondary wave length," gives the capacity of the 

 secondary circuit as abscissae and the resulting syntonic secondary 

 wave length as ordinates. The other similar curves are got by multi- 

 plying the ordinates of the last-mentioned curve by 2, 3, 4, etc. The 



remaining curve marked r^ = 1.71, needs a word of explanation. 



Several measurements were taken of the natural period of the primary 

 circuit when adjusted to give maximum secondary current, for different 

 secondary wave lengths, and it was found that this natural primary 

 period divided by the corresponding secondary period was, in every 

 case, within one or two per cent of the quantity 1.71. This would be 

 slightly different for different coefficients of coupling. The curve in 

 question is the locus of the intersections of the vertical C2 lines and 

 the C'l curves which fulfill this condition. 



The use of the diagram of Figure 7 may be made clearer by the 

 following. Suppose that the secondary wave length desired is 

 75 meters. The secondary wave length curve gives 40 X 10~'^ t^.f. 



as the secondary capacity, and passing vertically up to the — curve, 



A2 



it is seen that the primary capacity must be 80 X 10~^ /i./. If, now, 

 the vertical C^, = 40 line be followed to the intersection of the 

 3X2 curve, and then horizontally to the same Ci = 80 curve, aud down 

 to the current axis, one gets the cun-ent /„ = 1.1. This current gives 

 the discharge frequency, with Cg = 80, corresponding to a wave length 

 of 225 meters, which is three times the secondary wave length, and 

 therefore shows that, with that /„, the primary condenser is discharg- 

 ing every third secondary oscillation. In other words, the I. C. F. is 

 3. Similarly it is seen that for an I. C. F. of 4 the main current must 

 be 0.69 amperes ; for I. C. F. equal to 5, Ig must be 0.54 amperes, etc. 



Among other things the diagram shows that in general the supply 

 currents which give the large values of I. C. F. differ but slightly, 

 which is an advantage for some purposes. It is readily seen that 

 small values of I. C. F. are impossible to obtain unless the wave length 

 is short and the supply current very large. 



The coupling between the primary and secondary circuits should be 



