1002 m. F, JENKIN’S EXPEEIMENTAL EESEAECHES ON THE TEANSmSSION 
amplitudes for all speeds through all lengths of cable ; and conversely, the obseiTations 
made on various lengths should, when thus geometrically represented, agree in defining 
one curve. The agreement between theory and observation may be very readily tested 
by comparing the observations through various lengths in this manner. But Professor 
Thomson has also stated *, as a development of the theory, that if the resistance of the 
battery and receiving instrument bear but a small proportion to the total resistance of 
the cable, their effect in retarding and weakening the signals will be sensibly the same 
as that of adding an equal length of actual cable with its usual electrostatic capacity. 
(Evidence before Board of Trade Committee.) 
It will thus be necessary, in comparing the observations, to add in each case 160 
knots, equivalent to the resistance of the battery and galvanometer, to the length of the 
cable. Table XV. and fig. 11, Plate LI. show the results of the comparison. The first 
and second columns of the Table give the number of beats and corresponding amplitudes, 
extracted from Tables IV., VI., and XIII. The third column contains the product of 
the number of beats into the square of the length of the cable. The fourth column 
gives the similar product when 160 knots has been added to the length of each cable. 
Fig. 11 gives the geometrical representation of the observations made by using 
the entries in the second and fourth columns of the Table as ordinates and abscissee 
respectively. 
The star, cross, and circle respectively denote observations with 1500, 1802, and 
2192 knots in circuit. All these marks fall sensibly on one curve, affording a perfect 
experimental proof that the rate of transmission does vary inversely as the square of the 
lengthy whether hy rate of transmission he meant that speed at which the repeated signals 
fail to produce any sensible effect, or the rate producing so great an amplitude that 
common hand signals can he received without confusion. 
Moreover, it will be found that the curve is more accurately defined by taking the 
absciss® from the fourth than from the third column; verifying Professor Thomson’s 
conclusion as to the effect of the resistance of the battery and receiving instrument. 
These points have been much debated, but no doubt should now be felt of the sound- 
ness of the theoretical conclusions. 
The above is neither the only nor the most remarkable confirmation of the mathe- 
matical theory. Professor Thomson has been so kind as to give the author a Table 
(XVI.f) of calculated ordinates for the curve in question J. The full black line (fig. 11) 
was constructed from this Table, and coincides with the recorded observations in the 
most striking manner ; no more perfect verification of complicated mathematical calcu- 
lations was probably ever obtained by experiment. 
The curve shows at once the relative number of signals per minute which will pro- 
* Vide Evidence before the Committee of the Board of Trade on the Construction of Submarine Cables, 
A.D. 1861, p. 125. 
. t Appendix, Section II. 
J Proceedings of the Eoyal Society, 1855 and 1856, and Philosophical Magazine, 1856 and 1857. 
