Prof. Perry on Long- Distance Telephony. 



225 



Table II. — Limiting distances Y in millions of centimetres 

 for various amounts of leakage and self-induction. 



Values of 

 SXIO 10 - 







Values of £xl0 10 . 







2-6373 



26-373 



79-118 



131-863 



184-61 



263-73 



1-459 



1-484 



1-778 



2-665 



3-719 



4-996 



7-239 



•01 







1-783 











•10 







1-800 











1 







1-893 











5 



1-889 



1-927 



2-424 



4-142 



6-674 



10-472 



20-29 



10 



2-426 



2-482 



3-297 



6-639 



14-130 



28-88 



116-36 



20 



3-752 



3-874 



5-796 



18-700 



82-59 



very 

 large 



18-184 



7512 



40 



7-292 



7-649 



15-152 



566-36 



76-55 



7-214 



70 



15-216 



17-342 



57-965 



76-304 



11-493 



5-266 



2-815 



100 



27-078 



30-147 



283-49 



22-70 



0354 



3-267 



1-810 



150 



58-35 















200 



106-43 















250 



170-36 















It will be noticed that although X and Y are derived in 

 different ways, by taking certain values for m and n they 

 could be made much the same in value, and altering s or I 

 seems to produce the same sort of effects on X and Y. 



Mr. Beeston has drawn curves from the calculated numbers, 

 but these need not be published. 



If there is no self-induction, increasing the leakage increases 

 the distance to which we can telephone. If there is no 

 leakage, increasing the self-induction increases the distance. 



When the amounts of s and I are not too great, increasing 

 either increases the distance. These and other important 

 facts are visible in the tables. 



Without such tables as these and this method of study it 

 would be almost impossible for the average mathematician 

 to make anything of his mathematical results. Thus, for 

 example, when equation (1) applies to such a function as smpt 

 it is just the same as 



d 2 c ( sr\ d% n 7 dc , v 



Hence we see that the effect of leakage is to diminish the 

 self-induction by the amount sr/kp 2 , and to increase the 



