Page:Science vol. 5.djvu/36

 |T«- T„ Ko. 1«tA

��cxprocsioiiEi Tor Llic various consLaiils 

CR

��e of the lumps.

��= energy developed in

��ductora.

The energy consumed in the lamiis (Cr) is the aaine as at first, as shown by Professor Carhnrt, and, being constant Cor the plant of lamps, need not lie furlber considered. The total running-expense, then, due to condtictors (Including interest on thelrcoiit), is

��In terms of C-R. This should be a minimum. Its first differential coefficient with reference to k, placed equal to xero, gives

ical section. ' Lhe total ninnl)

1 In, 1 In 1 /—

��^^J^^

��1

�� �^.'SZf ■.■r.-™?"

� ��.■!,.^„.!,^s^.--'^-

�(n-l)'

�-

�■^ ' a'.aca a n.wo

�1.000 011+ Cr l.OIW LOW '■ ■■ 0.31i l.00« - " 0.323

�i!oon

�.0(M JtTS

��PHOfiBsaa Ciauim'B

�� �,

�J

� � �,

�»■<■»

�"■

�• -l'

�n^"*

�Of.

�aC"-i)

�«-i

�JC-lJ

� �IJJOO

�looocii'

�Or

�1000

�1«X)

� � � � � � � � � � � � � � � � �0.2i0

�0.260 I'

� � �D.WU

�0.ST6

�� �,i,-k^"**

�ik-^'^i^.-fy

�i-Vi.

�3 t.ODO

S 1 0.1l|8

S Oj"

�1.000 CE ' O- O.M« "

�1.O00 ' I.OOO

o.su o.ais

�i.aa

oItbi

O.OM

��as the corresponding diSerence of potential s.. .__ termiiiHls of each of the n — 1 dynamos.

Substituting now In these dllTerent expressions, and also in corresponding ones for the Edison sys- tem and for Professor Carhart's plan, values of n from 2 to 0, we have the various data given in the following table.

��Some very interesting comparisons of relative ad- vantages might be noted, did space permit. The most important is the rapid increase iu the ratio of beat- c>nergy to capacity of conductor In the Edison sys- tem, wliic^h might make it necessary to lay the wires so as to admit of pretty free radiation of heat.

Tills question of temperature of electric-lighting conductors promises to protrude itself the more they are laid undergrouTid, Tliu desideratum for an insu- lating covering would seem to be a non-conductor ul electricity and good conductor of heat, — apparently inconsistent qualities. Perhaps the eventual solution will be In bare or loosely covered wires on highly insulated points of support, thus adniilling of free radiation of lieat, like aerial lines. II. M. Paul.

�� �