## Nikola Tesla Books

as secondary period of the coil with ball or

$! {T_{s} = {0.8164 \over 10^{5}} = {81.64 \over 10^{7}}} $! Now *T*_{p} was = $! {267 \over 10^{7}} $!, from this

$! {{T_{s} \over T_{p}} = {81.64 \over 267} = 0.306 = {\sqrt{38.1 \over 38.1 + C}}} $! from previous analogy - and from this

$! {0.306^{2} = {38.1 \over {38.1 + C}}} $! or $! {C = {38.1 \over 0.09364} - 38.1 = {{38.1 \times 0.90636} \over 0.09364} = 38.1 \times 9.68 = 368.8} $!

Now

$! {T_{p}' = {{2 \pi \over 10^{3}} \sqrt{0.04 \times {368.8 + c \over {9 \times 10^{5}}}}}} $! and $! {T_{p}'' = {{2 \pi \over 10^{3}} \sqrt{0.04 \times {368.8 + c' \over {9 \times 10^{5}}}}}} $!

but $! {T_{p}'' = {279 \over 10^{7}}} $! and from this

$! {{T_{p}' \over T_{p}''} = {267 \over 279} = {\sqrt{{0.04 \times {{368.8 + c} \over {9 \times 10^{5}}}} \over {{0.04 \times {{368.8 + c'} \over {9 \times 10^{5}}}}}}}} $! $! {1.045 = 279 \over 267} $! and from this

$! {(1.045)^{2} = {368.8 + c' \over 368.8 + c}} $! now *c* = 38.1

$! {1.092 \times (368.8 + 38.1) = 368.8 + c'} $! and

$! {c' = 368.8 \times (1.092 - 1) + 38.1 \times 1.092 = 75.53} $! cm.

This value is but little smaller than that before found. From this result it would then appear that by lifting the sphere from 33.66 to 34.66 feet the capacity was increased from 38.1 to 75.53 cm, or approximately 98.3%, a trifle less than before found.

*Colorado Springs*

Oct. 16, 1899

Inductance of secondary modified by winding another wire No. 10 in multiple with the first. All other particulars remaining:

Readings: *I* = 7.1 *E* = 60.5 *R* = 1.382 ω = 880

$! {E \over I = 8.521} $!

$! {L = {\sqrt{8.521^{2} - 1.382^{2}}} = {\sqrt{70.6975} \over 880}} $!

*225*

Tesla: “System of electric lighting”, U.S. Patent 454 622, June 23, 1891, Appl. Apr. 25, 1891, P-208.

“Electric incandescent lamp”, U.S. Patent 455 069, June 30, 1891, Appl. May 14, 1891, P-213.

October 15

Because of the arithmetical error made on October 9th (see commentary), he mistakenly concludes that the capacities of the ball are now somewhat less than before. Had he used the correct values, his conclusion would have been just the opposite.

October 15

He continues the measurements from Oct. 9 with corrections in parameters according to the results obtained on Oct. 12. Due to a calculation error made on Oct. 9, he draws the wrong conclusion that the newly obtained sphere capacitances are somewhat smaller than the previous one. With accurate values the conclusion would be exactly opposite.