Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 225

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}} $!

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