Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 266

Inductance of extra coil before measured was 0.02042 henry. This owing to one turn less without change of length should be reduced to ratio $! {\left({105 \over 106}\right)^{2}} $! or about 2% making the inductance very approx. 20,000,000 cm. or 0.02 henry.

From the above:

$! {{{2 \pi \over 10^{3}} \sqrt{{C_{s}}_{1} \times 0.02}} = {{2 \pi \over 10^{3}} \sqrt{0.1287 \times 0.000079}}} $!

and

C_s1 = $! {{0.1287 \times 0.000079} \over 0.02} $! mfd,

or in centimeters:

C_s1 = $! {{9 \times 10^{5} \times 0.1287 \times 0.000079} \over 0.02} $! = 457.5 cm.

Similarly we have

C_s2 = $! {{0.1287 \times 0.00002526} \over 0.02} $! mfd, or

C_s2 = $! {{9 \times 10^{5} \times 0.1287 \times 0.00002526} \over 0.02} $! = 146.29 cm.

This would give for the capacity of the structure according to this method only C_s1 - C_s2 = 457.5 - 146.29 = 311.21 cm.

This inferior result I attribute to the fact that the capacity is partially to be taken as distributed, owing to the length of the structure. But determining by the same method with a vibration which would be much slower this error should be very small.

Taking now the values for the set of readings with the experimental coil of 346 turns we have:

The inductance of the experimental coil measured being 6,040,000 cm, or 0.00604 henry we have:

T'_s1 = $! {{{2 \pi \over 10^{3}} \sqrt{{0.00604 \times C'_{s}}_{1}}}} $! and T'_s2 = $! {{{2 \pi \over 10^{3}} \sqrt{{0.00604 \times C'_{s}}_{2}}}} $!

from these relations follows:

C'_s1 = $! {{0.0477 \times 0.00005486} \over 0.00604} $! mfd. and

C'_s2 = $! {{0.0477 \times 0.00001116} \over 0.00604} $! mfd

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