Nikola Tesla Books
Books written by or about Nikola Tesla
It may be of further interest to compare the capacity as found with capacities which would be obtained if the surface of the cable were converted into the surface of a disc or sphere, for instance. Taking first the latter and calling its radius r' we have 4â¼r'2 = â¼37,500 and $! {r'^{2} = {37,500 \over 4}, r' = {\sqrt{37,500} \over 2} = {193.65 \over 2} =} $! 96.825 cm. and this should be the theoretical capacity C1 of the sphere. Taking now a disk of radius R, its capacity C2 would be C2 = $! {2 R \over \pi} $!. Now on the above assumption of an equal surface we would have 2â¼R2 = â¼37,500 R2 = 18,750 and R = $! {\sqrt{18,750}} $! = 136.93 cm. Hence C2 = $! {273.86 \over \pi} $! = 87.2 cm. This is still smaller than the capacity of a sphere of the same surface. Suppose now the surface of the cable were converted into small spherical surfaces of a diameter equal to that of the cable and inquire what capacity would be obtained in this manner with the given surface. The surface of one of the small spheres being 4â¼r2 and calling their number n we have 4â¼nr2 = â¼ x 37,500 and
$! {n = {37,500 \over 4r^{2}} = {37,500 \over {4 \times 0.13^{2}}} = {37,500 \over {4 \times 0.0169}} = {37,500 \over 0,0676} = 554,734 = n} $!
The total capacity C3 of all these small spheres, neglecting mutual screening action, will be n times the capacity of one of the spheres and since the latter is = 0.13 we would have total capacity C3 = 554,734 x 0.13 = 72,115 cm.! A very large value indeed, which would have been still greater if the diameter of the spheres would have been smaller. These primitive considerations show that to get the largest possible capacity with a given surface we must use the latter in the form of minute surfaces of the smallest possible curvature. This makes it obvious why exhausted bulbs show under certain conditions such comparatively large capacity. And this explains the virtue of bulbs when used in telegraphy for the purpose of supplanting a large elevated plate or wire leading to a great height. Such a bulb or tube, particularly when filled with hydrogen, is (as I have found) very effective and I look to a valuable use in the future of such rarefied vessels in connection with telegraphy through the media or the like. The greatest capacity with a given surface will, of course, be obtained with spheres of the smallest possible diameter, as the spheres of hydrogen. The next best form to give to the surface would be a cylinder of great length and minute diameter. The above considerations make it plain why thin wires have such a comparatively large capacity. Taking two such wires of the same length L and diameters δ and δ1, we would have their capacities as
$! {{L \over {2 \log_{e} {2L \over δ}}} : {L \over {2 \log_{e} {2 L \over δ_{1}}}}} $! or as $! {{\log_{e} {2 L \over δ_{1}}} : {\log_{e} {2 L \over δ}}} $!.
Now suppose, for the sake of illustration, that $! {2 L \over δ} $! were = 10, and $! {2 L \over δ_{1}} $! = 1000, then the above capacities would be as $! {{1 \over {2.3 \times 3}} : {1 \over {2.3 \times 1}}} $! or as $! {{1 \over 3}:1} $!. In other words, making the diameter of one wire 100 times as great as that of another, but keeping the length of the wires the same, the capacity of the thick wire or cylinder would be only three times that of the thin one.
105
July 24
During that day the notes are divided in three parts (previous day in two parts), which is shown by designation of original handwritten pages. The first part pertains to experiments with oscillator secondary with 35 turns, and it is described on three pages; second part on five pages, pertains to this experiments continuation, and third part on three pages is devoted to the question of oscillator secondary capacitance. The oscillator secondary consists of 35 turns.
When adjusting the oscillator; Tesla most frequently changes the regulating coil in the primary, and so obtains the maximum voltage in secondary (which he determines according to the longest spark). In the secondary he connects "additional coil" to the open secondary terminal. He checks the operation with harmonics so that he doubles the primary capacitance*, and by small regulations of primary inductance he changes the primary operating frequency, in order to achieve maximum effect on the secondary which is supposed to oscillate at double frequency - primary harmonic. He doesn't obtain the expected results and continues the experiment with capacitive loading changes in secondary circuit, and looks for most suitable elements in the primary circuit. He considers that he obtained the best result when sparks in the secondary are most powerful.
In continuation of experiments with the transmitter, he looks for an explanation for the appearance of largest current streamers in the secondary when the inductance of regulating coil in the primary circuit is reduced to a minimum (and then it is practically disconnected from the circuit). Tesla was confused with the fact that maximum voltage at the open end of the additional coil (this coil is connected to the secondary similar as on Fig. 2 on July 11) doesn't occur when the excitation current frequency is equal to the coil's self resonant frequency. After an extensive analysis, Tesla came to the correct conclusion (opposite to the one of June 30 which was correct only in a special case) that in cases where the secondary free vibration is emphasized, parameters, of the primary circuit have to be weighed such as to achieve the maximum voltage in the secondary, and the additional coil self-resonant frequency has to be equal to the frequency of the combined system primary-secondary. It appears Tesla did not assume that when the link is good, the combined system produces a distinguished spectrum during and after spark interruption. It seems to us that much more important is the abovementioned conclusion which he established when combining the experimental results, simple theory and intuition.
When experimenting with his oscillator, Tesla observed that during a discharge in the secondary the sparking appears on lighting arresters as well. As these arresters are connected to the supply feeder, he assumed that the high frequency voltage originates from a wave which propagated through the ground, and at a certain location entered the feeder. The data is missing which would help to establish whether this high frequency voltage is actually a consequence of the oscillator link via supply transformer with the supply feeder.
In third part of notes on July 24 he gives measurement results of secondary coil capacitance as a whole with respect to the ground. He didn't mentioned how he performed the measurement by comparison with standard capacitor and then, by using several methods he calculates the wire capacitance of the same length as coil wire (C1) according to the equation for capacitance of a single ellipsoide of which the longer axis is considerably longer than short one, and C2 according to the equation for conductor capacitance above an ideally conductive plane under the condition when the distance from the plane is considerably larger than wire radius). Expanding on considerations for capacitances, he describes the methods for achieving the largest capacitances, and moves further and further away from his initial topic. He ends the notes with a discussion on the spheres filled with hydrogen which were supposed to have maximum capacitance for given dimensions, and which would therefore be used for telegraphy without wires.
* In order to get the primary to oscillate on two times lower frequency, the capacitance has to be four-fold. It is possible instead of series connection 8-9 jars which is equivalent to 4-4 1/2 jars he connected two previous series connections in parallel, and obtained the equivalent capacitance of 16-18 jars, that is four times larger than the equivalent capacitance of jars connected in series.
