Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 82

convenient of the two. I have also found it practicable in some cases to avail myself of some methods of tuning allowing exact observations as to the rise of pressure in the excited circuit, and to tune a small number of turns first to a much higher harmonic and, after completing this adjustment, to calculate the dimensions of the coil for the fundamental vibrations from the experimental data secured. But in most cases such resources are not readily available and an approximate idea must be gained in other ways. There are a number of different considerations which, when followed out in connection with the preceding, will lead to the establishment of simple relations between the quantities primarily adopted and will enable an experimenter to construct such a coil to suit source, without previous experiment and some of these I propose to consider on other occasions. Presently I shall indicate a way which, in some cases to which the calculated data were applied, has given satisfactory results.

The ideal capacity C which should satisfy the equation LC = $! {1 \over p^{2}} $! is always a function of the distributed capacity C₁ and furthermore a linear function, so that C = K₁C₁, where K₁ is a constant, the value of which is to be deducted from the results of many varied experiments carried on to this end. But this capacity C₁ is, as has been found in many experiments with coils of widely different dimensions, directly proportionate to the length of wire and to the diameter of the same and furthermore to the diameter of the drum. The latter will be understood when it is considered that the greater the diameter of the drum the greater is the potential difference between the turns and, consequently, the greater is the amount of the energy stored in the coil with a given length and diameter of the wire. Finally the quantity C₁ is inversely proportionate to the distance of the turns τ. As to the dielectric constant it is only then important to consider when the turns are quite close together so that the entire space between the turns is filled with the dielectric. When the turns are far apart this constant may be taken = 1. From this it follows that the capacity C interpreted as above may be expressed by the following equation: $! {C = K {Ddl \over {τ \times 9 \times 10^{11}}}} $! when the dielectric constant can be neglected. Here D is the diameter of the drum, d diameter of the wire, l length of wire, τ the distance between the turns. C is the “ideal” capacity which will satisfy equation LC = $! {1 \over p^{2}} $! expressed in farads. The constant K is determined by practical experiments. When the turns are very close the dielectric constant must be introduced and C will be multiplied with the latter quantity. Now the inductance of the extra coil to be constructed is L = $! {{4 \pi A N^{2}} \over {1_{1} \times 10^{9}}} $! henry. Here A = area of coil in cm. square, N = number of turns, and l₁ length of coil in cm. Now A = $! {{\pi \over 4} D^{2}} $!, l₁ = $! {N (τ+d) } $!. Hence the inductance will be L = $! {} $! = $! {} $! henry. Taking these values for L and C we have, with reference to above, $! {1 \over p^{2}} $! = $! {{{\pi^{2} D^{2} N} \over {(τ + d) 10^{9}}} \times {{dlD} \over {τ \times 9 \times 10^{11}}}K} $! or $! p^{2} = {{(τ + d) τ \times 9 \times 10^{20}} \over {\pi^{2} D^{3} d l N K}} $!

Since in the preceding the diameter of the drum is assumed, from practical considerations it will be convenient to find the number of turns N. The quantities D and τ are,

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