Primary/Secondary Frequency Difference?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

I have run the numbers and the figures for the primary do not appear to agree
with the figures for the secondary.
 
 
The formula for inductance is Wheeler's formala for a flat spiral ie.
L = (r^2*n^2)/ (8*r + 11*w)
 
 
I have trimmed the primary leads to a total of no more than 2 metres and have
increased of turns to the tapping point from 3 1/2turns  to 5 1/2 turns for
best performance (where spark length is at its max length of circa 2 inches)
Now here is the problem- Looking at the table primary resonance should be
somewhere between 1178 and 972 kilohertz,yet acccording to  my calculations
(using Wheeler's and Medhurst's) secondary resonance for 10 7/8" tall 3" dia
440 turn secondary should not be more than 700kHz, even without a toroid.
 
 
Min rad, Pitch and Capacitance are all constants:
minrad 1.5   
pitch 0.375    
capacitance 4.7E-09     
 turns ave rad max rad     w                      inductance                kHz
 1       1.6875     1.875     0.375                0.165081522            
5713.759691
 2       1.875       2.25      0.75                 
0.625                        2936.508038
 3       2.0625     2.625     1.125                1.37964527              
1976.45752
 4       2.25         3           1.5                   2.454545455            
1481.7866
 5       2.4375     3.375     1.875                3.883272059            
1178.073247
 6       2.625       3.75       2.25                 5.702586207              
972.1544602
 7       2.8125     4.125     2.625                7.950721154              
823.3186278
 8       3             4.5         3                  
10.66666667                  710.8154205
 9       3.1875     4.875     3.375             13.88983386                 
622.9062338
 10     3.375       5.25       3.75               17.65988372                
552.4300352
 11     3.5625     5.625     4.125              22.01663306                
494.7613325
 12     3.75         6           4.5                
27                                446.7754702
 
Capacitance in Farad.
Inductance in microhenry.
w = max rad" - min rad"
Min rad, Ave rad, Max rad, and w all measured in inches
 
Are calculated figures likely to be significantly inaccurate, or are small
construction errors likely to result in gross deviations from calculated values
-I am speaking particularly with regard to the primary capacitance and the
primary and secondary inductances.
I understand that 24SWG wire (0.022" dia) is a bit thin for a primary but could
this account for apparently wide differences between the calculated primary and
secondary resonant frequencies?
Also, is it likely that the coronal sheet around the saltwater capacitor is
increasing the plate surface area and hence increasing capacitance
significantly -making the primary resonate at the frequency of the secondary
with fewer turns?
 
Jolyon.