The 'Multiple Balance' can be thought of as the big fish in the sea of UEF, changing its body to cope with the invisible (and changing) field. How fast does the fish's body change, can be a direct indicator of how fast the field changes.
The point of equilibrium in the multiple Balance is of special importance. It is 'nudged' towards a value of 1 by gravity in the rods that are closer to the surface. I am presenting the equations below.
Figure1, shows the Multiple Balance, the red spheres are the masses. Each mass is separated from its neighbor by .
The rods have been assumed of negligible mass but sufficient strength.
We will consider the nth rod configuration, where the mass 'm' is at a distance n from the surface. Total number of masses below the nth mass = n-1+1 (bottom rod supports 2 masses) = n. Figure2 shows the nth rod configuration.
Considering moments about P, eq1. (Where g' is the acceleration due to gravity at distance n from the surface). The value of F (which is the sum of all the forces being exerted on the masses below the nth mass) is given by:
Substituting the value of F in equation1:
(eq2) Please note n *belongs to* N.
The above equation yields the value of n which is clearly independent of
Testing equation2 for value n=1, we have n = 1 which is true for the bottom rod.
Figure 1(a) shows another form of the Balance. In this apparatus, the spherical masses are absent, but the rods have been assumed to have mass. Mass per unit length == m/l. Rest, everything remains same as in the original Multiple Balance. To derive the equations, we will again consider the nth rod configuration.
Since the rods have an even distribution of mass, we will consider an infinitesimally small element dx at a distance x from the equilibrium point. This element contributes to the moment given by xg dx.
Thus total moment provided by l2 =
Similarly, total moment provided by l1 =
F is the total weight of the remaining rods below the nth rod, given by
Thus we have
Substituting the value of g, we have
Canceling the terms on both sides, we have
The term above still gives us the equilibrium point though not in the ratio form.
Moving further, it can be easily noted that n is a characteristic of the field and the Multiple Balance.
However, it does yield another quantity which is a characteristic of the field. This quantity will be the rate of change of value of n as we move to higher rods.
Let's call it (gravity gradient). I investigated n-1 , n and n+1 for various values of n, but they seem to be in some mysterious progression. Perhaps a new mathematical series. If anybody has software that can graph series and sequences, try plotting the n against various values of n.
Now some readers might groan "Where is this leading to?" So, here it is: I suspect sequence is unique to each patch of land on this planet (and other planets for that matter). It is independent of the length of the rods (if a different length of rods was taken, the ratio would still be the same!), and the masses of the spheres in the multiple balance. But since the mass distribution below the surface determines the gravity, any change in it will change the sequence too!!
So, multiple balance might be capable of detecting differences in the local UEF of any number of places, and not to forget about the UEF fluctuations at the same place!! (Ladies and Gentlemen, we have a geological instrument on our hands) It is not hard to guess that this instrument will be affected by the underground magma flow, underground water distribution, displacements of layers of rocks deep below etc etc and last but not the least, earthquakes!!
Well, in that case the good old seismograph will be a better instrument!
Here is how it can (and hopefully) will be put to use: (refer to figure3)
A cylinder of a researched length and diameter big enough to just accommodate the entire balance without any sphere touching the wall, will constitute the outer casing. The top of the cylinder will be the point of suspension of the balance which will hang freely inside this cylinder. A vacuum pump brings the air pressure to minimum preventing any air currents from affecting the structure. Two strips of a suitable material (bright green), will keep the rods from turning about their points of suspension. The blue boxes are the sliding mechanisms that will automatically slide to bring point P to equilibrium if the field of gravity changes.
Won't their mass affect the accuracy of the balance?
NO!! The equations are free of any mass either of the spheres or earth. But, extreme caution should be exercised in designing and making the sliding mechanisms. They should be of EQUAL mass and sensitivity.
(Some trouble there, but I am sure modern technology will take care of that).!
The sliding mechanisms can be designed easily (have one design in mind already). One point to be noted: the balance's accuracy will increase with the number of rods employed. (Please refer to equation3) This is because 'n' will increase, contributing to the accuracy. The length of the rod in the balance perhaps contributes to sensitivity, research needed.
The magenta lines are the scales. These scales pass very close to the sliding mechanisms and are illuminated by a laser pointer fixed on the blue boxes, which in turn generates signals in the scale which are picked up by a computer, courtesy modern electronics. Yes, there can be a lot more clever improvements in this design, especially using laser sensors that can detect even the minutest fluctuations. But the spine of this idea is that when a variation occurs, it will be first felt in the lower regions and then in the higher ones.
The computer analyses the inputs and computes the value of and of course any changes in it. (So, if this structure is built on an active volcano and the computer lights up, the personnel better start running downhill to the city). A more interesting version will be a portable one where some miniaturization of the sliding mechanisms will be required. With this version, one can compare (and investigate) the value of at many places. Anybody volunteering to check in the Bermuda Triangle? Lastly, I think that astrology which makes predictions based on the birthplace and even regarding change of place might be a clever science after all.
The equilibrium points of the two structures might be a key to something more fundamental or might be nothing more than trivial algebric expressions.
I end this paper by quoting a few lines from 'Probabilites of The Quantum World' by Danile D. Danin (MIR PUBLISHERS MOSCOW)
"The Balmer formula described the regularity of the spectral lines of Hydrogen: to adapt Bohr's words, nobody thought that this formula provided evidence of fundamental laws of Physics. The school teacher Balmer certainly did not imagine that when he published the formula in 1885. He had simply once boasted that he could find a formula establishing a relationship between any given four numbers, in response to which a friend gave him the wavelengths of red,green,blue and violet spectral lines of Hydrogen to try. He pulled off the trick, and for 28 years upto 1913, the brilliant result of this number trick remained uninterpreted by physicsts. Nobody could even imagine that behind the simple arithematics of the Balmer rule, the atomic depths yawned invitingly."
Author: Eklavya Yadav (91-141-2554259)
Add: 14/13 Mal. Nagar Jaipur, Rajasthan, India 302017