matter on the surface of the cylinder, or -, be to 60 1.00 64 , or as 129 is to 100. This ratio may be stated more accurately as 1.30 to 1.00, which is the mean of a great number of experiments.
Exp. 2. When the cylinder was 15 or even 10 inches When the diameter of the cylinder was two inches, the mean density of the cylinder was to that of the globe as 1.00 to 1.30 When the diameter of the cylinder was one inch, the mean densities were as 1.00 to 2.00 When the diameter of the cylinder was two lines, the mean densities were 1.00 to 9.00 Hence the augmentation of density follows a smaller ra tio than the diameters of the cylinders.
This experiment furnishes us with a beautiful expla nation of the influence of points in dissipating electrici ty. Points may be considered as cylinders of small dia meter and great length. Now, in the preceding expe riments, we have seen that a cylinder two lines in dia meter, and 30 inches long, had its electric density nine times greater than that of a globe. But when a cylin der was electrified and terminated by a hemisphere, the electrical density of the extremity was to that of the middle of the cylinder as 2.30 to 1.00. Now, this ratio ought to be greater when the cylinder is very long, and has one of its extremities in contact with a large globe. Suppose, therefore, that the cylinder, two lines in diame ter, has its extremity rounded into a hemisphere, the electrical density of the extremity of the axis will be to that on the surface of a globe of eight inches, as 9X 2.30=20.70 is to 1.00 ; but as the air is an imperfect electric, it follows, that in making small cylinder touch a globe of eight inches diameter, the electric fluid ought to escape by the extremity of the cylinder, with a degree of rapidity proportional to the electrical density of the globe.
Mien the globes have a diameter much greater than that of the cylinder, eight times greater, for example, or more, the elect, ical density of the different globes in contact with the cylinder being supposed equal to the same quantity I), the densities or the electric fluid on the surface of the cylinder, will be to one another as the diameters of the globes. If, for example, we take the globe of eight inches in contact with a cylinder of one inch, we have seen that the density of the globe being D, that of the cylinder is nearly 2 D ; but if in place of the globe of eight inches, we put in contact with the same cylinder a globe of 24 inches, and whose electrical density we suppose to be D, then the mean electrical density of the fluid in the cylinder will be nearly equal to 6 D.
From the preceding experiments, we may determine the ratio between the electrical density of a globe, and that of a cylinder of any diameter, touching the globe by one of its extremities. It follows, from the results in Exp. 4. that the electrical densities of different cylin ders are in the inverse ratio of the power of their dia meters, which approaches very much to unity when the diameter of the globe is very much greater than that of the cylinder. For different globes and the same cylin der, the density of the cylinder will be as the diameters of the globes, if their diameter is much greater than that of the cylinder. Supposing D, then, to be the den sity of the globe, R its radius, d the mean density of the DR cylinder, and r its radius, we shall have d = m or 71 d = in when R is much greater than r. In this equation, the constant co-efficient 7n may be determined from experiments in the following manner.
When a globe four inches radius was in contact with a cylinder 30 inches long, and two lines in diameter, the mean density of the cylinder rd was d=9 D. But R 4 inchesin this case = 1 line = ' in 48 hence d = 48 D, and 48 m d=9 D, and dividing by D, we have in= the constant co-efficient.
48' Coulomb has applied this result very beautifully to the phenomena of the electrical kite flying in a thunder storm, and having its cord made to conduct by a wire, insulated at its lower extremity. The cord of the kite emits sparks with the greatest violence to all the con ducting bodies in its neighbourhood. Let us suppose that the cloud charged with the electric fluid has the form of a globe 1000 feet radius; that the cord of the kite is one line in radius ; then the mean density on the m DR surface of the cord will be d= , and X12X12XD=27000. But we have already seen, that the electrical density at the end of a cylinder terminat ed by a hemisphere, is to the density of the middle as 2.30 is to 100 ; consequently, d=2.30 x2700 D=62000D, or 62,000 times greater than the density of the fluid which is supposed to reside in the surface of the cloud. It is, therefore, not to be wondered at, that the electric fluid, in a state of such high condensation, should be emitted in sparks on every side.