ELECTRICITY. 



4-55 



When the 

 cylinders 

 have the 

 same 



lengths but 

 different di< 

 misters. 



when the cylinder was only two lines in diameter, and 

 six inches long, the mean density of the cylinder was 

 to that of the globe as 8 to 1. 



E.rp. 4. When the globe was eight inches in diame- 

 ter, and 30 inches long ; then, 



When the diameter of the cylinder 

 was two inches, the mean densi- 

 ty of the cylinder was to that of the 

 globe as '. 1.00 to 1.50 



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 

 ratio than the diameters of the cylinders. 



F \-phnation This experiment furnishes us with a beautiful expla- 

 of the c- nation of the influence of points in dissipating electri- 

 city. Points may be considered as cylinders of small 

 P UiU ' diameter and great length. Now, in the preceding 

 experiments, we have seen that a cylinder two lines in 

 diameter, and 30 inches long, had its electric density 

 nine times greater than that of a globe. But when a 

 cylinder was electrified and tenninated by a hemi- 

 sphere, 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 cy- 

 linder, two lines in diameter, has its extremity round- 

 ed into a hemisphere, the electrical density of the ex- 

 tremity of the a\is will be to that on the surface of a 

 globe of eight inches, ag 9 x 2.30=20.70 is to 1.00; 

 but as the air is an imperfect electric, it follows, that 

 in making the 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 rapi- 

 dity proportional to the electrical density of the globe. 

 When the When the globes have a diameter much greater than 

 globes have tnat f tnc cylinder, eight times greater, for example, 

 drfticntdi- or more, the clectric.il density of the different globes in 

 ameters and contact with the cylinder being supposed equal to the 

 the cylinder game q uallt ity 1), the densities of the electric fluid on 

 IL ' 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 li 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 F,xp. 4. that the electrical densities of different cy- 

 linders are in the inverse ratio of the power \ of their 

 diameters, 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 

 cylinder, the density of the cylinder will be as the di- 

 ameters of the globes, if their diameter is much great- 

 er tlian that of the cylinder. Supposing D, then, to 

 be the density of the globe, R its radius, d the mean 



density of the cylinder, and its radius, we shall have r>e 



1 - T> 



OT d = , when R is much greater 



d = 



n DR 



; r 



than r. In this equation, the constant co-efficient ni may 

 bedetermined 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 tf=.9 D. But 



in this case = -^ - = 48 ; hence d = 48 m D, 



r 1 line 

 and 48 m d =. D, and dividing by D, we have 



m = , the constant co-efficient. 



Coulomb has applied this result very beautifully to Phenomen. 

 the phenomena of the electrical kite flying in a thun- O u ^^"' 

 der-storm, and having its cord made to conduct by a ^pi^ned. 

 wire, insulated at its lower extremity. The cord of the 

 kite emits sparks with the greatest violence to all the 

 conducting bodies in its neighbourhood. Let us sup- 

 pose that the cloud charged with the electric fluid has 

 the form of a globs 1000 feet radius ; that the cord 

 of the kite is one line in radius ; then the mean den- 



. m DR . 

 sity on the surface of the cord will be d= , and 



rf= T '-j x 1000 X 12 X 12 X D=27000. But we have al- 

 ready seen, that the electrical density at the end of a cy- 

 linder tenninated by a hemisphere, is to the density of the 

 middle as 'J..-50 is to'lOO; consequently, d'2.m X STOOD 

 =62000 D, or 62,000 times greater" than the density of 

 the fluid which is supposed to reside in the sin-face 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. 



E.I/I. 5. Having electrified, positively, a globe eight A globs 

 inches in diameter, and nl.-o the needle of the balance, he *;* j" 

 found the electrical density of the globe to be 144 , by Uu 1)Iane 

 means of a small globe one inch in diameter, and then 

 touched the globe with a circular plane 16 inches in 

 diameter and Jth of a line thick, so that a diameter of 

 the globe was perpendicular to the plane at the point 

 of contact. lie again determined the electrical densi- 

 ty of the globe by the small one-inch globe, and found 

 it equal to 47. The electricity of the globe being re- 

 duced from Hi to 47, the plane obviously carried off 

 14447=97 ; so that the quantity taken by the plane 

 was double that which it left in the globe. Now, since 

 the area of a globe of eight inches in diameter, is = 201 .<>', 

 and the area of both the surfaces of the circular plane 

 = 403.2, which is exactly double of the former, it fol- 

 lows, that the electricity is distributed between the 

 plane and the globe, in the ratio of their surfaces. 



The preceding result was obtained in a great num- 

 ber of other experiments made with globes nnd planes 

 of different sizes ; and the ratio above mentioned was 

 always more exact when the plane was small in pro- 

 portion to the surface of the globe. A plane, for example, 

 six lines in diameter, when made to touch tangentially 

 a globe of eight inches, takes upon each of its sur- 

 faces an electrical density equal to that of the globe, 

 or, what is the same thing, the small plane is charged 

 with a quantity of electricity double that of the portion 

 of the surface of the globe which it touches. 



Exp. 6. Having insulated an electrified globe A, 

 eight inches in diameter, and also two equal globes b, c, 

 two inches in diameter, placed at a distance from it, 

 b being insulated upon a cylinder of glass coated, and PLATE 

 surmounted by four Vanehes of gum lac, and c being ^ X ^ V ' 

 insulated by a vertical support, the same as in Fig. 3, Mg ' 



