i: M: CTKICIT v. 



e*riptirc It will appear by exnr: I snvHtli column, thnt 



^ rt ^; the ratio of the electric : . tin- total foriv i- a 



'"* eoMlant quantity ill or while tin- air 



!>.!- tin ;.n.c >!i'^i\ c of ljiin)Jd!:\ . t'n'iis u !:>. !) it Jiillow s 



that the loss of electricity is i 'jiortionul in the 



came State of the air to the < l<rtri'.;:l density. 



From these experiments ('nuli)nih has shewn how to 



determine tin' electricity of the two ! any given 



Thus ('nun the first set of experiments in the Table, 



v lien the dissi] K ition i.s _,', c\ery minute, he has shewn, 



it' we make / = the interval of time, </= the elec- 



i'cach ball, niul 1) tiie primitive density 



liuid in each ball, and u. the modulus 



of the logarithmic systii.;, thin vc shall have 



but as the distance is constant, D* is proportional to 

 the primitive action, and <." to the action while the time 

 is /. Hence in using the ordinary table, where the 

 modulus /t=0.4Si 3, we shall have 



0.4U1 ; /U" 



I palpation 

 of electricity 

 the same 

 for bodies 

 of til fomu 

 and magni- 

 tude* when 

 theqiuntity 

 of electrici- 

 ty U small. 



If we now seek from this formula the value of d 

 in the 1st experiment, h will be found that at the 

 first experiment D 8 = 1 50, and that at the 6th ex- 



j>eriment rf*=50. Hence - / = log. - = log. 

 3, and consequently <= - = 45 toy the experi- 



U.'* jxO 



ment. N'ow the first experiment commenced at 6 h 32' 

 30" and the sixth at 7 h 17', the difference of which is 

 44' 30" instead of 45', as found by the experiment. 



Coulomb has also shewn, that the ratio of the force 

 lost in a minute to the total force, is double of the ratio 

 of the loss of the density of each body to the total den- 

 sity. For calling d their electrical density, and a their 

 distance, then since the two balls nre equal, and receive 

 at first the same quantity of electricity, their reciprocal 



action will be represented by t , and consequently its 

 momentary diminution will be proportional to -f- 

 </'. I lence the ratio of this variation of repulsion to there- 

 puUion itself, will be, neglecting d*, equal to = . But - 



is the relation of the loss of density of each ball to its own 

 density, and consequently the dissipation is only one- 

 half of the diminution of repulsion. Thus in the expe- 

 riment of the '28th of June, the diminution of repulsion 

 was -,', , from which it follows that the dissipation was 



T minute. 



( )ur -author made a great number of experiments of 

 a similar kind with balls of different magnitudes, and 

 when the quantity of electricity, as well as the elec- 

 trical density of each ball, were very different, he 

 always found, that the ratio of the dissipation of the 

 electric force during a minute, to the total force, was 

 uniformly a constant quantity. On the 28th June, for 

 example, though he presented to the ball a a ball dou- 

 ble the size, and though he communicated to this ball 

 a degree of electricity greater or less than that of the 

 ball n, yet the loss of the electrical force was constantly 

 Z ' T per minute. 



The im-t important result, however, which he ob- 

 tained, y>at, that when the i.ir was dry, and the i! 



. . tricity not groat, the r. ,.ae of the 



electrical density to the density itself, was nlv 



nit quantity, whatever was the form, and what- 

 ever the magnitude of the electrified body. This ex- 

 periment was nir.ile with a globe a foot 'in diameter, 

 and with cylinders of all lengths and magnitude* : !> 

 even substituted, in the place of the lulls circles of pa- 

 per and of metal; and, on a day particularly <lr\ . I . 

 armed one of the balls with a small copper'w ire [th 

 of a line in diameter, mid in lines long; and ii: 

 Miring the dissipation of its electricity, lie found that 

 e\ery body which he used on thnt day lo^t , ' th part 

 of its electricity in a minute. It must be earei'ully ob- 

 served, however, that this equality of dissipation exists 

 only when the electric density has been reduced to a 

 certain point ; for, when the elei tricitv is very strong, 

 all angular bodies dissipate their electricity according 

 to a law which will afterwards be determined. 



The nature of the body, too, has no influence on tin- 

 law of the dissipation. On the 28th June, the electri- 

 city decreased ,' T per minute when pith balls were 

 i.~; il ; and the same result was obtained when the balls 

 were made of copper or of sealing-wax. 



The next object of Coulomb was to discover the re- 

 lation which subsisted between the humidity of the air 

 and the dissipation of electricity. He therefore drew 

 up the following Table, in which the /inl column 

 marks the day when the observations were made ; the 

 second the state of Saussure's hygrometer ; the third 

 the quantity of water dissolved in a cubic foot of air, 

 when the thermometer is between 15 and 16 of Reau- 

 mur, according to the experiments of Saussure ;* and 

 the Joint/i, the dissipation of electricity per minute. 



JVrr 



Klcrt. 



Tlic dissipa- 

 tion is the 

 unie fur 

 bodies of all 

 kinds. 



Relation 

 between the 

 dissipation 

 and the hu- 

 midity of 

 the aii. 



If we now wish to determine the law betwwn the 

 dissipation of the electricity and the quantity of water 

 in the atmosphere when the thermometer is between 

 15 and 16, the temperature when the four experi- 

 ments were made, let us call m the power which ex- 

 presses that relation ; then comparing the experiment 

 with the three others, we shall obtain, 



Experiments compared. 



(~.197\ m 

 rr- \ , whence m = 2.76 



/8.045X* 

 1st and 3d, | = IgTgo/ > whence m = 2.76 



1st and 4th, iff = 



\O.loO/ 



, whence m = 3.61 



Mean 



3)9. 13 Sum 

 m 3.04 



Hence it follows, that the diminution of the repul- 

 sive force, or, what is the same, of the electric density, 



See Saussure 's Eiioiflfygromttric, chap. x. p. 173, where he has gien a small Table, expressing, for every degree of the ther- 

 mometer, the quantity of water dissolved in the air relative to the degrees of humidity marked upon his own hygrometer. 





