30 REPORT 1860. 



two points may be found within the opposed hemispheres in which we may con- 

 ceive the whole force to be collected, and to be the same as if proceeding from every 

 point of the opposed hemispheres. These points approach the surface, and become 

 the touching points when the spheres touch ; as the spheres separate they approach 

 the centre, and reach the centre when the distance is infinite. If we call a the 

 distance between the points of contact, and ?— the radius of sphere, we have, 



putting F = the total attractive force, F as ; and calling the points of centre 



a(a + 2r) 



of force=qq', we have distance qq'=the tangent from either of the touching points 

 to the opposite sphere; or if distance qq' = D, we have Yet =p«r ct — . 



Several very remarkable experiments were now adduced in evidence of the truth of 

 these formulae. Spheres of variable diameters were put in opposition in the balance, 

 the quantity of electricity measured, and weights placed in the scale-pan, as deter- 

 mined by calculation ; the distances being regulated accordingly, the scale beam 

 bowed in obedience to the given law of force with extreme and wonderful exactitude : 

 the experiments elicited much commendation. 



The author thinks that every observed operation of electrical action is reducible 

 to simple and elementary laws free of complication, and may be investigated and ex- 

 pressed by an easy mathematical analysis and forms of expression. He thinks that 

 all the laws of nature are of the most simple kind, and only involve a simple rela- 

 tion of cause and effect ; if we double the cause we double the effect. To suppose 

 an effect to be as the square or cube of its cause, is to suppose the effect to depend 

 partly on the cause and partly on nothing. There is probably, taken as a simple 

 elementary law, no such a law in nature as that of a force being in the inverse 

 duplicate ratio of the distance. Take, for example, the case of gravity as central 

 force, and assumed to be a species of emanation from a centre, it is true that 

 at twice the distance we have only one-fourth the force ; but this is because the areas 

 of the concave spherical surfaces, which we may imagine the emanation to fall upon 

 at these distances, are to each other as 1 : 4 ; so that in any one point of the outer 

 sphere there is only one-fourth the agency upon which the force depends, conse- 

 quently only one-fourth the attraction; but this is a simple relation of cause and 

 effect. Taking light as an emanation from a centre, the same result ensues. If 

 there be only one-fourth the quantity of the emanation in any point, we can only 

 have one-fourth the light, and thus light or gravity may be said to be in the inverse 

 duplicate ratio of the distance. 



On the different Motions of Electric Fluid. By the Rev. T. Rankin. 



The author, from several very striking and vividly-described thunder-storms and 

 their permanent effects, concludes that sometimes the electric fluid moves downward, 

 sometimes upward, and sometimes horizontally. On one occasion, some years since, 

 about two o'clock, on a night on which it had thundered almost incessantly, a loud 

 whizzing sound was heard to pass over the rectory-house, which he judged to bean 

 aerolite ; a tree in the direction it had passed was struck; and from the nature of the 

 injury inflicted, the conclusion was drawn that the motion of either the aerolite or 

 of the electric fluid had been nearly horizontal. 



On the Phenomena of Electrical Vacuum Tubes, in a letter to Mr. Gassiot. 

 By Professor W. B. Rogers, Boston, U.S. 



I send you, by my brother, a printed abstract of remarks made some months ago 

 on the phenomena of the vacuum tubes, and a hypothesis as to the condition and 

 cause of the stratifications. 



You will see that, with the aid of Mr. Ritchie and our skilful photographer, Mr. 

 Black, I have been experimenting on the actinism of these electrical discharges. 



In some more recent trials I have obtained beautiful photographs of the stratifica- 

 tion, of which I send you a specimen. The tube, as you will see, is a straight one, of 



