24 REPORT — 1839. 



flame by pump work, which will afford a very indifferent light in one 

 of the French Annular or Sinumbral lamps, where the supply is given 

 by a very slight pressure. 



Notice of a comparative Pendulum. By W. J. Frodsham, F.R.S. 

 The principle of this pendulum is the same as that which was pro- 

 posed some years ago by Mr. Reid of Woolwich, but the construction 

 IS different. Over the steel rod of a common pendulum Mr. Frodsham 

 slips a zinc tube, which rests on the adjusting screw at the loAver end 

 of the rod, the bob being fastened at the centre by two connecting rods 

 of steel to the tube at the point where the expansion of the tube is the 

 same as that of the rod. By making the zinc tube a little too short, 

 and applying small rings cut from the same tube, as correcting pieces, 

 until the proper length is found, the evils of the irregularity of expan- 

 sion of different specimens of the same metals are overcome. The 

 author describes the means whereby he secures access for the air to 

 the zinc tube where it passes through the bob, and to its inner surface 

 surrounding the steel rod. 



Mr. Frodsham also describes improvements in the mode of suspend- 

 ing the pendulum, particularly the application of a brass tube, called 

 an ' isochronal piece,' which slides on the rod, and at its upper part is 

 made to embrace the suspending spring, the acting part of which is 

 thus made variable in length without affecting the compensation of the 

 pendulum. When the suspending spring is in a state of rest and in 

 Its natural and unconstrained position, the isochronal piece is made to 

 embrace and unite it firmly to the rod, by two screws at the upper 

 end, thereby preventing any strain or warp to which the spring is 

 subject by the method usually employed. To any given weight of the 

 bob of the pendulum, it appears that some particular length and 

 strength of the suspending spring is better adapted than any other to 

 produce isochronism in the pendulum, and the use of the 'isochronal 

 piece,' in producing in any spring the nearest approach to this condi- 

 tion, is obvious. 



On the Motion of Points or Atoms subject to any law of force. 

 By J. K. Smythies. 



The method of investigating the motions of points proposed is, to 

 find equations necessarily existing between their distances ; thence to 

 deduce others involving any required combination of the distances, and 

 their differentials of any orders necessarily true for all moving systems; 

 and then, combining those equations, which assign a particular law of 

 motion, with those which are true for all motions, to eliminate the dif- 

 ferentials of all or any required number of orders by a simple mode of 

 elimination. 



If there are any number of points (w) in space, the following equa- 

 tion subsists between their distances, where 12 or 21 denotes the 



