150 Royal Society* 



translation of U to any parallel position in space, in such wise that 

 every point or element of U is caused to describe the distance m, is 

 termed the translation of U along u. 



This translation consists generally of two distinct changes, one the 

 lateral shifting of the line of direction of U, and the other the motion 

 of U along its line of direction. The former is called the trans- 

 verse effectf the latter the longitudinal effect of the translation of U 

 along u. 



Both these effects are shown to be products of U and u ; the 

 transverse effect is represented by wU, and the longitudinal by t^.U, 

 inserting a dot between the factors in the latter for the sake of 

 distinction. 



The author then goes on to apply the principles established to the 

 proof of the Parallelogram of Forces ^ and the determination of the 

 effect of any set of forces on a rigid body. In doing this a remark- 

 able symbolization of the point of application, as well as the direc- 

 tion and magnitude of a force, is obtained, namely, that the expres- 

 sion (l+w)U represents a force U acting at a distance u from the 

 origin. 



The principles of statics are deduced with remarkable facility 

 from the symbolical representation of the translation of a force along 

 a given distance. 



2. " On an Air-Engine." By James Prescott Joule, F.R.S. «&c. 

 Received May 13, 1851. 



The air-engine described in this paper consists of a pump by 

 which air is compressed into a heated receiver; and a cylinder, 

 through which the air passes again into the atmosphere. The dif- 

 ference between the work evolved by the cylinder and that absorbed 

 by the pump, constitutes the work evolved by the engine on the 

 whole. Two tables are given ; the first of which contains the pres- 

 sure, temperature and work absorbed, for various stages of the 

 compression of a given volume of air. The second table gives the 

 theoretical duty of the air-engine described, worked at various pres- 

 sures and temperatures. The temperature recommended to be 

 adopted in practice is as little below the red heat as possible, which 

 would involve the consumption of only about one-third the amount 

 of fuel consumed by the best steam-engines at present constructed. 



?/. " Experiments made at York (Lat. 53° 58' N.) on the Deviation 

 of the Plane ot Vibration of a Pendulum from the meridional and 

 other vertical planes." By John Phillips, Esq., F.ll.S. Received 

 June 3, 1851. 



The following is the author's account of these experiments. 



The experiments, of which the following is a notice, were made 

 partly in the north-western Tower of the Minster, and partly in a room 

 of my residence. The latter attempts have only within a few days 

 acquired sufficient method and consistency to deserve reporting; 

 nor have the trials in the Minster been uniformly successful. 



Mr. Thomas Cooke, an able optician of York, began the experi- 

 ments in the Minster. On the 30th of April, Mr. Gray and myself 

 observed the vibration of his pendulum, and found it so accurate as 



