TRANSACTIONS OF SECTION A. 291 



,\ dc. + 4 dr. = _ C J^J, and .'. from,(3) 2 c (d¥- F ^) = o, or 

 9i ' V 9 / 



2c0d(*) = o (4) 



■which is the condition sought, and must he identically true for every point on the 



curve, the initial velocity heing given by the equation v 2 = (2 F c - J . 



One consequence of the condition (4) is that if an orbit be describable by a 

 particle under the action of each of a number of forces, acting towards fixed, or 

 movable, centres, including the case where some of the centres may be at an 

 infinite distance, this orbit can also be described by a particle acted on by these 

 forces simultaneously, each being multiplied by an arbitrary constant, while the 

 square of the initial velocity is the sum of the squares of the initial velocities cor- 

 responding to the forces separately, these squares being multiplied by the same 

 constants respectively. Any laws being assumed for all the forces, F 1} F 2 , &c, 

 except one, the equation (4) determines the remaining force. Special applications 

 to an ellipse, the forces being directed towards the centre and foci, are made in 

 the paper. 



II. A condition identical with (4) exists in the case of a string acted on by a 

 number of forces and in equilibrium in any given form. 



Special applications to the case of an ellipse, the forces being directed towards 

 the centre and foci, are made in the paper. 



12. On a Theorem relating to the Transformation of Series. 

 By the Eev. S. Earnshaw, M.A. 



i 



13. Improved Photographic Screens. By J. H. Stabling, F.G.S., A.I.C. 



There have been many attempts from time to time to devise a particular form of 

 lens-covering or cap for photographic cameras which would permit the operator to 

 expose or cover the lens as quickly as possible, and with the least possible disturb- 

 ance of the apparatus. 



The old and usual form of cap cannot be said to fulfil these requirements, since 

 the rapidity of manipulation depends entirely upon the operator. Moreover, how- 

 ever skilfully this is used, it is almost impossible to avoid disturbing the apparatus 

 more or less. 



The spring sliding shutter, which is by no means a new invention, although an 

 improvement as regards mere mechanism in the above, can only be used for rapid 

 working. A third form of lens-covering has been devised by a Mr. Cadet, which 

 consists simply of a circular disc, which can be made to open or shut externally or 

 internally on an ordinary hinge by means of suitable mechanism. 



It occurred to the inventors that the kind of covering which would meet the prac- 

 tical requirements necessary for the perfect working of a camera must be one which 

 should open if possible from the centre, and be so under the control of the operator 

 as to be opened or shut either rapidly or slowly, and at the same time noiselessly, 

 so that it might be used either for landscape, photography, or portraiture. 



The present invention, which I have the honour of bringing before your notice, 

 may without doubt be said to fulfil these somewhat difficult conditions. 



By means of a suitable transmitting power, which may be used at any required 

 distance from the camera, the covering, which you will perceive consists of two 

 peculiarly curved halves, is caused to be opened or shut much in the same manner 

 as a pair of shears, thus exposing the lens from the first at the centre, and gradually 

 increasing the opening towards the circumference. This may be done rapidly or 



u2 



