351 



rian telescope, when the small speculum receives the rays after they 

 have arived at the focus, and after they have become sufficiently con- 

 centrated to interfere with each other's motion. 



2. In a subsequent paper, the experimental research relating to 

 the same subject is further prosecuted, and the conclusion arrived at 

 is, that the illuminating power of the Cassegrainian telescope, as 

 compared to the Gregorian, is in the proportion of to 1. 



3 . His next communication to the Society relates to "An improved 

 method of dividing Astronomical circles and other instruments." 

 The general principle of the method there proposed is the same as 

 that of the beam compass ; but the apparatus, instead of having points, 

 is furnished with two micrometer microscopes, adjustable to different 

 distances, as aliquot parts of the arc or line to be divided. Asa spe- 

 cimen of the method by which this apparatus is to be used, Capt. 

 Kater describes the series of divisions and subdivisions which he 

 thinks most convenient in a circle of two feet diameter. 



4. The series of investigations in which Capt. Kater was engaged 

 for many years, relative to the pendulum, commences with a paper 

 entitled, " An account of experiments for determining the length of 

 the Pendulum vibrating seconds in the Latitude of London." To 

 ascertain with exactness the length of the seconds pendulum, an 

 object of considerable importance in Physical Science, was scarcely 

 possible by the methods which had been before resorted to : for the 

 determination of the precise centre of oscillation of a body vibrating 

 as a pendulum, depending as it does on the regular figure and uni- 

 form density of that body, involves difficulties which might be re- 

 garded as insurmountable. Capt. Kater fortunately discovered the 

 means of solving this problem, by the application of a mathematical 

 property already known to belong to the centre of oscillation, but 

 which had never hitherto been practically employed with this view ; 

 namely, that this centre and the centre of suspension are reciprocal to 

 one another : that is to say, that if a body, vibrating as a pendulum, be 

 inverted, and suspended by its former centre of oscillation, its former 

 point of suspension will become its centre of oscillation in its new 

 position ; and the vibrations in both positions will be performed in 

 equal times. This property, therefore, furnishes an easy method of 

 determining the exact distance between these two points, in a body 

 of any form, or however irregular may be the densities of its different 

 parts ; for it will be only necessary, for that purpose, to provide a 

 second axis of suspension, placed by estimation very near to the 

 centre of oscillation, while the body is vibrating on its first axis, 

 and also capable of adjustment as to distance, and as to its being kept 

 in the line passing through the first axis, and the centre of gravity : 

 thus by repeated trials of the number of vibrations performed, in a 

 given time, by that body, when suspended on either of these two axes, 

 and by altering the place of the moveable axis until this number be- 

 comes the same in both positions, we obtain a final adjustment which 

 gives the exact distance between the centres of suspension and os- 

 cillation in that body ; a distance equivalent to the length of a sim- 

 ple pendulum performing the observed number of vibrations in a cer- 

 tain time. 



