292 



larly made before and after each observation of coincidences, and is 

 followed by a table of the deduced rates of the former clock . 



Tables are next given of the observed coincidences, noting the 

 times of the disappearance and reappearance, and their mean for each 

 of ten coincidences, the arcs of vibration, the mean arc, the intervals 

 in seconds, and the corrections for the arcs of vibration ; and summed 

 up at the end of each observation, so as to give the mean intervals ; 

 the number of vibrations in 24 hours, as observed and as corrected 

 for the arc ; the state of the barometer and thermometers is also 

 given at the beginning and end of each observation, which were con- 

 tinued twice a day to the 25th. The whole of the observations are 

 then summed up in one table, and these are then reduced for the 

 rate of the clock, and presented together in a table of results ; after 

 taking the mean of which, the proper corrections for buoyancy and 

 elevation above the level of the sea are applied to the result. 



The same system of registering is followed in the experiments at 

 Port Bowen ; only that here the observations of the transits by which 

 the rate of the clock is determined are prefixed, and the hygrometric 

 state of the atmosphere is also quoted in each observation of coinci- 

 dences. The observations of coincidences set down in the first series 

 extend from June 14th to June 23rd, and were repeated four times a 

 day. The rates of the clock, as deduced separately from the sun and 

 stars, are tabulated, and the results separately computed for each. 

 In each coincidence, the number of transit observations on which the 

 time depends, multiplied by the interval in days between them, is re- 

 garded as a factor, and the sum of these factors is taken to express 

 the weight of the mean determination. The mean of these determi- 

 nations, according to their weight, is then taken, and the corrections 

 applied as usual for buoyancy, and for geological and local situation. 



The second series at Port Bowen extends from July 6 to July 10 ; 

 but the arrangement of the observations being in all respects similar 

 to that just stated, need not be repeated. 



The third experiment at Greenwich is stated in a manner precisely 

 similar to the first, and continued four days, each of ten coincidences 

 being observed twice a day. 



The general results may be summed up as follows : 



At Greenwich, the number of vibrations per diem, all corrections 

 made, = 86159'368 ; at Port Bowen, = 86230'172. 



The latitude of Greenwich is well known. The observations for 

 that of Port Bowen are not given here, but that element is assumed 

 from observations stated in the Appendix to Captain Parry's third 

 voyage. 



Computing on it, the author obtains an ellipticity of TTry--T-r anf l 

 an equatorial pendulum of 39*009805 inches. These are by the 

 method of disappearances, the difference between these and the re- 

 sults obtained by reappearances is insensible. 



