Mr. G. B. Airy on the Mean Density of the Earth. 229 



Mr. Ellis from the Royal Observatory, Mr. Pogson from the Obser- 

 vatory of Oxford, Mr. Creswick fr(^ the Observatory of Cambridge, 

 Mr. G. Rumker from the Observatory of Durham, and Mr. Sim- 

 monds from Mr. Carrington's Red Hill Observatory. 



The plan of operations was this. Simultaneous observations of 

 the two pendulums (one in the upper and the other in the lower 

 station) were kept up incessantly during the whole working time 

 (day and night) of one week ; then the pendulums v/ere interchanged 

 and were observed in the same manner through another week ; after 

 this the pendulums were twice interchanged, but the two last series 

 of observations were so much shortened that both were included in 

 one week. Each pendulum had six swings of nearly four hours 

 each, on every day of observation ; and between the end of one 

 swing and the beginning of the next, numerous galvanic signals were 

 passed for the comparison of the clocks. 



The second section gives the details (as far as space permits) 

 of the comparisons of clocks by the galvanic signals. On examining 

 the proportion of rates, it was found that there was distinctly a per- 

 sonal equation in the observation of the galvanic signals. Approxi- 

 mate values for the different observers were obtained, and the pro- 

 portion of rates was corrected (where necessary) for these equations. 



The third section describes the general system of observing the 

 pendulums and reducing the observations. For ascertaining the 

 time of a coincidence of the vibration of the detached pendulum 

 with that of the clock pendulum, the mean of the times of the first 

 disappearance and the last re-appearance was employed. Several 

 coincidences were observed at the beginning of a swing and the mean 

 was taken : and several were observed, and the mean taken, at the 

 end of the swing. From these means, a mean interval of coin- 

 cidences was obtained ; from which the ratio of the actual rate of 

 the detached pendulum to that of the clock pendulum was found. 

 This requires several corrections. 



The correction depending on the arc of vibration, with no data 

 except the first and last arcs of vibration, and no assumption of a 

 mathematical law for the intermediate arcs, is made to depend on 

 the results of experimental observations on the numerical decrease of 

 the arc by a peculiar process. 



The corrections depending on the temperature and the atmospheric 

 pressure are based mainly on Sabine's experiments. 



The fourth section contains an abstract of the Pendulum Obser- 

 vations at the Upper Station, with the corrected logarithm of the 

 rate of the detached pendulum on the clock pendulum for every 

 swing ; and the fifth section contains a similar abstract for the 

 Lower Station. 



The sixth section gives the computation of the logarithm of the 

 rate of the lower detached pendulum upon the upper detached pen- 

 dulum (for which the preceding sections have furnished the ele- 

 ments). Then is given in detail the investigation, by the Theory of 

 Probabilities, of the formula for the best combination of the results 

 of the different swings. The advantage of the method of incessant 



