13 



most of them were made, and barometer 30 inches. The time of vibration of 

 the pendulum under these conditions, the mean of all of the results, was.— 



ti = .999834 seconds. 



On the summit of the mountain, during the time of making the experiments, 

 the barometer was tolerably constant at about 19.0 inches and the temperature 

 S'.ö and to these conditions the results were reduced, after correcting for arc and 

 chronometer rate. 



Finally the mean of all is reduced to the Tokio conditions as to temperature 

 and pres.sure. 



CORRECTIONS. 



The connections for arc of vibration have been made by means of well known 

 formulae. The mean arc of vibration in both the Tokio and Fujinoyama experi- 

 ments was about one degree and a half la making the con-ection for temperature 

 the co-eÖBcient of expansion has been assumed to l>e .TOOOIST as no means were 

 at hand for detennining it precisely. This is a commonly accepted co-efficient 

 for bniss and a comjiarison of the vibration periods of the i)endulum under 

 different temperatures indicates that it can not be far from correct. 



The correction for difference of barometric pressure is the most difficult to 

 determine. W"ere it possible to vibrate the pendulum at the same place under 

 pressures widely differing it might be determined experimentally. Lacking this, 

 I wiv« fortunately able to refer to a recent elaborate and exhaustive discussion of 

 the whole subject, from an experimental as well as a theoretical standpoint, by 

 C. S. Peii-ce Es<i. of the United States Coast Survey.-' In this valualile memoir 

 3Ir. Peirce gives a graphical representation of the periods of vibration of his 

 pendulum, under various pressures, from 30 inches down to practically a vacuum. 

 By interjwlation the period for any jiressure can be very closely ascertained, 

 as also the correction in going from one pressure to another. There are impor- 

 tant differences between the jiendulum used by Mr. I'eirce and that in use here, 

 the princij>al being the difference in the sliapo of the cylindrical weights and the 

 fact that in our f>endulum only one cylinder was attached. Nevertheless a 

 fair apiiroximation to the proper correction may be taken from liis cnrve show- 

 ing the results with "hearv- end down" and observing that the differences in the 

 two pendulums are such as to make the correction for our iieiidtilum considerably 

 less than for that of the Coju<t Survey. In this way and by considering these 

 differences the correction use<l in the reduction was reacheil. After it had l>een 

 established I wa-s fortunate in finding in this country a volume of the Philoso- 



* .\I>a><iirtMniii- ■il" liiiiiin a! liiiiuii .'^iiit..iii- >ii Ahiviiia aiitj Kiin>|>'-A||.<.-iiili\ NU. l'> L'. S. 

 Coast Surrey Kcport-of IHT«.— 



