used in tliese (.Icterminatiun is by Alvau Clark and Sons, anil i'or uniformity of 

 speed it is everything that could be desired. Tlie line made by the pen is sharp 

 and clear. The length of one second on the sheet is about 8 mm., so that it 

 can be easily measured with a microscope of low power with a niici-ouieter eye 

 piece. It will easily be seen that even if the total time dm-ing whicli the pen- 

 dulum is made to swing be not great, its value can be ascertained within a very 

 small fraction of itself. By this process, therefore, it becomes possible to mahe 

 the duration of the experiment extremely short compared with that required 

 in the method of coincidences and yet to reach the same degree of accuracy. 

 As a proof of this it may be stated that in muuerous instances in which the du- 

 ration of the exi)eriment was only twenty minutes, three independent measiu'e- 

 ments of the total time, made from the chronogroph sheet, did not differ among 

 themselves by more than one sixty-tliousainlth part of the whole. The advan- 

 tages in thus reducing the whole duration of the experiment from hours to 

 minutes are many. All of the conditions may be maintained nearly constant 

 during the whole time of the swing, and this is especially important in regard 

 to temperature and arc of vibratiim, the latter being also made much smaller to 

 begin with than would otherwise be possible. Again, the method eliminates 

 '"judgment" to a great e.xtent as the pendulum marks for itself the beginning 

 and the end of the period of time. Another important gain is that the use of 

 the clock may Ikj dispensed with, and, without loss of accuracy, the break-circuit 

 chronometer substituted, thus rendering the whole apparatus for such a deter- 

 mination easily portable. 



Time was obtained from a break-circuit sideral chronometer Negus 1629. 

 The chronometer remained in the transit room of the astronomical observatory 

 which is nearly two miles distant from the physical laboratory but a telegraph 

 line connects the two points so that the chronometer could at any moment lie 

 made to record its beats ui)on the chronograph in the laboratory. The rate of the 

 chronometer was determined by star transits observed for several nights in suc- 

 cession before and after the vibration expeiiments. In the results given the 

 periods of vibration are stated in mean solar time, corrected for chronometer 

 rate and also for arc of vibration. 



Besides these corrections applied to the period, the final results must be 

 coiTccted for the effect of the atmosphere; in other words, they nmst be reduced 

 to a vacuum. Aside from simply les.setiing the actual effect of gravity ujjon the 

 jKjndulum, a portion of air is carried with the vibrating body in its motion so 

 that it may be said that its real density is less while in motion than while at 

 rest. Tliis fact seems first to have been noticed by Du Buat, who made sonu; 

 investigations concerning it in the latter part of tlic last century, but it was not re- 

 cognized by more recent olwervers until its rc-di.scovcry by Bessel. Ithas been mad«^ 

 the siiliject of extensive experiment by Baily aTid has been disciissetl analyliially 

 by s<!veral mathematicians. Tlu: ipiaritity of air carried liy the pi'ndiilum is 

 found not In dipciiil nn tjjc material of wliiuh it is composed or on its density 



