( 243 ) 

 wiieiiCG for each of those niosi prohahlc orroi's (he relation: 



Theoretically — t-t-^ contains all the unknown (jnantities ƒ, practicall3^ 



.''7 



howevei-, besides /',/ only (he 3 oi' 4 preceding' and foUowijig ones, 

 since, owing to the small coefficients, the other (erms may t)e neglected. 

 The most probable errors occni* in it in a linear form, and hence 

 the complete system of error-eipiations is sul'ticlenl (o determine 

 them all. 



§ 5. In this manner I have treated (31 clock con'ec( ions determined 

 by observations made from Jan. J4, 1903 to Jan. 14, 1904 by 

 E. F. VAN DE Sandk Bakhuyzkn and A. Pannekokk. This |)roblem 

 was somewhat complicated because the observed rates depend on 

 the pressure and the temperature of the air in which the pendulum 

 moves. An increase of atmospheric pressure of 1 mm. mercury gives 

 to the clock rate a retardation of 0.015 seconds a day, while an 

 inci'ease of temperature of 1 dcg. C accelerates the rate by about 

 0.030 seconds a day. 



I have found that also the ditferences of temperature observed in 

 the clockcase have a perceptible inlluence on the rate ^). 



1) This temperaturo o-i-adient forms a r.ew element in tlie rednclion of tlie clock rales, 

 in so far as at the Leyden Observatory it was not accounted for until 1003. 

 Although in the clockcase of Hohwii 17 two thermometers have l)een suspended 

 at different heights since 186G, the influence of the temperature gradient did 

 not clearly appear from the earlier observations owing to the inaccuracy of 

 those readings. Although Dr. E. V. van de Sande Bakhuyzen delected a yearly 

 periodicity in the differences between tliose liiermometers, which might explain the 

 phenomenon of the yearly periodicily in the rates (Proc. Kon. Ak. v. W. 1902) 

 yet at that lime he still doubted of their reality, because the Ihermometcrs were 

 graduated according to Reaumur and the accuracy of the reader in estimating 

 the tenth parts was insulficient to warrant an inequality of O.P R. in the monthly 

 means of the difference in temperature. 



In order to obtain certainty on this point, two thermometers were placed into 

 the clockcase in January 1903, which were divided into tenth parts of a centigrade 

 and had been compared with each other beforehand by the director of the Obser- 

 vatory; since that time they have been read with accurate estimation to a hundredth 

 part of a centigrade. 



The vertical distance between these thermometers is G3 cm. It soon appeared 

 that in the clockcase there is a variable temperature gradient, which cannot but 

 cause a considerable variation of rate. 



In July 1903 it was derived from observations liiat a dillerence between the 



