192 CARNEGIE INSTITUTION OF WASHINGTON. 



sible. Thus, when certain peculiarities became evident during the course of 

 the reduction of the observations, an effort was made to trace them to their 

 cause, and various considerations led to an investigation of atmospheric 

 effects. In the first place, a correction to the constant of refraction is intro- 

 duced for zenith-distances. To this is added a differential term. 



The question next arose as to the connection between the observational 

 peculiarities noted and the differential refraction as represented by the deduced 

 formulae. Observation had shown a diurnal effect. This might correspond 

 to diurnal changes in barometer, thermometer, and hygrometer, but, from 

 observation it appears that the temperature and not the barometer is the 

 controlling factor in producing changes. The records of the shade thermom- 

 eter had necessarily to be used at first. 



Assuming the Pulkova Refraction Tables as a standard of reference, the 

 relative refraction and the rate of change can be obtained for the period of 

 observation. The sum of the products of these quantities into the differen- 

 tial of refraction form the equation representing the shifting conditions of the 

 atmosphere. 



Proceeding with these equations, certain series of observations, chosen at 

 random, were treated for differential refraction and the results were very 

 satisfactory. There is an unmistakable connection between differential re- 

 fraction and the peculiar observational results. By employing the derived 

 corrections, observations taken at all times of day are brought into better 

 harmony. 



The effects we are dealing with are more dependent upon sun temperature 

 and humidity than upon shade temperature, but no records of sun tempera- 

 ture and humidity were available, and we therefore resorted to a Fourier 

 series which represents the changes. Thus we are not only taking into 

 account surface effects, but are integrating the conditions of atmosphere from 

 the earth's surface outward. Using a Fourier series, the accordance between 

 observations taken at all times of day is greatly improved. Thus it is shown 

 that differential refraction explains the apparent irregularity of the clock. It 

 also accounts for the effect between night and day observations. But, per- 

 haps more important than all, it helps to straighten the lines of reference from 

 which we reckon star positions. It will also have an influence upon the varia- 

 tion of latitude. 



It is important that future programs of meridian observations be arranged 

 with a view to determining the shift in the positions of stars dependent upon 

 atmospheric conditions, and this can not be properly tested unless the obser- 

 vations are taken in a strictly fundamental way. While the theory is fully 

 understood, observational programs in the past have not been arranged in a 

 manner to obtain truly fundamental results. The very basic principles are 

 often lost sight of. Therefore, it may be in order to restate them. 



FUNDAMENTAL OBSERVATIONS. 

 It is absolutely necessary to observe successive culminations of polar stars. 

 In dealing with right-ascensions we determine the time of transit across a 

 vertical plane passing through the pole. There is only one way to locate the 

 pole, fundamentally speaking, and that is through successive culminations 

 of the same circumpolar star. Likewise with declinations. Declinations are 

 determined by combining the circle reading at the pole with that on the star; 



