530 



SCIENCE 



[N. S. Vol. XXXIV. No. 877 



These were taken in 650 series, of whieli a full 

 night would include two. 



Above 300 fundamental series had been made, 

 each including the observations for groups of 

 primary clock stars twelve hours apart, and those 

 for the combination of successive upper and lower 

 culminations of one or more circumpolar stars. 



For the study of the refraction 3,000 observa- 

 tions of stars at large zenith distances were made. 



For the corrections to the instrument, coUima- 

 tion had been regularly observed; flexure at the 

 beginning and end of the work; pivot error and 

 division error were measured with sufficient detail 

 to confirm the more elaborate investigations at 

 Albany; and 400 reflection observations were ob- 

 tained, an average of 40 for each ten degrees 

 employed. 



For the personal corrections of the observers, 

 over 2,000 determinations of the magnitude equa- 

 tion were made, by the five telescope observers. 



Special determinations of the value of the 

 screen employed accompany this correction. For 

 the bisection error and transit error (N.-S.) 1,750 

 observations were made. The difference of eye 

 and ear minus chronograph was determined for 

 the observers. 



The instrument was dismembered in February 

 of this year, and was returned to the Dudley 

 Observatory, where the reductions will be com- 

 pleted. 



Short Formula for Computation of Circum- 

 meridian Azimuths: C. C. Smith. (Introduced 



by Dr. W. F. King.) 



A short formula for the computation of azi- 

 muths observed near the meridian is here given. 

 The ordinary formula for azimuth requires the 

 use of a subtraction logarithm. In the short 

 formula 1 + cot 5 tan cos t is expanded in a 

 series and after rearrangement and reduction gives 

 a formula for azimuth which requires the looking 

 up only of the natural logarithm of the declina- 

 tion, after which the multiplications may be 

 quickly carried out on the arithmometer. The 

 formula is much shorter and gives less chance for 

 error than the ordinary formula, especially where 

 a considerable number of observations have been 

 taken at each station. 



Changes in Collimation and Level of the Ottawa 



Meridian Circle: E. M. Stewart. 



This paper deals with the observations made at 

 Ottawa from March to December, 1910. Measure- 

 ments of coUimation and level were made usually 



twice in the course of an evening's work; the 

 changes during the interval (four hours on the 

 average) are here investigated. The average 

 change of collimation was -\- 0".03 for Clamp East 

 and — 0".20 for Clamp West; these changes run 

 with great regularity, changing invariably with 

 the reversal of the instrument, and appear to be 

 entirely independent of seasonal and temperature 

 changes or of the interval between the observa- 

 tions. The changes of level were not sensibly 

 affected by reversal of the instrument, but there 

 is some evidence of a small seasonal effect. 



Preliminary Measures of the Solar Rotation: J. S. 



Plaskett. 



This paper is a first contribution towards the 

 scheme of cooperation in determining the solar 

 rotation by the Doppler displacement of the spec- 

 tral lines, which was organized at the meeting of 

 the Solar Union at Mt. "Wilson last September. 

 A large amount of preliminary work w'hich is 

 briefly described has been performed for the pur- 

 pose of ascertaining the most suitable apparatus 

 and methods for accurate work. The mean of 23 

 rotation plates, obtained in June and July of the 

 present year, gives, at the equator, a velocity of 

 2.034 ± 0.004 kms., the probable error of a 

 single plate from the mean of the plates being 

 ± 0.017 km. The average probable error of a 

 single line is ± 0.021 km., varying from ± 0.010 

 to ± 0.030 km. in the different plates. 



The measures of upwards of 50 spectra, in the 

 region allotted to this observatory X 5,500 to 

 X 5,700 give no definite indication that the velocity 

 due to any particular lines or elements differs 

 from that of the general reversing layer. Tabu- 

 lating the residuals from the lines on these plates, 

 it is found that the mean residual, taking account 

 of the signs, is in only one case, and that a faint 

 and diffuse line, equal to as much as one half the 

 average numerical residual. Furthermore, the 

 measures of twelve plates of the spectrum of the 

 sun's limb, which had impressed upon them an 

 arbitrary displacement of the same magnitude and 

 character as the rotation plates, differing from the 

 latter only in the displacement being the same for 

 each line, show small varying displacements of 

 different lines of the same order as those obtained 

 for the rotation plates. It is probable, therefore, 

 that in the region under consideration there is no 

 systematic difference in the velocities of rotation 

 obtained for different lines or elements, the very 

 small differences observed being probably due to 

 the character of the lines for measurement. 



