1884.] 



Level of the Cape Transit Circle. 



These adjustments are very constant from day to day and tlirough- 

 out the day; no appreciable change has been detected in them 

 depending on the time of day, though the range of temperature from 

 noon to midnight is often very large. 



The observatory is situated on the northern end of a small bill, and 

 is only 37 feet above sea-level. The Liesbeek on the west and the 

 Black river on the east, which carry oif a great part of the rain falling 

 on the Flats and the East side of Table Mountain, overflow their 

 banks in the winter, and a large sheet of water stands for a consider- 

 able time to the north and north-east of the hill. It has generally 

 been supposed hitherto that the rains or pressure in some way from 

 this standing water were the chief agents in producing the changes of 

 adjustment in the Transit- circle, and it was to test the truth of this 

 supposition that I undertook the present investigation. 



Tables of the values of the errors were formed for every half -month 

 from 1856 to 1882 by taking the mean of three or four determinations 

 about the first of the month as the error on the first, and similarly for 

 the 15th. The means of these semi-monthly values, though not strictly 

 the mean of the year, will not differ much from the true mean. On 

 three occasions, in 1856, 1860, and 1872, the amount of the level error 

 was reduced by the insertion of tinfoil under the bearing plate of the 

 western pivot ; but as the level error was taken before and after these 

 changes I have been able easily to allow for these changes and tabu- 

 late the errors in one uniform system. The following are the means 

 of the 27 semi-monthly results for the level error, to which I propose 

 chiefly to confine myself to-night : — 





s. 





s. 





s. 





s. 



Jan. 1 . 



. —0-58 



Apr. 1 . 



—1-35 



July I . 



. —1-47 



Oct. 1 . 



. -0-77 



„ 15 . 



. —0-66 



,, 15 . 



. —1-47 



„ 15 . 



. —1-32 



„ 15 . 



. -0-68 



Feb. 1 . 



. —0-79 



May 1 . 



. —1-55 



Aug. 1 . 



. —1-21 



Nov. 1 . 



. —0-62 



„ 15 . 



—0-91 



„ 15 . 



— l-o7 



„ 15 . 



. -1-09 



„ 15 . 



. —0-59 



Mar. 1 . 



—1-07 



June 1 . 



. —1-56 



Sept. 1 . 



. —0-96 



Dec. 1 . 



. — 0-56 



,, 15 . 



— 1-23 



„ 15 . 



—1-53 



„ 15 . 



. —0-85 



„ 15 . 



. —0-58 



A miaus sign denotes that tha western pier is lower than the 

 eastern, and an error of — l*Os. corresponds to a relative depression 

 of '0048 of an inch. Thus the western pier is about yoWths of an inch 

 lower in May and June than in December. If the differences of 

 these values from the mean of all be laid down to scale and a curve 

 swept through them, we have the continuous black curve in fig. 1 , 

 shewing the relative motion of the east pier. To find a formula 

 which will represent these changes I assume — 



L = ti + <? sin (® -f A) + ^ sin (® + B.) 

 Where L = the level error at any time 



= 0° for Jan. 1,15° for Jan. 15, &c., &c. 

 and c, a, h, A and B are constants to be determined. 



Each of the semi-monthly values above gives an equation of this 

 form, and solving the 24 equations bv the method of least squares I 

 find— 



s. s. s. 



L=— 1-035 —0-519 sin (®— 55° 3^ —0-044 sin (2 0-}- 203°.2'.) 



If with this formula we compute the Y^leus of L for each half 

 VOL, IV. ^ I 



