512 PROFESSOR CHALLIS, ON THE DETERMINATION OF THE LONGITUDE 



Method (B). 



h. m. fn. s. 



May 17, at 11.49 sidereal time, Hardy slow 1.20,497 

 18, at 14.17 1.22,380 



Comparing these with the errors of Hardy already used, the corrections of the longitude 



are - S ,332 for method (A) and - S ,343 for method (B) on May 17, and - 0',307 for 



method (A) and - S ,340 for method (B) on May 18. The following are consequently the 



corrected determinations of the longitude : — 



t. 

 May 17 by method (A) 22,660 



18 22,731 



Mean 22,696 



May 17, by method (B) 22,599 



18, 22,798 



Mean 22,698 



Concluded Mean 22,697 



The accordance of the results by the two methods is sufficiently close on each day, and 

 the mean results of the two days are extremely close. It will be seen that this agreement 

 has been improved by the application of corrections for the forms of the pivots. I am at a 

 loss to account for the mean excess S ,135 of the determination of May 18 above that of 

 May 17, as (at least under the same circumstances) there appeared to be no difference of 

 personal equation between the observers. 



It remains to give an account of the observations and- calculations by which the 

 corrections for the forms of the pivots were ascertained. Let £ represent the angle which 

 a line drawn from the middle wire of the transit-telescope, at the point where the transits are 

 taken, and passing through the optical centre of the object-glass, makes with the plane of the 

 meridian. This angle was ascertained for various zenith distances by the method of 

 bisection of dots at the extremities of the pivots, as described in the communication to the 

 Royal Astronomical Society already cited. The same angle was found on the supposition of 

 equal and cylindrical pivots, the collimation and level errors being determined by the 

 collimating eye-piece and by reversing the instrument. Let £, be its value thus determined. 

 Then as exactly the same data- (given by the collimating eye-piece and by transits of Polaris) 

 were used in the two calculations, if the supposition of equal and cylindrical pivots had been 

 correct, there should have been no constant difference between the values of £ and £,. The 

 actual differences as determined by trials made in 1850 and 1854 are subjoined. A trial 

 made in 1852 failed on account of accidental unsteadiness in the attachment of one of the dots 

 to the pivot. The level error used in the observations of 1853, May 16 — 18, for the clock- 

 errors on those days, was obtained in the ordinary manner by levelling with the spirit-level. 

 By the mean of six comparisons of levellings obtained in this manner in 1852 and 1854, with 

 an equal number obtained simultaneously by the collimating eye-piece and reversing the 



