November, 1902.] 



KNOWLEDGE, 



249 



That for flexure of the telescope tube is abolished. The 

 observer takes a natural attitude, the same for all stars, 

 in place of iuvertins: himself upon the usual observing 

 coueh. These are some of the advantages of allowing the 

 axis of rotation to be determined b_v gravity and not by 

 the instrument maker. 



Of course the advantages are not all on one side. The 

 transit circle can take every star that is visible ; for the 

 almucantar we draw a ring upon the sky, passing hori- 

 zontally through the pole, and disregard all that is nut 

 carried across it ; at Durham this limits us to stars not 



The Durliani Ahmuantur. 



more than 70° from the pole ; a more southerly latitude 

 would be better, but, as we cannot change the latitude, 

 we must be content that there is more work within reach 

 than we can ever do. A complaint that will require 

 more investigation is that the stars cross the wires 

 obliquely. Each star cuts the wires at au angle equal to 

 its hour angle at the time of transit, thus varying for 

 different stars from a right angle at the pole to zero at the 

 southern limit. As a consequence a change of declination 

 j)roduces more effect upon the transit of a southern star 

 tban upon one more northerly; and declinations are better 

 determined for the former than the latter. Declination 

 should be very well determined at the lower range of the 

 instrument, for all the measures are absolute measures 

 from the pole, not as iu the transit circle, measures made 

 by reference to a divided circle and some reflecting 

 apparatus. 



As to the Ciilculations involved, I believe that when 

 large numbers of stars are discussed the advantage lies 

 with the almucantar. 



Exactly what an almucantar observation gives may be 

 shown by a diagram. The difference is observed between 

 the times which we could predict for the star's passage, 

 according to the Nautiral Almanac, and the time at which 

 it actually appears. This difference has to be shared in 

 proper proportions between corrections to the latitude, if 

 erroneous, to the clock, to the zenith distance of the tele- 

 scopic axis, and to the co-ordinates of the star, for each of 

 these contributes a share. The diagram below shows the 

 amount of error in latitude, zenith setting, or declination 

 which would contribute au error of U' 1 iu a transit, and 

 inversely it shows how accurately we may expect to deter- 

 mine these quantities by sifting tbein oul from the 

 inevitable errors of observation. The fact tiiat all these 

 unknown corrections are mingled together iu a single 

 statement of difference between observed and predicted 

 times is no disadvantage. On the contrary, it is a positive 



gain ; for it permits the ready application of the 

 rule known as " Least Squares " for combining a set 

 of observations to the best advantage so as to 

 derive clock correction and the rest from them. At 

 the same time, as everything is got out of the observa- 

 tion itself, the observer is relieved from vexatious sup- 

 plementary measures of faults of adjustment of his 

 instrument. 



Dr. Chandler observed for thirteen months— or sixty- 

 three nights in all. If the almucantar is lo be a serious 

 rival of the transit circle, such a series is uot large enough 

 to do it justice. Such a series, dating from when tiie 

 instrument was first set up, might be expected to make 

 out a ^(/('md/aciV case, and point out promising lines of 

 investigation. That it did this and more does not admit 

 of question. It was confined to observations of stars in 

 the catalogue of the Berliner Jahrhtich, and as these are 

 very well observed stars, a rough and ready test of Dr. 

 Chandler's success is to take the residuals which are to 

 give corrections to co-ordinates of the stars, and see 

 whether these depart much from zero. The first twenty 

 stars upon his list which are not close to the limits of 

 his range give thus ±0'08(> ; if stars about TtP declina- 

 tion be omitted it becomes ±0'0(3(j. We may put this 

 in the form, that a single observation used to determine 

 right ascension would, on the average, depart so much 

 from the truth, and this is based upon assuming that the 

 Berliner Jahrbuch's places require no correction at all. If 

 we make those allowances for a new instrument which 

 anyone's experience will suggest — but which, be it 

 remarked, Dr. Chandler himself does not claim— it is out 

 of reason to expect anything finer. 



But that the almucantar will do even better I believe 

 we have already proved at Durham, though we have only 

 emerged some two or three months from the ditHculties of 

 a start ; in evidence of this I cjuote below the results of 

 the last night's observations that have been fully reduced,* 

 1901, November 15. E. or W. attached to a star indicates 



C'liart of .Umucautar Constants for Latitude of Durham Objervatorv 

 (54» 46' 6 '2 X). 

 AbsL-issa = declination of object. 

 Ordinate.s : — ^i = error in deduced declination for O"! error in tran,-it. 

 ■^* = ,, ,> latitude ,, „ ,, 



-'• = ,, ,, collimution „ ,, ,, 



the side of the meridian on wliich the tran.sit was taken, 

 and the fractions of a secimd opposite to it correspond to 

 the numbers of which I have given the mean iu I>r. 

 Chandler's observations. 



* This vas written in January last. 



