Klotz. — Transpacific Longitxides. 55 



The effect of the coUimation-error on the times of transit 

 varies directly as the secant of the declination of the star, hence 

 the collimation factor is sec 8. 



In order, therefore, to obtain a satisfactory time-determina- 

 tion — which is really the quantity sought — we observe more than 

 the absolutely necessary three stars, and find the most probable 

 value by the method of least squares. 



In the programme of the transpacific longitudes it was 

 arranged that (barring cloudy nights) on each night there should 

 be two independent time - determinations ; each determination 

 to be derived from fourteen stars, divided into two groups of 

 seven each, of which one was a polar. Furthermore, one group 

 was observed clamp east, and the other clamp west. The six 

 other stars of each group were " time " stars, and selected near 

 the zenith and south (in the Northern Hemisphere) thereof. 

 Instead of three we now have fourteen observation equations 

 from which to deduce the three unknowns, already mentioned, 

 by the usual method of forming the three normal equations. 

 It is desirable to reduce the effect of azimuth and collimation 

 on the derived clock-correction : we attain this by making the 

 algebraic sum of the azimuth-factor as small as possible, and 

 similarly with the algebraic sum of the collimation-factors. 



In deducing the time - correction it evidently must signify 

 the correction at some particular epoch, for every clock and 

 chronometer has a rate. The epoch chosen is generally the 

 mean of the various transits constituting a set, and the transit 

 of each star is corrected for rate, as if all stars had been observed 

 at that mean time. If, after having obtained the azimuth and 

 collimation errors, we apply them with their respective factors 

 to each transit and compare this corrected transit with the 

 apparent right ascension corrected for aberration, we obtain the 

 clock-correction of that transit or star, and the difference 

 between this and the clock-correction of the normal equation 

 gives us a residual. Each star thus furnishes a residual, and 

 from them is found the probable error of a single observation 

 as well as of the deduced clock-correction from all the stars. 

 The average probable error of the latter is about 0-01 s. for good 

 work. 



A word about rate. Rate is one of the most difficult prob- 

 lems with which we have to deal in field longitude work. It is 

 not the magnitude of the rate, although a small rate is very 

 desirable, but the constancy : this is the crux. A chronometer 

 may have an apparently constant daily rate, yet the hourh- 

 rate for the twenty-four hours may and does vary. Again, the 

 rate is not the same when the current is on as when it is off : 

 the former obtaining when observing and the latter the rest of 



