316 



Transactions. 



In form B the fourth column contains the values of + 8"" 6 sin (a — 173°). 

 The fifth column contains the values of — 3""0 sin (2a — 76°). 



The sixth column is the computed values of 



B - A = - 24"'25 + 8"- 6 sin (a - 173°) - 3"'0 sin (2a - 76°). 

 Subtracting these from the observed values of B — A in column (2) we 

 obtain the residuals in column (7), which represent the accidental errors 

 of graduation and reading. 



These results show that the circle is exceedingly well graduated. 



The accidental errors of graduation are not reducible to any regular law. 

 They may occur at any division of the circle with either positive or 

 negative signs with equal probability. They may be found directly by 

 testing the divisions with a micrometer microscope. On an instrument 

 equipped with verniers, the angle between any two divisions of the vernier 

 may be used for this purpose. Such errors may be reduced by a greater 

 number of reading microscopes or verniers, but they cannot be wholly 

 eliminated by any special method of observation. 



•+■ 2a 



-20 



3<L0 



A graphical representation of the results is shown in fig. 3. 

 The firm curve shows the values of B— A as ordinate, for corresponding 

 values o f x, 0°, 30°, &c 



The two dotted curves are the first and second harmonics. 



Art. XL VII. — Harmonic Tidal Constatits of Neiv Zealand Ports — 



Dunedin and Port Chalmers. 



By C. E. Adams, M.Sc, F.R.A.S., Government Astronomer of New Zealand. 

 [Read before the Wellington Philosophical Society, 22nd October, 1913.] 



As in the case of Wellington and Auckland,* the harmonic tidal constants 

 for Dunedin have been obtained from an harmonic analysis of the hourly 

 ordinates from the automatic tide-gauge records at Dunedin. The tidal 

 abacus of Sir G. H. Darwin was used, and the whole of the calcula- 

 tions have been carried out in duplicate, and with independent checks 



* Trans. N.Z. Inst., vol. 45, 1912, p. 20. 



