408 Transactions. — Chemistry and Physics. 



that a light and regular haze overspread the atmosphere, and 

 the sun was observed lighting up the haze near the earth's 

 surface through the rifts in the tree-tops, causing straight lines 

 of light. This haze may be connected with the bright bands 

 of light which later on, at 8.15 a.m., were observed radiating 

 fanlike from the south part of the horizon and extending near 

 to the zenith. The sun was east-north-east, shining right 

 across the bands. The sky was generally clear excepting a 

 few filmy cirrus clouds. The spaces between the bands were 

 about the same breadth as the bands. 



It may be observed that nature is generally in her calm and 

 serener moods when these phenomena occur. It is to be re- 

 gretted that no means were at hand to make spectroscopic or 

 magnetic examinations of these streams of light, but this com- 

 munication is intended as giving observations only, and may 

 indicate a line of future research. 



Art. LI. — On the Construction of a Tabic of Natural Sines by 

 Means of a Neiv Relation between the Leading Differences. 



By C. E. Adams, B.Sc (Honours), A. I. A., late Engineering 

 Entrance Scholar and Engineering Exhibitioner, Canter- 

 bury College ; late Senior Scholar in Physical Science, 

 New Zealand University. 



[Read before the Wellington Philosophical Society, 18th November, 



1902.] 



Part I. 



The art of calculating tables of the numerical values of the 

 trigonometrical ratios seems to have fallen into disuse for over 

 a century, as the greater portion of this work was done in the 

 seventeenth and eighteenth centuries, and modern tables are 

 in almost every instance but reprints of the earlier ones. 



It appears from the report of the British Association for 

 Advancement of Science, 1873, on mathematical tables, that 

 the most extensive table of natural sines is that given by 

 Erancois Callet in his " Tables Portatives de Logarithmes," 

 Paris, 1795 (Tirage, 1860). In this work the natural sines 

 are given to fifteen places of decimals for every 0001 of the 

 quadrant — that is, for every 5' 24". In the introduction the 

 process of calculating the table is described, and from it the 

 following summary and extracts are made. 



