70 REPORT— 1879. 



(II.) To calcu^e te p u .— 



(leu) (kuy (kuy 



p « = l + -j- + f7Y+ XT2T3 + &c - ; 



p = 0-76. 

 Therefore, since Jo == log e (p) = — - 274 ; 



, (0-274w) (0-274w) 2 (0-274 ? 3 . 

 r =l- 1 + ! . 2 ~ 1 . 2 . 3 + &c - 



Since u ranges from 1 to 12 - 65, this series does not converge rapidly- 

 enough, and it is usually better to obtain p u directly, as follows : — 



log (p u ) = u log p ; 



log (p«) = - u x 0-119. (5) 



2°. The next step was to determine how long the sun remains in any 

 zone of zenith distance, one degree in width, in the course of a year. 



This was done, for the latitudes 0°, 30°, 60°, in the following manner ; 

 and although the calculations are not yet completed, involving as they do 

 300 folio sheets, enough has been accomplished to induce the Association 

 to proceed with the calculations for other latitudes. 



We here append the form of the tables used in computing the time 

 spent by the sun in each zone, of one degree of width in zenith distance, 

 and, as it would be a useless expenditure of money to print in full the 

 details of the calculations, we propose to have two fair copies of the 

 calculations prepared and bound together; one to be deposited in the 

 library of Trinity College, Dublin, and the other placed at the disposal 

 of the British Association. 



A complete summary of the entire results will, of course, be printed 

 in the Proceedings of the Association. 



It will require an additional grant of 25Z. to complete the calculations 

 for the latitudes 0°, 30°, and 60°, and a grant of 501. would enable us to 

 complete the whole calculations for the latitudes 0°, 30°, 40°, 50°, and 60°. 



The mean annual temperatures (as given by observations) between 

 0° and 30° are disturbed by the distribution of land and water, and the 

 temperatures of latitudes above 60° rest upon insufficient data of obser- 

 vation ; for which reasons we propose to limit our calculations to the 

 latitudes above indicated. 



III. — Sun-heat Formulce. 



Let h = sun's hour angle, 



X = latitude of place, 

 b = sun's declination, 

 z = sun's zenith distance ; 



cos z H 1 sin X sin b 



cos h = 



cos X cos o ' 

 cos z' hP sin X sin 2 



UUS It, = T 5 , 



cos A cos b 



h — h' = time of passing through the zone (z — z'), 



degrees of arc being converted into minutes of time, as follows, 1° = 4™ : 

 sin b = sin A sin I, 



