OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



181 



From these values of a l9 ft v a 2 , and /3 2 , the corresponding values of a x , r x , a 2 , and r^ 

 were deduced. 







Old. 







New. 





*1 



h 



h 





h 



k 



h 



h 



a. 2 



»*2 



0-627 

 88°-58'-6 

 0-020 

 198°-4'-6 



2-304 

 167°-18'-9 



0-120 

 308°-54'-2 



4-796 

 209°-23'-0 



0-400 

 359°-42'-0 



7-113 



230°-ll'-8 

 0-705 

 25°-51'-8 



0-936 

 115°-18'-6 



0-041 

 224°-l'-3 



2-699 

 179°-42'-3 



0-133 

 329°-6'-5 



5-522 

 220°-25'-0 

 0-458 

 25°-ll'-0 



6-979 



233°-6'-0 



0-719 



35°-l'-5 



Substituting these values in the original general equation, we have the following 

 eight equations to the annual curves for the two sets of thermometers. 



i old t x 



T = 



47°- 



old t 2 



T = 



46 • 



old t 3 



T = 



46 • 



old t 4 



T = 



46 • 



new t 1 



T = 



46 -. 



new t, 2 



T = 



45 • 



new t 3 



T = 



45 • 



new t 4 



T = 



45 • 



260 + 0-627 sin (2tt/+ 88°-58'-6) + 0"020 s 

 961 + 2-304 sin (2tt/+ 167 '18 -9) + 0-120 s: 

 620 + 4-796 sin (2tt/+ 209 -23 -0) + 0-400 s 

 365 + 7-113 sin (2tt/+ 230 -11 -8) + 0-705s 

 281 + 0-936 sin (2ir/+ 115 -18 -6) + 0-041 s 

 918 + 2-699 sin (2tt/+ 179 -42 -3) + 0-133 s 

 612 + 5-522 sin (2tt/+ 220 -25 -0) + 0-458 s 

 484 + 6-979 sin (2tt/+ 233 ■ 6 -0) + 0719 s 



n(47r/+198 c 

 n(47r/+308 c 

 n(47r/+359 e 

 n(47r/+ 25 c 

 n(47r/+224 c 

 n(47r/+329 

 n(4«/+ 25 

 n(47r/+ 35 



4' 

 54' 

 42' 

 51' 



r 



6 



ii 

 i 



•6) + &c. 

 •3)+&c. 

 ■0) + &c. 

 •8) + &c. 

 •3) + &c. 

 •5) + &c. 

 •0) + &c. 

 •5) + &c. 



The maximum and minimum values of the annual and semi-annual terms in these 

 equations will be found by making the various sines successively equal to + 1 and — 1, 

 or the angles concerned equal to ±90°. The values of f, the fraction of the year 

 (reckoning from the mean date of the first Monday) corresponding to the maximum 

 and minimum values of the several terms, were deduced from the equations so formed. 

 The following is a synopsis of the eight thermometers arranged in order of depth, 

 showing the amplitudes and dates of maxima and minima of the annual and semi- 

 annual terms respectively. 



ANNUAL TERM. 







Feet. 



Semi- 

 Amplitude. 



Dates of 





Maximum. 



Minimum. 



Old t x . 

 New t l . 

 Old t. 2 . 

 New t 2 . 

 Old t s . 

 New ^ . 

 Old t A . 

 New t t . 





25-6 



21-0 



12-8 



11-1 



6-4 



5-0 



3-2 



3-1 



0-627 

 0-936 

 2-304 

 2-699 

 4-796 

 5-522 

 7-113 

 6-979 



January 5'1 

 December 9'5 

 October 17 "9 

 October 5 "2 

 September 5 '2 

 August 24-9 

 August 15 "1 

 August 12'0 



July 6-7 

 June 9-9 

 April 18-3 

 April 5-6 

 March 6-6 

 February 23'3 

 February 13 - 5 

 February 10'4 



VOL. XL. PART I. (NO. 8). 



2 C 



