from the Hourly Observations at Leith in 1824-25. 45 



These extremely general theoretical results are amply con- 

 firmed by the above-mentioned observations. 



London, December 8, 1841. S. M. D. 



APPENDIX. 



These Leith observations give the temperature at 



P.M. 



lh r = 51-149 

 51-470 

 51-532 

 51-239 

 50-872 

 50-294 



P.M. 



7h r 



8 



9 

 10 

 11 

 12 



49-544 

 48*624 

 47-829 

 47*276 

 46-803 

 46-398 



A.M. 



lh r = 46-134 



45-933 

 45-689 

 45-449 

 45-394 

 45-653 



A.M. 



7h r 



8 



9 

 10 

 11 

 12 



The sums of the homonymous hours are — 



p.m. and a.m. 

 1 h r = 97-283 



97*403 

 97-221 

 96-688 

 96-266 

 95-947 



p.m. and a.m. 

 7 h r = 95-827 



8 



9 



10 



11 



12 



95-653 

 95-888 

 96-288 

 96-753 

 97-175 



Sums. 

 193-110 

 193-056 

 193-109 

 192-976 

 193-019 

 193-122 



46-283 

 47*029 

 48-055 

 49-012 

 49-950 

 50-777 



Diff. 

 + 1-456 

 + 1-750 

 + 1-333 

 + 0-400 



— 0-487 



— 1-228 



The near agreement in the third column shows the series 



'expressing the daily temperature to be very nearly a periodic 



one, and of the form A=H + Asin*+# cos t + B sin 2 t 



+ b cos 2 t + C sin 3 * + c cos 3 / + E sin 4 t + e cos 4 t ; h, 



H, &c. being thermometric degrees, and t the time. 



Hence, as in my paper on the Plymouth barometric oscil- 

 lations*, we can deduce the rule, that if the thermometer be 

 observed only four times a day, at intervals of six hours, com- 

 mencing at any time, the resulting average is all but equal to 

 that deducible from twenty-four hourly observations. The 

 greatest difference is here 48°-266 (mean) — I (l92°-976) 

 = 0°*022 = one forty -Jifth of a degree of Fahrenheit. 



The differences of the homonymous hours (p.m. — a.m.) are 



lh r = +5-015 4 h r =+ 5*795 |7h r =+ 3-161 10h r = — 1-736 



2 +5-537 5 +5-478 8 +1*595 11 —3*147 



3 +5-843 6 +4-641 1 9 — 0'226 12 —4-379 



Whence by a process exactly similar to the one in the paper 

 above alluded to, there results 



temp, from noon =A = 48°-266 + 2°*1437 sin* + 2°- 1354 cos* 



+ 0-295 sin 2 t + 0-308 cos 2 t — 0*1302 



* Phil. Mag., June 1842 (Third Series, vol. xx. p. 477). 



