40s 



Results of Makerstoun Observations, 1844. 



TABLE IV. — Errors of the Approximate Mean Temperatures, deduced from one or two Daily 

 Observations, for each Month, and the Year 1844. 









Approximate Means ( + ) c 



;reater, or 



( — ) less than true Means. 





Months 

 and 



True 





















Max. 



17h l()m 



21b 4Qm 



21h 40 m 



22>> 10- 



22h 10 m 



17 h 10'" 



21 >> 10" 





Year. 





and 



and 



and 



and 



and 



and 



and 



and 



7 h 10". 







Min. 



4 h 10 m . 



10 h 10-. 



9 h 40-. 



ll h 10- 



10k l()m. 



23 h 10- 



9 L 10 m . 





January 



36-92 



-0-29 



-0-37 



-0-35 



-0-27 



+ 0°-02 



-0-07 



-0°-12 



-0°-47 



-0-33 



February 



32-22 



+ 0-25 



+ 0-18 



-0-25 



-0-13 



+ 0-28 



+ 0-23 



+ 0-63 



-0-52 



-0-32 



March 



38-23 



+ 0-37 



+ 0-17 



-0-26 



-0-18 



+ 010 



+ 017 



-0-23 



-0-53 



-0-10 



April 



46-60 



+ 0-48 



-0-30 



-003 



+ 0-20 



+ 0-25 



+ 0-65 



000 



-0-25 



0-00 



May 



48-46 



+ 0-23 



+ 0-24 



-0-49 



-0-21 



-0-59 



-011 



-0-41 



-0-31 



+ 1-16 



June 



54-20 



I +1-06 



0-00 



-0-23 



000 



-0-11 



+ 0-25 



+ 0-70 



-0-25 



+ 0-49 



July 



55-56 



1 +0-51 



-005 



-011 



+ 0-21 



-0-05 



+ 019 



-011 



+ 0-24 



+ 1-55 



August 



54-32 



+ 1-55 



+ 0-03 



-0-22 



+ 003 



-0-14 



+ 0-23 



-0-32 



-017 



+ 0-26 



September 



52-46 



+ 0-56 



-0-36 



+ 0-19 



+ 0-41 



+ 0-36 



+ 0-64 



-006 



+ 019 



+ 0-13 



October 



45-71 



+ 0-62 



-0-21 



-0-21 



-0-16 



+ 0-32 



+ 0-29 



+ 0-19 



-0-61 



-0-38 



November 



42-66 



; -0-78 



-016 



-0-29 



-0-26 



0-00 



-011 



+ 0-34 



-0-35 



-0-25 



December 



31-63 



+ 0-10 



-0-23 



-0-56 



-0-51 



-0-27 



-0-33 



+ 0-12 



-0-68 



-0-42 



Year 



44-91 



] +0-39 



-009 



-0-23 



-007 



+ 0-01 



+ 0-17 



+ 0-06 



-0-31 



+ 0-15 



The 12 Mo 



iths. 





















Mean of E 



rrors 



0-57 



0-18 



0-26 



0-21 



0-21 



0-27 



0-27 



0-38 



0-45 



Range of ] 



Errors 



2-33 



0-61 



0-75 



0-92 



0-95 



0-98 



111 



0-92 



1-99 



Approximations to the Monthly Mean Temperatures. — The values of the approximations to the monthly 

 mean temperature, from observations at two hours each day, may be considered inversely proportional to the 

 mean of the errors ; they may also be considered inversely proportional to the range of the errors, whence the 

 values will be inversely proportional to their product. By means of this measure, we find the values of the 

 approximations to be in the following order, commencing with the highest : — 



1st. 5 h 10 m a.m., and 4 h 10 m p.m. 2d. 9 h 40 m a.m., and 10 h 10™ p.m. 3d. 9 h 40 m a.m., and 9 h 40™p. M . 

 4th. 10 h 10™ a.m., and ll h 10™ p.m. 5th. 10 h 10™ a.m., and 10 h 10™ p.m. 6th. 5 h 10 m a.m., and ll h 10™ a.m. 

 7th. 9 h 10™ a.m., and 9 h 10™ p.m. 8th. 7 h 10 m p.m. 9th. Max. and Min. 



The best approximation to the mean for the year is given by the observations at 10 h 10 m a.m. an 

 1 l h 10 m p.m., which differs only 0°-01 from it. If the approximations to the mean for the year should be nearl 

 constant from year to year, then the best approximations to the monthly means should be determined by em- 

 ploying the mean error after correcting by the yearly difference. Thus, if the monthly means for 9 h 40 m a.m. 

 and 10 h 10 m p.m., are corrected by +0'23 — the correction for the yearly mean from the observations at the 

 same hours — the average error of the monthly means is only 0°T3. 



The following are the errors of the yearly means, as deduced from each couple of homonymous hours : — 



a.m. and p.m. 12 h 10- l h 10- 2* 10™ 3 h 10- 4 h 10™ 5* 10"' 6>> 10- 7^ 10- & 10- 9 h 10- 10* 10- 

 + 0°-83 +0°-96 +0°-76 + 0°-34 -0°-22 -0°-75 -0°-92 -0°-87 -0°-69 -0°-31 +0°-17 



The following are the errors of the yearly means, as deduced from two observations made at intervals of 

 ll h , nearly the critical interval for the year: — 



i. 



I 



Hh 10m 



+ 0°-69 



ll h 10 

 10 10 



+ 0°01 



p.m. 



A.M. 



12ii 10" 

 11 10 



A.M. 

 A.M. 



l h 10 m A.M. 

 12 10 P.M. 



2h lo- 

 1 10 



3h 10° 

 2 10 



4 h 10- 

 3 10 



5h IQm 



4 10 



+ 0°-41 



+ 0°-71 +0°-78 +0°-62 +0°-29 -0°-09 



6 h 10- 

 5 10 



-0°-32 



7h 10m gh 10- 

 6 10 7 10 

 -0°-32 -0°-14 



9 h 10- 

 8 10 



10 h 10- 

 9 10 



+ 0°-09 +0°-49 



The average of the errors for the 12 homonymous hours is 



o, 63, and the range of errors is 1 0, 88. 



12 couples at the critical interval is 0°-36, and the range of errors is 1°T0. 



Observations at each of the following three couples of hours which are at the critical interval, give the 

 mean for the year to 0°-01, — namely, ll h 20 m p.m. and lO^ 10 m a.m., 5 h 20 m a.m. and 4 h 10 m P.M., and 8 h 20 m 

 a.m. and 7 h 10™ p.m. 



