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[^»j </w " Canadian Jowml,]
t-h
f I'
U-
'f^
ON THE DIURNAL AND ANNUAL
VARIATIONS OF TEMPERATURE
AT HALIFAX, NOVA SCOTIA. , ,.,- ..^.v,.
g! Tf^INGSTON, M.A., WCv , \^
BT
II
Director of the Magnetk Observatory, Toronto,
From Bi-Hoi'blt Observations by F. ALLISON, M.A.. Di-nisn thr THnp.E Yiam 186r-6».
For developing the climatology of this country, two or more chief
stations in each province are needed, differing from ordinary stations,
partly in the extent of their instrumental appliances, and partly in the
frequency of the observations.
One of the leading objects of these chief stations has been carried
out by Mr. Allison, of Halifax, by making the observations from which
the results given in this paper are derived. The nature and purpose
of these results will be understood from the following considerations.
The majority of observers, being engaged in their various callings,
cannot usually observe often enough in the day, nor persevere for a
sufficient number of years for the collection of materials adequate for
the calculation of the normal values of the elements proper to their
several stations.
Their observations can however to a great extent be made compar-
able with those carried on more frequently, and extended through a
lonf term of years, by applying corrections deduced from the observa-
tions made at a few well equipped chief stations and continued through
a long series of years, during a portion of which the observations have
been taken at equal intervals not exceeding three hours.
The corrections are of two kinds. First, the corrections by which
compensation is made for the insufficient frequency of the observations
ai: ordinary stations; and, secondly, those which compensate their
"7' . ,
J o^^jO'^-'^o ,
^.
(^
2 ON THE DIURNAL AND ANNUAL VARIATIONS OF
insufficient continuance. It is with tlio former class of corrections that
this article is concerned.
Mr. Allison lias furwardod to Toronto for reduction a scries of ther-
mouietric readings, made by hiiu or under his direction at every even
hour (with a very few exccplions) durinjj; the three years 1867-69.
In a few instances, when rcadinfrs at 2 a.ui. and 4 a.m. were not
talccn, the ob.servation.s of the whole day were set aside. As these,
invludimj Sunda^n, were only 22, the unbroken days in the three years
amounted to 1,074, and the readings employed in the calculation
12,888; giving, for each month, 80 or 90 readings for each of the
twelve bi-hourly means.
The primary object of the computation being to learn for each
month the quantity by which the temperature at each hour differs
from the mean temperature of the month for all hours collectively,
interpolating formulae for each month have been constructed, by aid of
which the most probable temperature could be computed for any
instant in the twenty-four hours.
The following is the general type of the formulre.where T„ represents
the required temperature at any time (n) reckoned from midnight, the
unit of time being one hour, <„, t,, t^, &c., certain constant tempera-
tures, and c^, Cj, &c., certain constant angles derived from the twelve
bi-hourly mean temperatures for the particular month under consi-
deration
^n = 'o + 'i ^in («X le + i-,) + t„ sin (2 n X IB -f c,,) + <, sin (8»iX 15 + e,)
+ <j sin (4 n X 15-f c^) + t^ sin (6 n X 16 -f c^) -f <^ sin (6 « X 16 + c„)
The values of the constants t^, <,, &c., c,, c,, &c., are given for each
month in the following table.
TABLE I.
Jan.
Fm.
JUn. !Armi.[ Mat.
Jdsb.
JBI.T.
Acq.
Stpr.
Oct.
NT.
DiO.
19. S3
23.18
27.13 |37 20
48.16
6§.62
64.35
64.13
68.19
46.01
30.02
25.21
1
3.3S
4.55
6.11 I 0.80
7.81
8.42
8.04
8.18
6.87
5.68
2.77
2.64
a
1.3;;
1.37
1.72 i 1.36
1.13
0.60
0.99
1.35
1.81
1.78
1.26
1.08
3
0.32
0.26
0.12
0.36
0.00
0-78
0.78
0.74
0.42
0.07
0.20
0.33
4
0.15
0.16
0.23
0.02
0.17
0.39
0.21
0.21
0.28
0.22
0.04
0.08
6
0.15
0.13
O.ll
0.14
0.21
0.07
0.10
0.13
0.14
0.30
0.17
COT
*«
0.02
0.02
0.08
0.02
0.03
O.OC
0.06
0.01
0.10
0.03
0.02
o.oe
k
-I \,
>r,T.
Dm.
.02
25.21
.77
2.64
.26
1.08
.20
0.36
.04
0.08
.17
0.07
.02
0.04
X
?
»-i \.-
"•^ fe^-
TEMPERATURE AT HALIFAX, NOVA HCOTIA.
TABLE 1.— {Continued.)
$
'l
o ,
22103
0/1 / ' /
225 5fl 233 03 237 34
o /
242 S3
,
240 14
238 41
2jS 3'a
24! 4'0
o ,
239 32
23? iV.
/
24U 42
«a
60 32
62 43
72 43
67 48
83 23
77 40
60 66
68 21
04 20
71 68
72 17
69 61
's
204
191
24
84
•
163
64
64
CO
64
70
033
2C1
224
«4
101
210
182
123
O'J
127
183
226
243
104
07
•=6
32
23
76
164
275
2S0
276
129
17
S3
16
'i
270
270
00
270
270
270
270
90
00
00
270
270
Taking each monthly formuli pepiirately, and Riving to n succes-
sively the values 0, 1,2, 3, &c., wo obtain for tliat month the mean
normal temperatures for each of the twetity-four hour.H. as far as the
normals can be procured from the observations of only throe years.
The results are given in the following table, in which the numbers in
the final column for the year are the arithmetic means from the corres-
ponding twelve monthly numbers.
TABLK II.
Monthly Mean Normal Temperatures, at Halifax, for each of the twenty-fuur houis, from
Hi-hourly Observations in the three yean lS67-e9.
F£B. MiR. Apr. Mat. Juki. I Jolt
20
18.47
20.39
22.07
23.38
24.10
2 "
24.38
3 •'
23.91!
4 "
23.01
5 "
21. 8S
20. 9S
6 "
7 "
20.37
8 "
19.9.')
9 "
19.60
10 "
19.34
11 "
19.13
Mean
19.83
20.90
20.32
19.74
19. ?8
r.i.(n.
19.12:
19.23;
19.581
20.54'
20. 2(1 ;
24.30i
28.091
27.44
2S.44
29.03
28.90
27.90
20.35
24.83
23.74
23.09
22.60
22.07
21.48
I
24.12;
•2..'..\\\
22.09
21.65,
21.39
21.35
21.04'
22.83
24.9s;
27.05
30.24
32.30
33.67
34.10
34.15',
33.76
32.681
,30.97!
29.16
27.67
26.. '■2
26.61
25.03
24.68
o
33.06
32.15
31.36
30.85;
.30. 70 1
31.001
32.12!
3:t.94i
.36.24]
3S.68i
40.69:
42.77
43.83
44.91
45.1!)
44.67{
43.31;
41.73
39.84;
37.70;
35.93'
34.80
34.24
33.32'
42.7.'!
42.11
41.44
.40.73
40.49
41.33
43. 2«
45.71
46.21
60,66
63.02
64.95
60.041
60.24,
65.90!
56.65
64.871
53. 4«'
61.14,
48.49
4B.,38i
45.10i
44.Cfl'
43.471
82.7.'ii
61.92
60.89,
6O.O61
6>.16!
61.61;
63.t,9
6'i.OSi
58.40
60.93
63.30
Co.U'i
66.23
66.66|
60.i!6i
66.49;
66.08;
65.04'
62.96
59.98
67.08
65.07.
53.99
63.38
Adi.
Sirr.
5§.79
57.73
66.04
56.88
65.96
.57.01
58.77,
01.03
63.78;
66.72'
69.231
70. 90 1
71.99
72.S1I
73.30!
73.17;
72.33
70.81
OS.. 53;
05.66
62.89
00.96
60.00:
69.451
." I
■'.8.97'
•58.04!
.57.131
56.63!
66.01
57.09!
',!•<. Vi'
60.67;
63.61
06.70
69.17!
70.78
71.83
72.54
72.88
72.65
71.65
69.84.
67.37!
64.63'
62.19'
60., 57
69.87
69.62
Oct. Nov. I Dec.
64.07 42
&3.:,3 42
62.82:41
62.27! 41
62.04 40,
62.21 140,
63.0t!!41
64.79!42
57.21 44
69.85,40
62.30 49
64.21 61
65.36 52
65.92 52,
60.22 52
66.00:52
64.7850
62.27 48
6».4S|46,
57.44145
66.22 45
55.37 44
54.72 43
64.36,42
.78 '.•!?,
,51 34
.86 ,34
.16 33
.83 33
.97,33
.49 33,
62 33
36 31
94 ."„■),
56 ,37
.42,38,
29,39,
.62..39,
77 1 39,
.36i39,
.88 .",8,
.65 '37
09 36
.65;;i5
.10. 35
,37 35
.51 34
.95 34
85,23.63
05 23.47
14 23.28
.59 23.06
34 23.06
38 23.27
48 23.46
70 23.62
45 23.88
90 24.91
00 26.38
27.13 37.20:
48.15J 68.62 64.35J
64.13; 68.19,46.01 36.02
.74
28.70
29.17
■ ,'.04
:i,->.28
27.19
26. 17
25.38
24.81
24.46
24.27
24.10
23.85
26.21
Veab
38.79
38.15
37.40
36.81
36.68
37.08
37.94
39.25
41.08
43.30
46.60
47.27
48.36
48.96
49.11
48.74
47.73
46.18
44.39
42.68
42.29
40.30
39.68
39.20
42.33
If the difference of each hourly normal in excess or defect from the
means for twenty-four hours given at the foot of each column be taken,
we have the diurnal, variations given in Table III.
ON TUE DIURNAL .ND ANNUAL VAR1ATI0N8 OP
TAULE III.
Mtan Diwnal Varlatloni o/TemperaUirc, nl HnVfur, for each month and for thi year, from
lli-hoiiily Oli3i:rvul!itns in the tjears tHC?-(!'J.
::t
nr^rzi—
HOUB.
jAlf,
Mliln.
— f.DO
U.iii.
— l.M
2 "
—2.43
3 "
-3.i;i
4 "
—3.34
6 "
-3.211
6 "
-3.11
7 "
—3. OS
8 "
— 2.r.3
"
-1.311
10 "
+ 0.47
11 "
+ 2.24
Noon.
+ 3..'>ri
1p.m.
+ 4.33]
2 "
+ 4..'>.^|
3 "
+ 4.13
4 "
+ 3.1h
6 "
+ 2.05
6 "
+ 1.U)
7 "
+ 0.&4
8 "
+ 0.12
9 "
—0.21
10 ■'
—0.49
11 "
—0.70
One of the uses of Table III. is to supply corrections to the monthly
means derived from less frequent observations' at the same station in
other years, so as to render them comparable with the means derived
from an hourly or bi-hourly series.
This has been done in the case of the temperatures at Halifax in
1870, when the observations were taken at equal intervals of four
hours, commencing at 4 a.m. The corrections (which arc very small)
were applied to the monthly means for 1870, and the corrected means
were then combined with the monthly means for the years 1867, 1868,
and 1869, as shown in the following table.
1870, nncorrecteil
Corrections for Diurnal Variation
ISTO, corrected for Diurnal Variation.
1867—1870
Jan.
29.48
+ 0.02
29. SO
22.24
Feb.
Mar.
Apb.
Mat.
JCMI.
23.79
+ 0.02
23.81
23.34
28.63
—O.OS
28.45
27.40
40.79
+ 0.02
40.81
38.10
40.39
+0.03
46.42
47.72
59.18
+ 0.06
69.24
68.70
1870, uncorrected
Corru'Ctious for Diurnal Variation
1870, corrected foi Diurnal Variation.
1867—1870
,lni.T.
AtTd.
Sept.
Oct.
Nov.
04.50 04.27! M-54
+ 0.00—0.011—0.09
04.021 04.261 fill. 45
04.421 64.161 57.76
48.16: 38.92
-0.03 +0.0i
48.12; :.8.94
46.641 36.75
D.C. YfAR.
30.78
+ 0.06
44.28
+ 0.01
30.84, 44.29
26.C1| 42.82
I
■ -~,,-,.<.viT7-. .■-«--■
TEMPEUATURE AT HALIFAX, NOVA SCOTIA.
IIk ytur, from
IT. Deo. ' YiiAB,
f.l7-?.
1.3-1-1.
I.8S'-1
J.43|-2.
;!.CS-2.
2.B4I— 1.
2.54,-1.
2.3e-l.
l.,'.7i-l,
0.12—
1.58 +1
2.K1I +2,
3. .511 +3
3.811+3
3.71+3
3.11+3
2.(i«, + l
1.011+0
0.27+0
O.lli —
0.3k
0.72
• 1.03
1.10
—3,54
-4. IS
4.93
—5.52
—5.66
-5.25
—4.30
-3.08
-1.26
+ 0.97
+ 3.17
+ 4.94
4Ui+fi.03
981+0.62
S.t'+0.78
07 +0.41
ftSI+5.40
9(1; +3.85
17; + 2.06
40+0.35
.70—1.04
.94 —2.03
.11 -2.66
.36—3.13
10 nionthly
I station in
ns derived
Halifax in
lis of fouv
very small)
cted means
1867,1868,
Jnifi.
»
59.18
+ 0.06
69.24
68.70
D<C.
YfAR.
30.78
+ 0.00
30.84
26.01
44.28
+ 0.01
, 44.29
42.82
XT*"
An interpolating formula being constructed from the twelve monthly
means in the lowest line, on the assumption that they are the tempe-
ratures proper to the middle dai/s of the several months; if the coeffi-
cients calculated on this erroneous assumption bo multiplied respec-
tively by the following factor.-!, the expression given below is obtained,
in which T„ denotes the daily mean temperature at any time jj,
reckoned from January 15, the unit of time being the twelfth part of
tho year.
n
12
n
12
2lL
12_
. 2 n
&c.
n
V'i
sin 6
n
12
7'
:42.82 + 21.82 8111 (»i X 30 + 255.4'») +0.77 sin (2(» X 80+ 66)
+ 5.18 sin (3u X 30 + 252) + 0.25 sin (in X 80)
+ 0.89 sin (5n X 3°) + 5) + 0. U sin (6« X 80 + 270)
From the preceding equation which, by giving suitable values to
(n), expresses tho normal daily mean temperature at Halifax on every
day in the year, the mean temperatures of the warmest and coldest days
are found, together with the days of their occurrence, and the days on
which the daily mean passes through its mean annual value.
Warmest day, August 28. Mean temperature, 6-4°.90.
Coldest day, January 13, 14. Mean temperature, 21°.95.
In Spring, tho mean of the day is below the mean of the year on
April 29, and exceeds it on Ap.ll 30.
In Autumn, the mean of the day passes through its annual value
between October 25 and October 26.
TABLE IV.
COUBIilATION.
Jaw.
+0.41
+0.25
+0.32
Feb.
..:.-..
Apr.
+ 0.78
—0.02
—0.02
Mat.
Ju.ll.
!
+ 0.56i+0.49
+ 0.27-0.08
+0.20-0.19
+0.77 +0.76
—0.18 —0.30
—0.32 —0.41
7 2, 9. 9
rt 2 in
COMBINATI M.
July.
ACQ.
Sept.
OOT.
Not.
Deo.
Year.
ArithmeUo Means from 7, 2, 9
7, 2, 9, 9
e 2 10'
+0.75
-0.29
-0.33
+ 0.54
—0.48
!— 0.44
+0.60
—0.25
-0.19
+0.64
—0.00
—0.09
+0.22
—0.01
+ 0.05
+0.40
+0.06
+0.32
+0.6S
-0.09
—0.09
1
ON THE mUKNAL AND ANNUAL VAU1ATI0N8 OF
In Table IV are shown tho errors in the approiJmnto monthly means
whrn the daily moan is considered as the simple arithmetic means of
tho tcmpcraturcH observed nt 7 a.m., 2 p.m. and p.m., and of those
observed at G a.m., 2 p.m. and 10 p.m. ; atid also when the daily mean
is taken as c(\\u\.\ to the fourth part of the sum of tho temperatures nt
7 a.m., 2 p.m., and twice the temperature at 9 p m.
It is seen that tho arithmetic nieim of observations at 7 a.m., 2 p.m.
and y p.m., gives a result too hi-h by 0." jG on the average of all
months, and nearly eight-tenths too high from April to July,
Tho arithmetic mean of observations at G a.m., 2 p.m. and 10 p.m.,
is in no ca.se more tlnn half a degree in error; it is too high from
November to lu-bruary, and too li.w during the re.^t of tho year, tho
average error irrespective of sign being a quarter of a degree, and tho
error in t!ic annual moan less tliaii one-tenth in defect.
When the observation at 9 p.m. is reckoned licicc, the greatest error
which occurs in any month is slightly greater, but the average error of
the twelve monthly means, tho signs of tho errors being disregarded,
is 0.° 18, and the error in the annual mean the same as in the
preceding ease.
These results accord in their general character with tho experienco
of other places at which tho observations have been sufficiently frequent
for determining tho dlurntil variations.
As regards suitability for yielding daily means, 7, 2, 9, 9, and G, 2,
10, may be regarded as of nearly equal merit ; and as 7, 2, 9, are in
many respects mure convenient to observers than the other combina-
tion, and less liable therefore to iiitonaptiHis, these hours arc recom-
mended to those observers in Canada who read their instruments three
times each day.*
The numbers in Table III, as the title states, are tho monthli/ means
of the diurnal variations, and are only adapted therefore for the reduc-
tion of monthli/ means at single hours to monthly means for all hours,
and for the converse reduction. Comparison of like hours in contiguous
months will show a considi. ruble uillcreucc in the analogous variations.
To correct daili/ means, therefore, it is necessary to possess tables in
which diurnal variations are ,;,'ivon at much shorter intervals. As
tiiree years is scarcely r,uf"ieioiit for tho elimination of accidental irre-
gularities, the computation of the diurnal variations for every fifth day
'tea^w
* 7 a.m., 2 p.m. and 9 v-m., have been aaoptea for m»uy years by the Smithsonian Institution.
,, 2 p.m.
TKMrKnATURK AT HALIFAX, NOVA 8t'l>TIA, J
has been postponed till at least two nioro years have been added to the
scries. For a like reason, the discussion of (juestions relating to the
comparative vavinbility of didoront niuntlis, and of daily means at diffe-
rent parts of the yoar, bus nut bet'ii luidprtakeu. Tho collection of
suitable materials for Halifax is howovcr in progress, as Mr. Allison
has been observing at c(iunl intorvais of tbrco hourssinco the begin-
ning of 1871.
It was stated at tlic coinuicnccnicnt of this article, that besides the
corrections for diurnal variations, or those needed to compensate for
tho insufficient frequency of tho observations, corrections are also
required in order that observations taken during a few years may be
rendered comparable with those continued during a long aeries of years.
In procuring data for the second class of corrections some other
observers have made considerable progress ; but in order to give full
effect to their past work, it is requisite that they should undertake for
u few years at least equidistant -observations at intervals not exceeding
three hours. Among these, Mr. Murdoch, C. E., of St. John's, New
Brunswick, who has been actively engaged in Meteorology for more
than ten years, is about, it is believed, to commence a system of three-
hour intervals. Should he persevere .in this undertaking for four or
five years, his series will be inferior to that of no station now in corres-
pondence with Toronto.
It is much to be desired also that a three-hour system could be esta-
blished under Dr. Smallwood, at Montreal, and Capt. Ashe, at Quebec,
in order that their observations in past years may be more effectively
utilized.
In connection with the subject of diurnal variations it is satisfactory
to mention that, through the kindness of the Rev. Dr. Fyfe, President
of the Canadian Literary Institute, the Baptist College at Woodstock,
Ontario, Mr. Montgomery, tho mathematical tutor, with other officers
of the establishment, have been engaged for some months in taking
observations of the temperature, day and night, at equal intervals of
three hours. Mr. Montgomery is fully alive to the importance of accu-
racy j and as his arrangements are very excellent, it is anticipated that
valuable aid will be supplied by his labours towards the reduction of
observations in other parts of West Ontario.
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