378 
MR. C. CHAMBERS ON THE SOLAR VARIATIONS OE 
indicate the maximum deviations expressed by each pair of terms in the respective 
months January, February, March, &c. to December, and for the whole year, and the 
angles A 01, A 02, A 0 3, &c., reckoned in a right-handed direction from AO, when 
converted into time, show the hours at which the several maxima occur. The curves 
having reference to Gottingen astronomical hours, it will be necessary, in order to adapt 
them to Bombay time, to turn backward (i. e. in a left-handed direction) the zero direc- 
tion line A O by an equivalent in each figure to 4 h 12 m . It will be seen that this method 
of exhibiting variations brings to light in the regular solar-diurnal variations niceties of 
change in character which would fail to be noticed on a mere inspection of the respective 
ordinary representative curves. For instance, if the supposition mentioned above, that 
the change from month to month in the character of the solar-diurnal variation was one 
of extent only, not affecting the relative deviation at different hours, the variation at 
different parts of the year might be expressed in the form 
fc^CKA), cos n -J- (B)j sin w+(A) 2 cos 2w+(B) 2 sin 2/4 -{- (A) 3 cos 3w+(B) 3 sin 3 n-Y & c.}, 
where (A) 1? (B)^ (A) 2 , B 2 , &c. would be constants, and C a function of the day of the 
year, or of the concurrent variable, the declination or right ascension of the sun. In 
this case a change in the value of any one of the coefficients A„ B„ A 2 , B 2 , &c. (equal 
respectively to Cx(A) 1? Cx(B) 15 Cx(A) 2 , Cx(B) 2 , &c.) would be attended by a pro- 
portional change in all the others, and the direction of the resultants of A! and B 1? A 2 
and B 2 , A 3 and B 3 , &c. respectively, would be invariable throughout the year. Thus in 
the curves Nos. 31 to 33, Plate XXVIII., the points 1, 2, 3, &c. to 12 and © r should in 
each case lie upon a straight line directed through the centre of coordinates. To such 
a requirement their positions do roughly conform ; but there is sufficient evidence of 
system in their departures from the rule to render the latter worthy of independent con- 
sideration. The most striking feature about all the three curves is undoubtedly the 
existence of the semiannual inequality in the values of the several maximum deviations, 
the greater values occurring about the northern solstice, the lesser about the southern 
solstice : this is in accord with the now well-known semiannual inequality in the diurnal 
variation, which inequality is shown for Bombay by the curve No. 21, Plate XXVI., and 
by the numbers at the foot of Table XII., and possesses the character commonly attributed 
to it as general throughout the globe. The points n, s, a , d in figures 31 to 33, Plate 
XXVIII., mark the mean values of the coefficients respectively for the half years, April 
to September, October to March, January to June, and July to December. Let us now 
confine our attention to the monthly excess or defect of the coefficients A,, B 1? A 2 , B 2 , 
A 3 , B 3 , &c. over the annual mean values ; or, what is to the same effect, let us imagine 
the centre of coordinates in the figures 31 to 33, Plate XXVIII. removed to the points 
© r, and let vertical lines be drawn upward from these points to A' ; then will the lines 
r 1, r 2, r 3, &c. to r 12 represent in magnitude and direction the monthly maximum de- 
flections that must be geometrically superimposed upon the annual mean maximum de- 
flection in order to produce the actual monthly maximum deflections ; and the angles 
A' r 1, A' r 2, A' r 3, &c., converted into time, will show the hours at which the monthly 
superimposed variation gives a maximum of deflection for each pair of terms of the 
