688 MR J. A. BROUN ON THE DIURNAL VARIATION OF THE 



This idea has since then (I have no doubt without any knowledge of my note 

 on the subject) been generalised in several discussions by General Sabine,* who, 

 in subtracting the ordinates of the mean curve for the whole year at any station 

 from the mean curves for the summer and winter half years, has obtained two 

 curves opposed to each other, representing the changes produced in the mean 

 curve by the sun in each hemisphere. 



It appears to me that this fact does not merit any greater value than that 

 attributed to it in the original note already cited ; since if we represent the two 

 curves for the half years when the sun is north and south of the equator by the 

 equations 



y n = o + a i sm (^ + c i) + a 2 sm (20 + c 2 ) + • • • 



y s = b + \ sin (0 + dj + 6 2 sin (20 + d>) + ... 

 The curve for the mean of the year will be represented by the equation 



_ a + b a x sin (0 + cj + \ sin (0 + c\) 



y 2 + 2 + • • • i 



and the curves representing the difference betwixt that for each half year and 

 the mean of the year will be given by the equations 



a n — b n /a, . .„ . 6, . , . \ 



yn- V = 2 + \2 Sin ^ + c i) ~ 2 sin ^ + d ^J + " • • 



y>- y = - " u 2 ° ~ \2 sin ^ + c ^ ~ 2 sin ^ + d J) + •-• * 

 or the two equations will have the form 



y n - y — A + A x sin (0 + CJ + A 2 sin (20 + C 2 ) + ... 

 y s — y = - A - A x sin (0 + Cj) + A 2 sin (20 + C 2 ) + . . . ; 



equations to two similar curves with opposed ordinates. When c x and d x do not 

 differ much, which is generally the case, the singular points in the difference 

 curves will occur nearly at the same time as in the curves for the whole year ; or 



G t = -i-g — i approximately. 



This, however, is true of any curves varying in range, as in the diurnal curve 

 of temperature for example, which obeys a law resembling that of the magnetic 



the two curves of maximum movement from each other where they have opposite forms (as the curve 

 of August from that of December at Trevandrum, and that of August from the curve of February 

 at St Helena), we shall find that the change of movement, or the range of the difference curve, is 

 three or four times greater near the equator than in high latitudes, St Helena being the station of 

 greatest change of form, the range of the difference curve being seven minutes and a half (7''5). 



If the variation of the movement of the free needle from summer to winter had been nearly as 

 gi'eat at Makerstoun, Hobarton, or Toronto, as near the equator, the curve would have been com- 

 pletely inverted. It is simply because the variation of range is less in high latitudes than near the 

 equator that the inversion does not take place there. This fact does not appear when we compare 

 the movements of the horizontal needle. 



* It has also been employed by the Rev. P. Secchi in the same way as by General Sabine. 

 Monthly Notices Roy. Ast. Soc. vol. xv. p. 27. 



