563 



Mr. J. A. Broun on the Variation 



[Feb. 22, 



or, what is the same thing, A A' is expressible in the two forms Mc?w and 

 M^rZwp BB' in the two forms M^c?a>^ and M/^w^ &c., the identity of the 

 two expressions for the same arc, of course, depending on the relation 

 between the two parameters. But any such monomial expression Mc?w 

 of an arc A A' would be of a complicated form, not obviously reducible to 

 elliptic functions. Casey does not obtain them at all ; but he finds geo- 

 metrically monomial expressions for the differences and sum BB'— AA', 

 CC -BB', DD' + CC, DD'- AA' (they cannot be all of them differences), 

 and thence a quadrinomial expression KK=^^dio^-{-^^d(x)^-\-'^^dio^-\-l^clu) 

 (his ds'~pdB-{-p'dQ'+p"dd"-\-p"'dd"'), and that without any explicit con- 

 sideration of the relations which connect the parameters. 



I propose to complete the analytical theory by establishing the mono- 

 mial equations AA'=M(:/w=M^c?o;^, &c., and the relations between the 

 parameters w, which belong to an inscribed quadrilateral ABCD, 



so as to show w^hat the process really is by which we pass from the mono- 

 mial form to a quadrinomial form AA.' ='^do)-\-'^^db}^-\-'N^dio^-\-'N^d(,i^^ 

 =dS, wherein each term is separately expressible as the differential 

 of an elliptic integral, and to further develop the theory of the trans- 

 formation to elliptic integrals. 



V. On the Influence of Height in the Atmosphere on the 

 Diurnal Variation of the Earth^s Magnetic Force.'''' By J. A. 

 BrouNj F.R.S. Received January 25, 1877. 



In a paper in the Society's Transactions on the earth's magnetic 

 intensity at Bombay, Mr. 0. Chambers has examined the question of the 

 influence of height on the diurnal inequality of the horizontal force*. 

 Two instruments were observed simultaneously at 0^ 22°^ and 2^ 29"' 

 P.M. : one, a bifilar magnetometer, was 6 feet above the ground ; the 

 other, a unifilar absolute-intensity instrument, was 38 feet above the 

 ground. 



Mr. Chambers has found that, in the interval between the two times 

 specified, the change of horizontal force given by the bifilar magnetometer 

 was rather more than one third (0*37) of the mean diurnal range, and 

 that the absolute- intensity instrument showed a change about one fifth 

 less than the bifilar. This difference he does not think instrumental ; and 

 he considers that, if true, " it suggests the attribution of a very con- 

 siderable magnetic influence to the state of the medium intervening 

 between the upper and lower places of observation," &c. 



The mean changes of horizontal force between 0^ 22"' and 2^ 29"' p.m. 

 by the two instruments were as follow : — 



"The Absolute Direction and Intensity of tlie Earth's Magnetic Force at Bom- 

 hay, &c." By Charles Chambers, F.E.S., Superintendent of the Colaba Observatory. 

 Phil. Trans. 1876^ p. H4. 



