Mr. Ivory on the Theory of the Astronomical Refractions, 89 
It will be my endeavour to ascertain the other localities visit- 
ed by this storm, as the former ones registered by my anemo- 
meter, and also by that used by Mr. Osier of Birmingham, 
w'ould appear to have occurred at the time that might have 
been expected for each locality within the circle of the storm, 
thereby bearing out most fully Col. Reid’s ingenious theory. 
Thestorm of Tuesday last was at its maximum at about a quar- 
ter to 5 a.m. of the 18th, being then at the pressure of 13 pounds 
on the square foot, or according to Dr. Hutton’s table, tra- 
velling at the rate of about 60 miles per hour. The barome- 
ter on Tuesday at 9 a.m. stood at 29‘82, it fell at 5 p.m. to 
29*58 ; at 9 a.m. on Wednesday (to-day) to 29*27, and at 
5 p.m. to 29*19, being a fall of 0*73 in the twenty-four hours. 
Should the above remarks be worth your acceptance, they 
are most perfectly at your service. 
I remain. Gentlemen, yours, See, 
Swansea, Dec. 18, 1839. J. W. G. GuTCH. 
XVI. The Baherian Lecture. — On the Theory of the Astro- 
nomical Refractions. By James Iyouy^K.H.j M.A..iF,R.S. 
L. 8^ Instit. Reg. Sc. Paris, Corresp. et Reg. Sc. Gotlin. 
Corresp. 
[Continued from vcl. xv. p. 507, and concluded.] 
12. Y\/^E next proceed to inquire into the influence which 
the term multiplied by f, before omitted, may 
have on the refractions. 
Investigation of the integral Q^. 
The expression of this integral is, 
/ W p (J np I 'j’3 » 
——[Sc-^^-Sc ^-\-7xc-‘^ — 2x'^ c~^ + — 
0 ^ ' 6 ' 
which is a negative quantity, as appears from the valuation of 
it in § 9 : it will therefore contribute to distinctness if its sign 
be changed, in which case it will be thus written, 
p*T)i e d X 
Qg = / 8 c-2«^-1-8c-^ — 
and the formula for refractions will now be, 
88 = sin8x ^^lt^)(Qo+xQ,-/Q,-/'Q3] . 
V 5 2 / 
Suppressing the tedious operations of reducing, we may 
