■ TRANSACTIONS OF THE SECTIONS. 41 



On the Connexion of the Weather with the Tide. By G. Webb Hall. 



From long observations in the vicinity of Bristol, the author has in- 

 ferred the following laws of phsenomena there occurring. 



1 . The barometer generally undulates at times corresponding with 

 the changes of the moon, and more frequently sinks than rises. 



2. The weather is generally unsettled at these periods, continuing 

 so for about two days ; high winds also prevail. 



3. The weather, having become determinate after such unsettled state, 

 retains the character which it assumes till the next change of the moon. 



4. These variations are found to obtain, not only at the full and new 

 moon, but at the quarters. 



5. The period from whence the weather assumes a determinate cha- 

 racter is coincident mth the occurrence of spring and neap tides. 



On Lucas's Method of Printing for the Blind. By Rev. L. Cakpenter*. 



On the Ratio of the Resistance of Fluids to the Velocity of IFaves. By 

 J. S. Russell, Esq.f 



Calculus of Principal Relations. By Professor Sir W. R. Hamilton. 



The method of principal relations is an extension of that mode of 

 analysis which Sir William Hamilton has applied before to the sciences 

 of optics and dynamics ; its nature and spirit may be understood from 

 the following sketch. 



Let x^, x^,, . . x„he any number n of functions of anyone independ- 

 ent variable s, with which they are connected by any one given differ- 

 ential equation of the first order, but not of the first degree, 



0=^ f (s, x^, . . Xr., ds, dx^, . . dx„), (1) 



and also by » — 1, other differential equations, of the second order, to 

 which the calculus of variations conducts, as supplementary to the o-iven 

 equation (1), and which may be thus denoted : 



f{x^-df{dx,) _ __ f'(x„)-df'(dx„) ' 



f {dx,) ••• /'(rfx„) ' ^^^ 



Let, also, a^, . . a„\>e the n initial values of the n functions x^, . -. x , 

 Emd let a',, . . «'„ be the n initial values of their n derived functions or 



differential coefficients x\ =— — -', . . x'„=^ — ", corresponding to any 



assumed initial value a of the independent variable x. If we could in- 

 tegrate the system of the n differential equations (1) and (2), we should 

 thereby obtain n expressions for the n functions j:,, . . x„, of the forms 



• In consequence of the request made to the Rev. William Taylor to complete a Ge- 

 neral Report on the processes of Printing for the Blind, it has been deemed unneces- 

 sary to give an unconnected abstract of Mr. Lucas's ingenious researches. 



t The Author is engaged in special researches to complete his views on the subject of 

 waves, at the request of the Association. 



