Prof. O^Brien on SymhoUcal Mechanics. 



121 



mfim' — Oil 



tiooIjiiM cr 

 -iCfSiiTroaq^ re 



m 



uuni limits 



mm= 90 "- '■ 



^c =119 34 



= 59 8 



= 138 59 



= 104 6 



= 111 50 



ss 43 4ih<iqi.i m ^m 



= 97 58 ' ' /> 



: ' 'i^i'dfessor Miller adds^ '^ A slice parallel to the plane c, 0'0204 

 incli thick^ being placed in a polarizing instrument having the 

 planes of polarization of the polarizer and analyser at right 

 angles to each other^ the angular radius of the first blue ring in 

 air was found to be 22° 81'/' 



Dr. Smith has also analysed a crystal of* the n urio- carbonate 

 of lead_, and has obtained — 



Chloride of lead . . . 51-784 

 Carbonate of lead . . . 48-215 



99-999 



corresponding to 1 atom of chloride combined with 1 atom of 

 carbonate^ which agrees with the proportions given by Klaproth 

 and Berzelius. 



NorclifFe Hall, near Wilmslow, Cheshire. 



XX. On Symbolical Mechanics. By the Rev. M. O'Brien, M.A., 



Professor of Natural Philosophy and Astronomy, King's Col- 

 lege, London, late Fellow ofCaius College, Cambridge"^. 



IN the previous paper I pointed out the distinction between 

 geometrical and mechanical addition ; the former consisting 

 in the successive tracing of lines, the latter in the simultaneous 

 action of forces. When + is used in 

 its geometrical sense, u-\-v, or AB + AC, 

 denotes the change of position produced 

 in a tracing point by causing it to de- 

 scribe the lines AB and BD in imme- 

 diate succession, BD being parallel and 

 equal to AC ; but when + has its mechanical signL.ication, 

 U + V denotes the mechanical effect produced by the simulta- 

 neous action of the two forces represented by U and V. In this 

 way it is that AB + AC denotes the line AD, while U -j- V de- 

 notes the resultant of U and V. 



* Communicated by the Author. 



