340 ON THE MOTION OF 



to the three dimensions of matter with absolute similarity, 

 the equations will necessarily form themselves into triplets 

 perfectly symmetrical, so that when the first of each triplet 

 is investigated, the others will be had without calculation by 

 changing simultaneously throughout the first triplet every 

 letter of the triplets of notation into the letter which follows 

 it circularly in that triplet. The same observation applies 

 equally to the accents $ to allow of which in all cases, it was 

 necessary to alter in some respects the usual notation, which 

 however will not be much disturbed if we make the triplets 

 of successive accents refer to the fixed axes and the triplets of 

 successive letters to the axes of the body. 



Among the quantities which I have distinguished by sym- 

 bols, there exist the following well known relations. 



x 

 (2) X 



t' = f + fl'^+i'^+c'^ 

 x" = £"-\-a"x / -\-b"y / -hc"z / 



x, = — £, -f- ## H- a'x' -f- a "x 

 (3) y, = — >?, -+- bx ■+■ b'x' -h b "x" 



z, = — £ -H ex -+- e'x' -+- c"x 



a ~*ii 



(4) 



a b -\-a'b' -\-a"b" = 



be -h b'c' -+- b"c" = 



c a -+- c'a' -+- c"a" = 



a a' -\- b b' -\- c & =0 



aV-h b'b"+c'c" = 



a" a -hb'b -4-c"c = 



dP = cdb + cdb'-hc'db" 



(5) dQ = adc-ha'dc'-ha"dc" 



dR = bda + b'da'-hb"da" 



