24 



DR THOMAS MUIR ON THE 



[0] 



[8] + [8'] [6] 



[0] 



[0] 

 [5] 



-2[7] -[3] 

 [6] 



+ SL9'] 



-[0'] 



[9] + [9'] [4] 



[o] [7]+ mi 



[6] [0] 



[9] + [9'] [4] 



[0] [7] + [7'] 



+ 1[4] 



■[3] [8] + [8'] [0] 

 [6] [0] [4] 



[5] [7] + [7'] 



[5] 



-[3] 



[0] 



- Z[4'] 





[6] 



[4] 





-[2] 



• 



[7] + [7'] 







[5] 



-[3] 





-[1] 



. 



[6] 





[4] 



-[2] 







[5] 

 -[2] 



■[3] 

 [6] 



[6] 



[9] + [91 



[0] 



- Z[io] 



+ Z[l] 



-[3] [8] + [8'] [6] 

 [6] [0] [9] + [9'] 

 [5] [0] 



[5] -[3] [8] + [8'] 

 [6] [0] 



-[2] • [5] 



The development of the first of these eight terms, if we agree to drop the rect- 

 angular brackets in [0], [l], . . . . , 



= 0(8 + 8')(9 + 9')(7 + 7') + 0000 + 0456 - ±004(8 + 8'), 



= 0789 + 0897' + 089'7 + 0897' + 08'97 + 08'97' + 08'9'7 + 08'9'7' + 0000 + 0456 \ 



- ±0048 - ±0048' j , 

 = 0789 + ±0789' + ±078'9' + 07'8'9' + 0000 + 0456 - ±0048 - ±0048'; 



that of each of the others is directly evident ; and the coHected and simplified whole is 



0000 

 + ±00111" 



-±0048 - ±0048 

 -±0048' 

 + ±0123 



-±0158 - ±0158 

 + ±0456 + 0456 

 -±0456' 

 + ±049lT 

 + ±04911 

 + 0789 

 + ±0789' 

 + ±078'9' 

 + 07'8'9' 

 + 0123 

 - 0'456 



(27) Taking now the result of § 14, viz., 

 a, &, c, 



+ 21268 



+ ±1268' +±1268' 



-±126'8 



-±126'8' 



+ ±1556 +±1556 



-±1556' 



-±16711 



- ±16711 

 + ±1788 

 + ±1788' 

 + ±17'88 

 + ±17'88' 

 + ±4488 

 + ±4488' 



- ±44611 

 -±4589 

 -±4589'. 



a 3 



9 



-1 



h 



-2 



A 



A 

 A 



5-5' 

 8 

 



<7i 



ffs 

 



6-6' 



9 



h 2 



K 



7 







4-4' 



