169 
PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
The coefficients A 0 , A 1} &c., B 0 , B 1? &c., are thus expanded in a series of ascending 
powers of c with numerical coefficients which do not converge. It seems, however, 
that if c is not greater than *6 the series are themselves convergent, and it is only 
necessary to go to the tenth or twelfth term, to which extent they have been 
calculated, and are as follows :— 
A 0 =-l-5c-3-75c 3 -6-565c 5 -9-8r)c 7 -13-51c 9 -17-6c n 
- {1 + 3c 2 + 5 •625tf t +8 -75c G + 12'225c 8 +16-2c 10 } x 
A 1 =1 + 4-5 c 2 +9-375c 4 +15-23c 6 +21-92c 8 + 29-8c 10 +38-6c 13 
+ {3c+7 < 5c 3 4-13T3c 5 -pl9-7c 7 +27-01c 9 +35-2c 11 }x 
A 2 =l-5c+5c 3 +9-85c 5 +15-75c 7 +22-56c 9 +20-24c n 
+ {3c 2 +7-5c 4 +13-13c r, + 19-7c 8 +27-02c 10 +35-2c 12 )x 
A 3 = —l-5c 3 —4-7c 4 —9-2c 6 -14-7c 8 —21-45c 10 
- (2-5c 3 + 6-56c 5 + 11 -78c 7 + 18'03c 9 + 25-4c n )x 
A 4 =-l-25c 3 —3-94c 5 —7-875c 7 —12-88c 9 —18-8C 11 
- {1 -875c 4 + 5-25c G + 9’85c 8 + 15-48c 10 + 22-45c T3 }x 
A 5 ='939 c 4 +3-07c 6 + 6-33c 8 +10-68c 10 
+ {2-63c 5 +3-94c 7 +7-76c 9 +12-6c n )x 
B 0 =l- {2'5c s +4T25c 4 +5-3125c G +6-54c 8 } 
-{3c+4'5c 3 +5-625c 5 +6-562c 7 +7-63c 9 )x 
B 1 = 2c+6c s +9-75c 5 +ll-3125c 7 
+ {6c 3 +9c 4 +ll-25c 6 +12-5c 8 }x 
Bo=2-5c 2 +5'5c 4 +7-97c 6 +10-06c 8 ‘ 
+ {4-5c 3 +7-5c 5 H-9-85c 7 +11-8c 9 }x 
B 3 =-2c 3 —4-375c s -6-5625c 7 —8-61c 9 
-{3c 4 +5-625c g + 7-873c 8 H-9-84c 10 }x 
B 4 =i-1-375c 4 —3-2c g —5-03c 8 
-{l-875c 5 + 3-94c 7 + 5-09c 9 }x 
