178 THEORY OF HEAT. [CHAP. III. 



among which the factor ( 1 - 4) only has been omitted ; it follows 

 that on multiplying by (l - J^J the quantity 



we obtain 1 - qP + (f Q - fR + q*S - &c. 



This comparison gives the following relations : 



&c.; 





&c. 



Employing the known values of P, Q, JR, ft and making ?i 

 equal to 1, 2, 3, 4, 5, &c. successively, we shall have the values of 

 P&RA, &c. ; those of P 2 QA^ &c - 5 those of P &3 R A &c 



214 From the foregoing theory it follows that the values 

 of a, b, c, d, e, &c., derived from the equations 



a + 26 + 3c + 4d + 5e + &c. = -4, 

 a + 2 3 6 + 3 3 c + 4 3 ^ + 5 s e + &c. = #, 

 a + 2 5 6 + 3 5 c + tfd + tfe + &c. = 0, 

 a + 2 7 6 + 3 7 c + 4 7 rf + 5 7 e + &c. = D, 

 a + 2 9 ^ + 3 9 c + W + 5e + &c. = ^, 

 &c., 



