Introduction 



ccxlix 



bases, mill tin <V-i76, PI-IIS, p-i-n. ".-!, V--7, V. , iWM> iv+-7, 



Wi-75i "+> y+a-75, wlicn- tin- MI!. f. i (,, ili.- , ..rresjxjiidiri^ m id -urdi nates, 



but tin- I only the half units. 



+1 



S-3 



On the assumption that it will be adequate to consider that the sixth differences 

 of the areas (or frequencies), for a range of six or seven bases, are negligible, w< 

 may take any area N from to the ordinate at a; as given by 



(i), 



N x = O.Q 4- CL\X 4- 



and determine the six a's by the first six areas ?V-a-5. " 8 _i-5, 

 We thus find : 



a a = T ^ ( 1 20n s _ 2 5 - 600,_ V6 4- 1 200w 8 _. 5 - 1 200n 8+ - 5 4- 600n, +1 . 5 - 

 ai = y^ ( 1044>/ i _ 15 2466// s _ 5 4- 2614 s+ 5 - 1346// 8f i 5 4- 274n,, +2 . 5 ) 

 a a = T ^ ff (- 58Qn s -n> + 1725 8 _ - 5 - 1995w s+ . 5 4- 1075/i s+1 - 5 - 225n, +2 . 5 ) 



8 _!. 5 4- 75/> s _. 5 - 1057? 8+5 + 65?/ 8+ i 5 - 15n, +8 . 5 ) 



(ii). 



It is clear that equation (i) with the use of the values of the coefficients in (ii) 

 will enable us to rearrange our areas (frequencies) round the ordinates s and *+ 1 

 with a fair degree of approximation. All we have to do is to evaluate N x for the 

 two values of x, say x and x z , corresponding to the ordinates bounding the area 

 and the required area = N X2 N Xl . For example, the frequency between z t and z, +1 

 can be broken up into subfrequencies on \ or \ the original bases, or, we can in 

 cases where we know or suspect the frequency to be distributed over half the unit 

 base at the terminals, rearrange our frequencies to suit this. (See the case of 

 Cloudiness dealt with on p. cci.) Of course, wherever possible we should work on 

 the mid-range between z 9 and z t+J , but this is not possible when we approach the 

 terminals of the total range, and accordingly for the case of halving the subranges 

 and altering the centres of the same subranges we have given the values suitable 

 for terminal subranges. 



