The final equations for the leveled data, N., , are given by: 

 (9.8) Nfj^ = N.j^ + . 010744 j + .000140 k- 5.256144 



(9. 9) Nj*k = Njk - .001575J + .003584k + 5.425500 



The leveled data are given in Tables 9. 1 and 9. 2. Data at the missing 

 points were determined by interpolating the leveled data at the neighboring 

 points. 



The preceding can be simplified by interpolating the data at the start 

 for the missing points. It will be shown that this method yields the same re- 

 sults to at least five significant figures. From equation (9. 8) the missing 

 data in the second run are given by: 



(39,45) : 4.830825 



(40,45) : 4.820081 



(41,45) : 4.809338 



(42,45) : 4.789590 

 if N?, is assumed to be zero at the missing points. By interpolation at the 

 neighboring points, one coixld assume the missing data to be given by: 



(39,45) : 5.02 



(40,45) : 5.03 



(41,45) : 4. 92 



(42,45) : 4. 77 



If one were to start the leveling over again, with the missing data 



tabulated above under the assumption that N-j^ were zero at the missing 



points thus using the entire 5400 points and the matrix A, there woxild be 



no change in the results. This is a fundamental property of a least square 



85 



