WATER CONSERVATION SURVEYS OF N.S.W. LXXXVII. 
Mr. C. J. Merrietp said that Mr. McKinney mentioned in his 
paper, that the limit of error allowable by the Government 
Department over which he had control was not to exceed one foot 
in one hundred miles. He would would like toask Mr. McKinney 
by what method or equation he would represent the error to be 
allowed in a short distance, say one mile. The United States 
Coast and Geodetic Survey, and other large departments of survey 
adopted an equation that varied as the square root of the distance 
to represent the limit of error; for example in the U.S. Coast 
Survey the limit of discrepancy in feet between duplicate lines, 
was not to exceed 0-029 VM, in which M equals the distance in 
miles, so that for a distance of one mile this equation would give 
0-029 as the limit of error allowable, in a distance of one hundred 
miles the limit would only be 0:29. Such a result could not be 
expected under the conditions that levelling was performed on the 
_ Surveys conducted by Mr. McKinney, indeed it could not be 
expected. Further, the function that was universally adopted for 
measuring the relative accuracy of different sets of observations 
was as follows 
Ss 
R= + 06745 eo" 
ym(m 
in which & equals the probable error of the mean, m equals the 
number of observations ; if v, v2 Us ete., is put to represent the 
residuals obtained by subtracting the several results from the 
mean, then = [v v] will be the summation of the squares of these 
residuals, If there are but two observations this formula reduces to 
R=+4}4V 
in which V equals the discrepancy between the two results. No 
doubt many of the members present would be familiar with these 
equations, which were deduced from the theory of least squares. 
The discrepancy which Mr. McKinney shewed between certain 
lines of levels certainly gave an idea of their accuracy, and shewed 
that the work must have been conducted with care. Mr. McKinney 
was to be complimented for fixing some standard of accuracy such 
ashe mentioned. _ 
