MECHANICAL PROPERTIES OF WOODS GROWN IN UNITED STATES. 19 
This power is given in column 3. Suppose, for example, it is de- 
sired to estimate the comparative strength in modulus of rupture 
and work to maximum load of a stick of timber whose specific grav- 
ity is known to be 25 per cent above the average. Since modulus 
of rupture varies as the first and work to maximum load as the sec- 
ond power of the specific gravity (see Table 3), it is probable that 
the modulus of rupture and work to maximum load are, respectively, 
about 125 and 156 per cent (1.56 = 1.25 2 ) of the average values for 
the species. 
COLUMNS 4 AND 5. 
The figures in columns 4 and 5 are derived from the original data 
on which the averages given in Table 1 are based, by the use of the 
processes usually employed to determine the accuracy of experi- 
mental data. They are not to be taken as too rigidly applicable to 
these averages (Table 1), but are a convenient approximate measure 
of the reliability of the averages and of the probability that an 
individual tree of a given species will be of average quality in any 
given property. 
COLUMN 4. 
The probable error of the species average as given in this column 
is a measure of the reliability of the present averages and of the 
probable change in these averages by future tests. For example: 
The probable error in modulus of rupture is given as 4 per cent; 
this means that there is one chance in four that the present average 
modulus of rupture for a given species (if based on tests from five 
trees) is below 96 per cent ( = 100 — 4) of the true, average, two chances 
in four that it is between 96 and 104 per cent of the true average. 
It follows that the two possibilities: (1) That the present average 
will be changed more than 4 per cent by future tests, and (2) that it 
will not be so changed, are equally probable. There is about one 
chance in 100 that the average will be changed by four times the 
probable error, or in this case 16 per cent. 
The figures given apply to cases where five trees have been tested. 
When the number tested is other than five the probable variation 
can be obtained from the rule that the probable variation varies 
inversely as the square root of the number of trees tested. For 
instance, if 20 trees have been tested, the probable variation of the 
average modulus of rupture is J— x4 per cent, or 2 per cent. 
COLUMN 5. 
Column 5 gives the probable variation from the species average of 
the average of tests from an individual tree taken at random. For 
instance, the figure given for modulus ol rupture is 9 per cent, which 
means that there is one chance in four that the modulus of rupture of a 
