MECHANICAL PROPERTIES OP 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 ©hanged, 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 - /—- x 4 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 of rupture is 9 per cent, which 

 means that there is one chance in four that the modulus of rupture of a 



