EXPLANATION OF SOURCE AND USE OF TABLES. CV 



and (gfTT-) or the length of a seconds pendukim, for intervals of 5° of geograph- 

 ical latitude. It was computed by the editor, and is based on the formula for ^ 

 given by Professor William Harkness in his memoir " On the Solar Parallax and 

 its Related Constants." * 



Table 41 gives the linear expansions of the principal metals. It was compiled 

 by the editor from various sources. The values given for the expansion per 

 degree Centigrade have been rounded (with one exception) to the nearest unit in 

 the millionths place, or to the nearest micron, since different specimens of the 

 same metal vary more or less in the ten-millionths place. 



Table 42 gives the fractional changes in numbers corresponding to changes in 

 the 4th, 5th, . . . 7th place of their logarithms. These fractions are often con- 

 venient in showing the approximate error in a number due to a given error in 

 its logarithm, or the converse. Thus, for example, referring to the remark in a 

 foot-note under explanation of Tables 36 and 37 above, the error in the loga- 

 rithm of Clarke's ratio of the yard to the metre is about 4 units in the sixth place 

 of decimals ; the Table 42 shows, then, that the metric equivalents in Tables 

 36 and 37 are erroneous by about i/ioooooth part. 



* Washington, Government Printing Office, 1891. 



