LOGARITHMIC FACTORS FOR USE IN WATER ANALYSIS. 
BY W. S. IIENDEIXSON. 
Every chemist who does work in the analysis of water frequently has 
occasion to calculate over data given in terms of compounds and grains 
per gallon, to ions per liter or parts per million. Frequently he must 
carry out the reverse processes and convert his ions per liter into grains 
of compounds per gallon in order to make his results more comprehensi- 
ble to the non-technical mind. Such operations are likely to be vexatious 
and time-consuming. 
Having recently had occasion to re-calculate the data of many old 
analyses in order to have them in modern terms, I have worked out a 
system of logarithmic factors to facilitate the work. Since I know of no 
other such factors I deem it worth while to offer them to the Academy 
for record in the Proceedings that they may lighten the work of others. 
I am quite aware that there are already published logarithmic factors in 
plenty for the calculation of chemical analyses. In the lists examined, 
however, many of the factors required in the work referred to have been 
found wanting. Tables for the conversion of grains per gallon into 
parts per million are, also, not wanting. No table is known to me by 
which one may convert grains per gallon of compounds into parts per 
million in ions. Moreover, according to a recent determination of the 
Bureau of Standards, the ratio that has been used for grains per gallon 
to parts per million contains a large error. According to the Bureau of 
Standards one grain per U. S. wine gallon equals 17.117967 parts per 
million. For four place or even five place logarithms it may be taken as 
17.118, and its logarithm is .23345. 
The two columns of logarithms require little explanation. The first 
contains the logarithms of chemical factors that are required in the re- 
calculation of the analytical data in the analysis of water. For exam- 
ple, for calcium in calcium carbonate the factor is 40.1-1-100.1 and its 
logarithm is .6027. In the second column are the logarithms of the 
chemical factors plus the logarithm to convert grains per U. S. gallon to 
parts per million; that opposite calcium carbonate being .8361. Is it 
hardly necessary to state that one obtains compounds corresponding to 
ions by subtracting the appropriate logarithms from the logarithms of 
the ions. 
In the calculation of the logarithms of this table the international 
atomic weights for 1905 have been used. Five place logarithms were 
used in the additions and subtractions, and the final logarithms taken 
to the nearest figure in the fourth decimal place. Four place logarithms 
are quite sufficiently accurate for such calculations. 
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