Sentence:  As the sine and cosine are always proper fractions their logarithms are negative, i.e. have negative <WSD>characteristics</WSD>. When we are given an angle, it is impossible to say, from inspection of the angle, what the <WSD>characteristic</WSD> of the logarithm of its sine, cosine or tangent may be; so the <WSD>characteristics</WSD> have to be printed with the mantissae. 
Meaning of the word marked with <WSD> tags:  The integer part of a logarithm.