LOGARITHMS 35 .1673. The difference between this mantissa and the next higher is .0030, while the difference between it and .1694 is .0021. We have, then, to increase the number 147, which corresponds to " the mantissa .1673, by |^ of 1, or .7. We find, then, that .1694 is the mantissa for 147.7 and, by the rule for pointing, M=.001477. The accuracy of results obtained by means of logarithms de- pends upon the number of decimal places given in the tables that are used, and this accuracy has reference to the significant figures counted from the left. In general, a table will give trustworthy re- sults in as many significant figures, counted from the left, a-s there are decimal places given in the logarithms. For example, four- place logarithms would show no difference between 35492367 and 35490000, while, on the other hand, a result like .00003459 would be considered accurate to the eighth decimal place. Logarithms cannot be used to any great extent in financial computations where large sums are involved. For example, it would take a nine-place table to yield exact results if the sums involved should reach a million dollars. EXAMPLES Find by logarithms the values of the expressions in Examples 1-3 and state the degree of accuracy in each case. V293. (-.034)1' , V2356.V^3426 3 /(35.62y (.004593)'-\ - 2345 ' " (.02345)3 ' \ . (29342)* / 4. By logarithms find an approximate value for the twentieth term of the series 1+^+^+.... 5. Find the simple interest on $6237.43 for 7 years and 3 months at 5.632 per cent. Assuming that the work has been done with four-place logarithms, is the result sufficiently accurate for commercial purposes? Explain. 6. Find the volume of a right circular cone whose base is 6 feet in diam- eter and whose altitude is 16 feet, assuming the formula ^ w'^h for volume. 7. Find the value of a solid sphere of copper 16 inches in diameter at 19.75 cents per pound, knowing that the specific gravity of copper is 8.838 and that a cubic foot of water weighs 62.5 pounds. sas'eo ja^dnns aqi m posn aq 01 poq^arn aqi. afB-EisTinT 01 BAJBS {{TAV sa[durBxa SuiAonoj aqi jo OAVI jo suoTirqos aqi inq 'uaAig aq TIBO suoifBnba pninauodxa jo nortn^os 9q^ joj 9^111 ^BjauaS oj^ » So\ — q §o\ S'B UO^TJAS. aq tonu'ea '(T ^q^ os ^na^onb B jo niq'^p'B §o\ oqt '»ou pn'B smq^Tj'Bgo^oAV't jo tnai^onb oq^ si (g) uop'Bnba jo apis ^qSu aq^ no uoissajdxa aq^ ^q^ pa^ou A^nja.reo aq tsnni '^ , ^ vSo\ (S) 'pot^^ 60TO^ '. q §0{ = » So[ x 'iBA^od B jo nnpT.TB§o{ aq^ roj niaroaq^ aq^ .iCg -sapis qqoq jo smq^u'eSot Svn-^ Xq A^Tp'Baj paAps aq ireo noi^BTiba STqj^ (l) $=.» , uoTi'enba - aq^ Aq naATg ST noTt'enba pituanodxa vs jo nuoj ^sa^dnns aqj^ uoifimba {vifU9uodx9 TIB pa^pa si ^nanod xa ire S'B sjnooo jaqninn uA^onspm aq^ qoiqAV m uon'Bnba UY A'BA^. am'BS aq^ m pa^Ba-q aq XBTO pu'e K=^t) noTreTiba aq^ s^ adA'^ anrBS aq^ 10 si noi^Tiba STqj^ "»nanodxa aq^ jo 'H'Bd B gi 'uAvou^nn aq^ 'M ajaqAi 'i-«(8)9==Slf'86 gaAT§ g § jo (,9) noT'^'Bnba 'ApAi-padsaj 'g pTiB 's-l:f'86 '9 are noissajgojd {Bou^amoag B jo OT^BJ aq^ pn'B 'mjat ^S'BI aq^ 'mjat '»SJTJ aq^ JT 'a{dm'Bxa roj tuanodxa TIB S'B SJTIOOO ^ aams 'su'eani Xj^nanlap A'q y pmj 0^ a^qissodmi A^u'empjo si ^ 'uA^ou^nn ST TioissajSojd ^BOuiainoaS B jo smja'} jo jaquiTiu aq^ uaqAV faq^ g § TIT pa^ou S'BAV 11 0=9+a-9+^ a^dnrBxa joj i nAvonsrun st luauodxa aq^ Aq pa'pajj'B jaqmnn aqi pnB nAvou3[ a-re sinauodxa aq^ Bjqa§['B ATO^naTiia^a nr jnooo '\vvft snoi'i'BTiba aq^ jo isoni ni snoTi'BTiba 1'Bpnanodxa 91: j.N:a::R[i,g3:A.(n s.o xaoaHj. ivonvxaHiiVM eg