. School: a monthly record of educational thought and progress. 576256 108 649037107316853453566312041152512 109 1298074214633706907132624082305024 110 2596148429267413814265248164610048 111 5192296S58534827628530496329220096 112 10384593717069655257060992658440192 113 20769187434139310514121985316880384 114 41538374868278621028243970633760768 115 83076749736557242056487941267521536 116 166153499473114484112975882535043072 117 332306998946228968225951765070086144 118 664613997892457936451903530140172288 119 1329227995784915872903807060280344576 120 2658455991569831745807614120560689152 121 531
. School: a monthly record of educational thought and progress. 576256 108 649037107316853453566312041152512 109 1298074214633706907132624082305024 110 2596148429267413814265248164610048 111 5192296S58534827628530496329220096 112 10384593717069655257060992658440192 113 20769187434139310514121985316880384 114 41538374868278621028243970633760768 115 83076749736557242056487941267521536 116 166153499473114484112975882535043072 117 332306998946228968225951765070086144 118 664613997892457936451903530140172288 119 1329227995784915872903807060280344576 120 2658455991569831745807614120560689152 121 5316911983139663491615228241121378304 122 1063382396627932698323045648224275660S 123 21267647932 5 5865 396646091296448 5 513 216 124 42535295865117307932921825928971026432 125 85070591730234615865843651857942052864 126 170141183460469231731687303715884105728 127 340282366920938463463374607431768211456 128 680564733841876926926749214863536422912 129 1361129467683753853853498429727072845824 130 The nature of logarithms may be illustrated graphicallythus : Fig. Along OX mark off equal parts, Oh, be, cd . ., thenOc = 2O6 ; Od = 3O6 . ., and so on ; so that if O/ bethe Mth term of the series Ob, Oc, Od . . then Ol = ,and the numerical measures of Ob, Oc, Od . . Ol in termsof are i, 2, 3 . . w. 68 SCHOOL: A MONTHLY RECORD OF Along OY mark off OA, OB such that OB = yOAand take a row of points, C, D, E . ., such that AB, BC,CD, DE . . form a whose common ratio is r. Thenit follows that OC = )-^OA ; OD = r^OX . ., and soon. So that if KL be the wth term of the progressionAB, BC, CD . ., then OL = ^.OA, and the numericalmeasures of OB, OC, OD . . OL in terms of arer, r-, r^ . . r.* Through B, C, D . . L draw parallels to OX meetingthe ordinates through 6, c, (/.../ in )3, 7, 8 ... X. Then the co-ordinates of any one of these points satisfythe equation y = r^. Bisect each of the lines Ob, he, cd, thus forming anarithmetical progression with double the number of termsa
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