Monday, November 25, 2019

Expressing Logarithms in Points of Royal Feet


Assorted retorts from yahoo boards and elsewhere : Medieval Quadrivium and Logarithms (quora) · Φιλολoγικά/Philologica : Expressing Logarithms in Points of Royal Feet · Previous Work on Logarithms · Yes, My Method Can Close In on Logarithms

As you may know, the English foot is 12 inches which are 144 lines. The French Royal Foot, which was exchanged for the metre system, is by contrast one more subdivision, namely 1728 points.

Here is a logarithmic table where 1000 points = 1.000000 in the normal logarithms, and if you correctly subdivide the foot (even an English one) you will get a functional slide rule./HGL

Origo 0.1
 
301 0.2  2 inches 1 line 1 point
477 0.3  3 inches 6 lines 9 points
602 0.4  4 inches 2 lines 2 points
699 0.5  4 inches 10 lines 3 points
778 0.6  5 inches 4 lines 10 points
791 φ  5 inches 5 lines 11 points
845 0.7  5 inches 10 lines 5 points
903 0.8  6 inches 3 lines 3 points
954 0.9  6 inches 7 lines 6 points
 
1000 1  6 inches 11 lines 4 points
 
1041 1.1  7 inches 2 lines 9 points
1079 1.2  7 inches 5 lines 11 points
1114 1.3  7 inches 8 lines 10 points
1146 1.4  7 inches 11 lines 6 points
1176 1.5  8 inches 2 lines
1204 1.6  8 inches 4 lines 4 points
1209 Φ  8 inches 4 lines 9 points
1230 1.7  8 inches 6 lines 6 points
1255 1.8  8 inches 8 lines 7 points
1279 1.9  8 inches 10 lines 7 points
1301 2  9 inches  5 points
1477 3  10 inches 3 lines 1 point
1497 π  10 inches 4 lines 9 points
1602 4  11 inches 1 line 6 points
1699 5  11 inches 9 lines 7 points
1778 6 1 foot  4 lines 2 points
1845 7 1 foot  11 lines 9 points
1903 8 1 foot 1 inch 2 lines 7 points
1954 9 1 foot 1 inch 5 lines 2 points
 
2000 10 1 foot 1 inch 10 lines 8 points
 
2041 11 1 foot 2 inches 2 lines 1 point
2079 12 1 foot 2 inches 5 lines 3 points
2114 13 1 foot 2 inches 8 lines 2 points
2146 14 1 foot 2 inches 10 lines 10 points
2176 15 1 foot 3 inches 1 line 4 points
2204 16 1 foot 3 inches 3 lines 8 points
2230 17 1 foot 3 inches 5 lines 10 points
2255 18 1 foot 3 inches 7 lines 11 points
2279 19 1 foot 3 inches 11 lines 11 points
2301 20 1 foot 3 inches 11 lines 9 points
2477 30 1 foot 5 inches 2 lines 5 points
2602 40 1 foot 6 inches 10 lines
2699 50 1 foot 6 inches 8 lines 11 points
2778 60 1 foot 7 inches 3 lines 6 points
2845 70 1 foot 7 inches 9 lines 1 point
2903 80 1 foot 8 inches 1 line, 11 points
2954 90 1 foot 8 inches 6 lines 2 points
 
3000 100 1 foot 8 inches 10 lines
 
3041 110 1 foot 9 inches 1 lines 5 points
3079 120 1 foot 9 inches 4 lines 7 points
3114 130 1 foot 9 inches 5 lines 10 points
3146 140 1 foot 9 inches 10 lines 2 points
3176 150 1 foot 9 inches 11 lines
3204 160 1 foot 10 inches 3 lines
3230 170 1 foot 10 inches 5 lines 2 points
3255 180 1 foot 10 inches 7 lines 3 points
3279 190 1 foot 10 inches 9 lines 3 points
3301 200 1 foot 10 inches 11 lines 1 point
3477 300 2 feet  1 line 9 points
3602 400 2 feet 1 inch  2 points
3699 500 2 feet 1 inch 8 lines 3 points
3778 600 2 feet 2 inches 2 lines 10 points
3845 700 2 feet 2 inches 8 lines 5 points
3903 800 2 feet 3 inches 1 line 3 points
3954 900 2 feet 3 inches 5 lines 6 points
 
4000 1000 2 feet 3 inches 9 lines 3 points

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