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MR EDWARD SANG ON THE MOTION OF A HEAVY RODY 



To obtain a clear view of the import of these results, let us describe a series 

 of circles all having the common nadir point N, and with diameters proportional 

 inversely to the squares of Ad, CB, ED, GF, IH, or, in the present example, 

 proportional directly to the numbers 1000, 3553, 6*615, 7*095, and 7*099. 

 Along these let arcs NU, NT, NX, NY, NZ, of 7°, 54° 01', 137° 15', 175° 55', 

 180°, that is homologous to the doubles of the maximum angles d', B', D/ F, 



and G' be laid off. Lastly, lay off arcs N 1 , N 2 on each of these circles, homolo- 

 gous to the doubles of the angles at d, B, D, F, and H, as obtained by com- 

 putation in the two cases. In the diagram, Jig. 11, the semicircles only are 

 drawn out ; for the sake of clearness, they are placed alternately to the right 

 and left of the common diameter NZ ; also in the smallest circle the arc NU 

 of 7° is also N 2 , and N 1 is so close to it as not to be seen in the figure. 



Let now a body be projected along the smallest circumference with a 

 velocity which would just carry it from N to U, another along the second cir- 

 cumference with a velocity sufficient to carry it to V, a third body along the 

 third circumference with speed enough to reach X, and so on. And imagine 

 that all these bodies set off simultaneously from N, then will they all reach the 

 points marked 1, 2 on the respective circumferences at the same instants. But 

 when the velocity is just sufficient to carry the body to the zenith point Z, we 

 can compute the time, and thus we are enabled to resolve our problem. 



As there are no tables of neperian log tangents, we must convert the 

 usual denary log tangents into neperian ones, by multiplying them by 2*3025, 

 the neperian logarithm of ten. Hence the final computations shown in the 

 preceding scheme ; these give 1*030520 and 1*572698 for the values oitJ(2g), 

 corresponding to arcs of 6° and 7° respectively. 



Thus, by a very easily understood and by no means an operose process, we 



