Rijli-d Shot.~~AIathcmatkal Correfpoiuhnce, 383 



the points of divlfion obliquely towards the poles. The wood between every pair of conti- 

 guous fpiials was then taken away, by cutting from the one line parallel to the axis, and 

 from the other perpendicular to a plane pafling through it. By this procefs, when the 

 axis was fet upright, there appeared, as it were, twelve roads Hoping upwards from the 

 equator towards the pole, bounded oa the fide next the wood by upright walls ; and the 

 fhot, when fufpendcd on an axis or centre point, could be blown round very fwiftly by the 

 breath direfted towards the pole. 



Shot of this kind were made and tried at a foundery in North Wales. By an experi- 

 ment with a brafs gun newly bored, it was afcertained that the fliot did really revolve in its 

 courfe along the bore ; but the trials with fhot of different weight and dimenfions did not 

 promife more accuracy of effe£tr than was obtained by common fpherical fliot ufed at the 

 fame time. Particular notice was taken of the manner in which the fhot flruck the butt : 

 the greatefl number of times, it fti-uck with the anterior end ; fometimes the flroke was 

 made with the broad fide, and, in a few inftances, the end which came lafl. out of the gun 

 arrived flrft at the mark. Hence it appears, that the very flight angular deviation at the 

 mouth of the piece is more than fufhcient to counteract any eiTeQ which might elfe have 

 been derived from the fubfequent aftion of the air upon a projeilile duly figured. 



It feems, neverthelefs, that this principle might be applied to advantage in bar fliot. If 

 the ends of this projeftile were chamfered or Hoped with refped: to the axis, it would pafs 

 through the air with a revolution of its extremities, inftead of one end following the path 

 of the other, as may fometimes be fuppofed to happen. 



With regard to the execrable pradice of war, I think it a decided queflion, that 

 increafe of power is, on the whole, in favour of reflitude and virtue ; and that wars are 

 likely to be fewer, lefs durable, and lefs pernicious, the more fcientifically they arc 

 conducled. 



MATHEMATICAL CORRESPONDENCE. 

 Question IX. Atifn'iTcd hy J. F — : — :—:—j}. 



In order to a folution of this problem, we have only to find the point in the plane of tlie 

 horizon, which is perpendicularly under the elevated object ; the didances of which point 

 from the three (lations are as the cotangents of the angles of elevation taken at c.ich re- 

 fpe£lively. This will be effected by the following 



CONSTRUCTION. 



LET A, B, and C be the three flations (Plate XV. Fig. i.) and n, b, and c the cotan- 

 gents of the refpeclive angles of elevation taken at each. Produce AB and CB towards 

 E and F, and make BF = BA, and BE = BC. Take FG to FB as c to b, and EG to EB 

 as a to b, and about the centres F and E with the refpeftive radii FG and EG dcfcribc 

 arcs inlcrfc£ling in G. Draw FG, BG, EG, and in GU produced take BD to AB as BE 

 to BC. 1 fay tiic point D is the required point in tlic horizontal plane. 



For, 



