VOL. XVt.J PHILOSOPHICAL TRANSACTIONS. 381 



point in the circumference will be also given, and consequently its radius. 

 Lastly, having described the circle, perpendiculars let fall from its intersections 

 with the parabola, to the axis, will give the roots of the equation, both 

 affirmative and negative, in the same manner as above. 



Now the centre of the circle is investigated by a very easy construction, 

 which is to be preferred to all others in cubics. Let A, fig. 9, pi. 10, be the 

 vertex, and A F the axis of the described parabola AMD; at a distance equal 

 to b, let D K be drawn parallel to the axis, to the right hand, if it be -\- b in 

 the equation ; and to the left, if it be — b, which may meet the parabola 

 in the point D ; on the centres D and A, with equal radii, describe on both 

 sides two faint arches, intersecting each other, and through the points of 

 intersection draw the indefinite line B C, a perpendicular to the middle of 

 the supposed line A D, and which may meet the axis in the the point E ; from E 

 set off E F = 4 /> downwards, if it be — p in the equation, but afterwards to- 

 wards A, if it be + p ; and from F ( or E if /> be wanting) erect the perpendi- 

 cular F G, meeting the line B C in G ; and in G F produced, take G H = -j. ^, 

 to the right hand, if it be — 9 in the equation ; but to the left, if -|- q, and H 

 will be the centre sought, and H D the radius of the circle, which, letting fall 

 perpendiculars upon the axis from its intersections with the parabola, will show 

 all the roots, as L M, of the equation. 



On a new kind of Magnetical Compass, with several curious Magnetical Experi- 

 ments. By M. de la Hire, of the Royal Academy of Sciences at Paris, 

 N° 188, p. 344. 



There is nothing which creates so much trouble in long voyages on the sea, 

 as the variation of the magnetical needle, both because this variation is different 

 in diflTerent places, and because in the same place it changes considerably in 

 process of time. It seems that if we had exact observations of the irregularities 

 of this variation made all over the earth, and at considerable intervals of time. 

 we might discover some period of this motion, and establish a system which 

 might be of great use in navigation, liut since our oldest observations were 

 made but about 100 years since, and in some particular places only, they only 

 serve to show, that if there be a regular motion, it must needs be very slow ; 

 so that we can conclude nothing certain for the time to come from all that ha» 

 been hitherto observed. This is not because of any difficulty that there is in 

 ascertaining this variation by observation, since it is found to change but few 

 minutes in a year ; but too much reliance must not be laid upon the observations 

 of pilots, by reason of the gross errors which it is not easy for them to avoid. 

 For it often happens that near the place where the compass is, there is much 



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