in the Vicinity of Manchester. 249 



not more than two feet four inches, including a seam of clunch 

 which divides it, and the other is not above a foot in thick- 

 ness, they are not worth following out. On the bed of the 

 river, between this point and the weir, a coal was observed, 

 and some of it picked out to burn in the lime-kiln. This was 

 in all probability the same as the fifteen-inch seam met with 

 at Ardwick. 



With what is immediately below the clays forming the base 

 of the Medlock section I am unacquainted, as the strata are 

 not exposed, the whole length being buried under the mass 

 of dihiviiMiii which becomes of considerable thickness, com- 

 pletely covering up everything down to the level of the river. 

 [To be continued.] 



L. On the relative Signs of' Coordinates. 

 By A. De Morgan, Esq.* 



13 Y the report given in the Atlienjeum of the proceedings of 

 -*-^ the British Association at Bristol, it appears that a dis- 

 cussion arose to this efflct. Tlie usual expression for the 

 perpendicular let fall from a point [m, n) to the straight line 

 y = a x' + b, namely, 



, a)n + b — 7i , , 



appears affected with a double sign. On the one hand, it was 

 contended that this double sign has a meaning deducible from 

 the existing convejitions by which signs are interpreted; while 

 on the other hand, the weight of authority seemed to be in 

 favour of the + sign in this case being purely indeterminate. 

 The first opinion was advanced by Professor Stevelly; the 

 last by gentlemen whom it is not fair to name, as their views 

 were given on the spur of the moment, at the first reading 

 of the communication, but whose opinions are not to be lightly 

 treated. 



On thinking of this question, it has appeared to me that ac- 

 cording to the sense in which words are used, both are right 

 or both are wrong, but that there is an interpretation winch 

 ought to be preferred from those strong reasons of convenience 

 which dictate the method of choosing between + and — in 

 other cases. Absolutely speaking, tiie preceding expression 

 is certainly indeterminate; but so, for instance, is the method 

 of fixing the sign of the angle made by a radius vector with 



• Communicated by the Author. 

 Third Sciics. Vol. 9. No. 5't. Oct. 183G. 2 F 



