VOL. XLII.] PHILOSOPHICAL TRANSACTIONS. 701 



were to be used for. One of these was by parallel cheeks intended for taking 

 the lengths of the standard rods above-mentioned to be kept in the Exchequer, 

 another was by rounded ends, one of which was moveable, designed to take 

 the lengths of such standards to consist of hollow beds or matrices, like those 

 already spoken of at the Exchequer, and the others, to be presently mentioned, 

 at Guildhall ; and a third beam-compass was fitted in the common way, with 

 fine points, for taking off, or laying down, such measures as are marked out 

 by the distance of points or lines, on any plane flat superficies. All which 

 compasses were severally so contrived, as to be lengthened by the turning of a 

 fine screw, one of whose revolutions answered accurately to the 40th part of 

 an inch, and to which there was applied an index, showing, on a small circular 

 plate with 20 divisions, the fractional part of a revolution; and on which the 

 place of the index might, by the eye,, be estimated to about the lOth part of a 

 division ; by which the motion of the moveable cheek, end, or point, might 

 consequently be judged of, to about the 8000th part of an inch. 



But Mr. Graham, when he determined by these instruments, the following 

 particulars, desired it might be observed, that though the alterations of the 

 compasses were sensible to so small a quantity; it was not to be supposed that 

 the measures here taken with them, could be estimated to the same exactness. 

 The hand cannot judge with so much nicety, of the shake of a rod, when ap- 

 plied between the cheeks, or when let into one of the hollow beds or matrices 

 above-mentioned; neither can the eye, though assisted with a magnifying-glass, 

 pretend to see, with that accuracy, the place of the compass-points, when ap- 

 plied to the taking off a measure, set out by points or lines, on the plane sur- 

 face of a rod or rule. All he therefore thinks possible, and that he has found 

 he could several times together, under the same or like circumstances, be con- 

 sistent in, is to take such measures to about the l600th part of an inch. 



We shall however, in what follows, give those measures as they actually did 

 come out, in revolutions, divisions, and lOths; all which are also, for the con- 

 venience of the reader, in a 2d column, reduced to the common decimals of 

 an inch ; and, in a 3d, to the vulgar fractions of the same. 



It may further be noted, that the absolute quantity of all measures, anywise 

 inscribed on standards of metal, must, from the nature of things, vary with 

 the alterations in the heat or coldness of the weather; and, for that reason, 

 the exact proportion between any two standards, taken at difi^erent times, can- 

 not be expected to be found the same to the most perfect degree of exactness, 

 unless the temperature of the air shall at those different times have been the 

 same, or that a proper allowance has been made for the alteration of it. Yet, 

 in the present case, as all the several measures referred to, are inscribed on the 



