420 Mr. S. Lupton on the Reduction of 



measured, though of course the accuracy is greater at one end 

 and less at the other. A wooden or steel, occasionally backed 

 by lead, lath is bent between the points and the curve drawn 

 along it. With sufficient trouble an arithmetical result can 

 be carried to any required degree of accuracy. But it is far 

 otherwise with a graphical one : probably about yoQo * s 

 the limit of careful work in this case. The value of ir 

 has been calculated by two independent individuals to 500 

 figures ; by careful drawing, Stanley Jevons could obtain 

 it only to 5^. Yery careful use of the ruler and com- 

 passes is required to obtain the sixth figure in the ratio of the 

 diagonal to the side of a square, while in a few minutes any 

 one may convince himself that V2 = 1'41421 35623 73 . . . . 



Mr. Pickering; gives no details as to the method used in 

 drawing his curves, but mentions one hundredth of an inch 

 as about the limit of accuracy ; it is therefore a little astonish- 

 ing to find him dealing with an abscissa of 50*06998 parts per 

 cent, of real acid, and a corresponding ordinate of 1*404296 

 grams per cubic centimetre. Even the latter value would 

 assume an accuracy of measurement of T -J- inch in 14,042 

 inches, or 390 yards: and of course he has to substitute another 

 method. 



Two points are specially worthy of notice : — 

 Even those who depend most upon this method, including 

 Mr. Pickering, allow that a strong personal element is intro- 

 duced, since two observers might take different views as to 

 the form of curve which would most fairly represent the 

 results ; hence considerable care and practice are requisite 

 before it can be safely used. For this reason alone, if an 

 arithmetical process can be found which will give the same 

 results in all hands, it ought to be preferred. 



Secondly, according to Mr. Pickering, when the steel lath 

 he used is bent by the two hands it is really fixed in four 

 points. He says it " does not form a curve of any particular 

 nature, and does not necessarily give a curve which will dif- 

 ferentiate eventually into a straight line ; but if the experi- 

 ments form a figure on to which the bent steel cannot be fitted, 

 that figure certainly does not consist of a single parabolic 

 curve " (Journ. C. S. 1890, p. 68). 



A chemist may certainly be excused if he avoids the mathe- 

 matics of a flexible plate deformed by four pressures ; but 

 does not the practical solution approximate to choosing four 

 points such that the curve drawn through them may lie evenly 

 among the experimental points ? Through four points a 

 curve of the second degree can be drawn in a variety of ways, 

 since a fifth point is required to determine a definite curve. 



