142 Mr. J. A. Tomkins on the 



arrangement. Instead o£ the carve in the diagram turning 

 in group viii. it would turn in group vii., each element Eu 

 to Er would be moved one to the left, so that Er comes into 

 the CI group, Tin comes under Cs as a new alkali metal, the 

 unknown metal (Moseley's Tm II.) where Rydberg has 

 wrongly placed Yb, and Yb and Lu go each one place to 

 the right. Another way would be to suppose the curve to 

 extend to the place between Rh and Ir. This would make 

 Sa and Eu come into group viii. and Gd into Rydberg's 

 group ix. This would not be absolutely contradicted by the 

 spectroscopic evidence, as we should expect triplet series in 

 an even group and doublets in an odd one — which Eu and 

 Gd respectively satisfy whilst Sa is unknown. But so far 

 as the evidence goes at present, it would seem that the first 

 suggested change is to be preferred. 



XVII. The Slip-Curves of an Amsler JPlanimeter. 

 To the Editors of the Philosojihical Magazine, 

 Gentlemen, 



IN a paper on " The Slip-Curves of an Amsler Plani- 

 meter," in the April number of the Philosophical 

 Magazine, Mr. A. 0. Allen obtains the equation of the slip- 

 curves, and explains their use in establishing the theory of 

 the instrument. 



A similar proof, involving the use of these curves, is given 

 in Williamson's ' Integral Calculus/ where it is attributed 

 to Prof. Ball. 



But it may be pointed out that this method of proof does 

 not require the use of the slip-curves as might at first sight 

 appear. 



In a proof due, 1 believe, to Sir George Greenhill, the 

 element PQRS (p. 647) consists of the two circular arcs 

 PQ, US, having the pole A as centre, and two other arcs 

 QR, PS, described by the tracer about the fixed joint H as 

 centre. In this case the records of the wheel along QR and 

 PS cancel. 



Further, it is obvious that QR and PS may be any two 

 similar curves whatever and the same method applied for 

 the records of the wheel, which will, in general, partly 

 slip and partly roll, along QR and PS will cancel and 

 the total record and area described will be the same in all 

 cases. 



