iv Proceedings. [Novemtcr ijth, igoo. 



called attention to the following formula, due, apparently, to 

 Schlfimilch, which provides a useful and rapidly converging 

 expression for the circumference of an ellipse whose semi-axes 

 are known — 



permieter ^ .{a + /»y+ -(^^ -^j + e^lTT/.) + ' " " /' 



where a and /-' are the semi-axes of the ellipse. No engineering 

 text book used in this country has included this formula, which 

 is superior to those ordinarily employed for the purpose. The 

 error of the first three terms of the series as above stated is 

 found 



when /^ - '211 to be less than '05 per cent. 

 )) " = I" ,, ,, ,, ,, 2 ,, ,, 

 >j = ,, ,, ., ,, "4 '1 )) 

 Mr. Thorp described a method by which he has succeeded 

 in silvering his diffraction films, the crucial point of which was 

 the device adopted to agitate the silvering fluid in a closed and 

 completely full vessel. The celluloid films having been obtained 

 from plane gratings, were naturally not optically perfect when 

 applied, as in the specimens exhibited, to curved surfaces. 

 Mr. Thorp explained a device by which he expects to remedy 

 this defect and to secure even films from concave surfaces, the 

 surface from which the copies are taken being rotated while the 

 celluloid is in process of solidification. He mentioned that he 

 proposed to apply the designation prismatic to the gratings 

 known as echelon gratings, as he considers that name more 

 accurately descriptive of these gratings. 



Professor Dixon referred to the reversal of the lithium line 

 observed by Professors Liveing and Dewar {Proc. Roy. Sac, 

 Vol. 36 (1884), p. 472) when spectroscopically examining the 

 light produced as an explosion-wave travelled towards the 

 observer along a tube in which salts of lithium had been spread. 

 The reversal of the line was taken by Professors Liveing and 

 Dewar as showing that the front of the advancing wave was 

 cooler than the following part. By photographing the explosion- 



