M. W. Haidiager on the Colours of Mausite. 215 



made from the properties of the circle to their analogues in the 

 parabola. 



The difference A between the arc of a parabola and its pro- 

 tangent may be expressed by an imaginary circular arc, meaning 

 by protangent the projection of the radius vector on the tangent 



to the cm-ve. As A= / 7,, let sin ^= a;, then A = /:^ 2; 



r dx ^ cos^ J i-x 



or A = /■= ; — — , whence 



J\ + {^/-\xf 



^_ tan-'(^A-]^) ^jQ^ 



^-1 



This gives a new meaning to the symbol a ^ — 1 . It does not 

 merely signify a change of angular position through a right 

 angle ; it has a meaning much more extensive. It indicates, as 

 we have shown*, that a property which is imaginary relatively 

 to the curve in question, whether it be a circle or a parabola, 

 becomes real when transferred to the parabola or the circle. 

 Thus imaginary logarithms represent real circular arcs; and 

 De Moi\Te's theorem is an example of a property of imaginary 

 circular arcs, which, when transferred to the parabola, becomes 

 a real positive geometrical theorem. It would be easy to mul- 

 tiply examples, the above will suffice. 



XXXII. On the Colours of Mausite. By W. HAiDiNGERf. 



" rpHE hexagonal saltof iron Fe^O^, SO^ + 3(K0) SO^ H- SH^O, 

 -L which furnished me such interesting results wath respect 

 to the presence of basic water;]:, forms ciystals which, perpen- 

 dicular to their axes, allow green light, and parallel to their axes 

 allow yellow or red-brown light (according to the length of the 

 six-sided columns or tables) to pass through them. This salt, 

 however, contains no trace of protoxide of iron, but only oxide of 

 iron, sulphuric acid, potash and water (basic water and water of 

 crystallization). Under certain circumstances, the same salt 

 forms a crystalline powder of a beautiful greenfinch colour, a 

 tint wherein yellow and green are both distinguishable." 



Thus writes my respected friend Prof. Scheerer of Freibm-g, 

 in a letter addressed to me on the 10th of May, 1853, concern- 

 ing the ciystals whose properties of colour form the subject of 

 the following remarks. 



The above memoir, "Beitrage zur naheren Kenntniss des 



* Philosophical Tr.insaction8foil852,part 2. p. 390; also sec Cambridge 

 and Dublin .Matbematical Journal for 1853. 



t Translated from Poggcudorff's Annalen, vol. .\c. p. 474; having been 

 communicated to the Academy at Vienna, July 1853,) 



X PoggendorfPs Annalen, vol. .\i. p 7'^. 



