300 The Rev. H. Moseley on Conchyliometry. 



The function f is arbitrary, and may be discontinuous. It is 

 supposed to be nothing at first. If it suddenly acquires a 

 finite value, the motion will begin with impact. It will be 

 easily seen that the equations of impulsive motion, and the 

 conditions with respect to the surfaces, will be satisfied by 

 the above values of u and v, and the value of the impulsive 



pressure C 1- (w 2 + r> 9 ). 



S6 



LII. On Conchyliometry. By the Rev. H. Moseley, M.A., 

 F.R.S., Professor of Natural Philosophy and Astronomy in 

 King's College, London. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 TN a paper printed in the Transactions of the Royal Society 

 ■*■ (1838, part ii.*) I have investigated certain properties of 

 the spiral curves traced upon the surfaces of shells (concho- 

 spiralsf) common to them and to the well-known logarithmic 

 spiral. 



The results deduced from my admeasurements have since 

 been confirmed by those of Professor Naumann of Freiberg 

 (PoggendorfF's Journal, 1840), who has developed, by an in- 

 dependent investigation, several new properties of these curves, 

 and determined with his accustomed accuracy, in respect to 

 an extensive series of Conchylia, the particular value of the 

 constant angle according to which each traces its concho- 

 spiral. 



With a view to a further development of the geometrical 

 properties of shells, I have in my paper, above referred to, 

 investigated certain formulae representing the equation to the 

 concho-spiral, the volume of a conchoidal solid, the position 

 of its centre of gravity, and the area of a conchoidal surface. 

 In the inclosed paper I have continued these researches in 

 respect to concho-spirals and conchoidal surfaces, and in 

 some particulars corrected them. 



King's College, London, Yours, &C, 



July 20, 1842. Henry Moseley. 



I. The Polar Equation to a Concho-spiral. 

 Let a logarithmic spiral, whose polar equation is R = R 

 g e cot A^ k e conceived to be wrapped upon a cone the angle at 



[* An abstract of Prof. Moseley's paper here referred to was given in 

 Phil. Mag. S. 3. vol. xiii.p. 464.] 

 f I have adopted the nomenclature of Prof. Naumann. 



