288 On Mr. Bate's Improvement in Medal Riding. 



The condition that the real part P should then be a maxi- 

 mum or minimum is expressed by the equation 



be- 



an equation which it is impossible to fulfill, since P and con- 

 sequently its partial differential coefficients are necessarily 

 real. 

 Caius College, March 5, 1833- R. Murphy. 



XLIX.Ow an Improvement inMedal Hiding. J5j/R.B.B ate, Esq, 

 My dear Sir David, 21 Poultry, London, March 14, 1833. 



A BOUT fifteen months ago, some printed representations 

 -*•*- of medals received from America were shown to me, with 

 an inquiry into the manner in which they were produced : it 

 was evident that they were the result of a ruling process; and 

 one of my sons, having been engaged in ruling micrometer 

 divisions, constructed an apparatus for performing this pro- 

 cess, upon a scale sufficiently large for medals, and obtained 

 the same results. 



The following diagram represents the construction of the 

 apparatus. 



a 

 u <Z e 



a. Being the medal. * sl °" 



