Mr. F. Y. Edgeworth's Problems in Probabilities, 371 



on the obscure glass, the position of which can he read on a scale 

 fixed to the glass precisely as in Jacob's well-known galvano- 

 meter arrangement. The lens may be dispensed with, and an 

 ordinary Thomson's spherical mirror substituted for the sus- 

 pended mirror by fixing the obscured glass in the end of a 

 third tube, which can be telescoped out of and into the tube 

 Tj so as to adjust the focus. One end of the coil is attached 

 to the pin p x and the other to the pin p 2 , while the wire w 

 conducts the current back parallel to the axis of the coil to a 

 third pin p 3 , fixed close to p x . From p r and p 3 the current is 

 conducted, by means of a pair of flexible electrodes twisted 

 together, to proper terminals on the platform P. 



In using the instrument, place it on a table in a well- 

 lighted room and level the platform P. Then turn the coil 

 until the central division of the scale s coincides with the 

 cross wires of the telescope, and take the reading on the scale 

 S. Pass a steady current through the coil and note how far 

 the tube has to be turned to bring the central division of s 

 again to the cross wire of the telescope. Repeat this reading 

 with the current reversed, and move the scale S if necessary, 

 until the angles on the two sides of zero are equal. The cur- 

 rent flowing through the coil is then given by the equation 



p_ H sin 6 



AlTT 



<«-*# 



where 6 is the angle through which the tube is turned from 

 the zero position to bring the central division of s to the cross- 

 wire of the telescope. The degree of accuracy attainable in 

 the determination of 6 is evidently very great, and can be 

 pushed to almost any extent by fine division of S and micro- 

 scope reading. 



XLYI. Problems in Probabilities. By F. Y. Edgeworth, 

 F.S.S., Lecturer at King^s College, London*. 



SOME interesting problems in the Calculus of Probabilities 

 are presented by the business of Bankingf. The profits 

 of the Banker depend upon the probability that he will not 

 be called upon to meet at once more than a certain amount of 

 his liabilities. Assuming that the demands made upon him 

 fluctuate, like so many other phenomena, according to the 

 exponential law of frequency, we may employ the Theory of 



* Communicated by the Author. 



t See the writer's paper " On the Mathematical Theory of Banking," 

 read before the British Association, September 1886. 



