For n lamps joined up in series we must put nl for /, and if joined in 



multiple arc we must put — for /, in the above formula. In either case, 

 ^ n * 



the value of H is found to be a maximum when the resistance of the lamp 



system is equal to that of the rest of the circuit. 



Mr. Preece then proceeds on the assumption that this condition cannot 

 be supplied when n is large, reaching the conclusion than when n is large 

 the amount of heat generated in each lamp varies inversely as the square 

 of the number of lamps. 



This is true in either of the two special cases discussed by him. If, 

 however, we have « lamps arranged in «' parallel circuits, in each of 

 which we have «" lamps, the previous equation becomes 



//'"=: 



r ^ + .+4,1 

 I «' J 



With this arrangement, it is alziayi possible to supply the condition 

 which makes // ' a maximum, entirely irrespective of the value of «. 



This condition 



where 



p-\-r = 



Hence, when this condition is supplied, the heat given out in the lamp 

 system becomes 



which is independent of the value of n. 



The heat generated in each lamp will then vary inversely as the num- 

 ber of lamps. 



C. V. Riley and Chas. Rau were elected to corresponding 

 membership. 



Election of officers for the ensuing year then took place, with 

 the following result : 



President — George E ngelmann. 



First Vice President — C. Shaler Smith. 



Second Vice President — Albert Todd. 



Corresponding Secretary — Nathaniel Holmes. 



Recording Secretary — Francis E. Nipher. 



Treasurer — Enno Sander. 



Librarian — F. M. Crunden. 



Curators — G.J. Engelmann, G. Hambach, W. B. Potter. 



