1886.] 



Mr Hill, On the series for, &c. 



415 



it was expected to do in the way of extracting air, and that 

 without interfering with the action of the ventilators, which still 

 behave as exhausts. 



Besides the Tobin inlets I have found that when the shaft W 

 is open, there is a supply of air from both the doors at B and C, 

 but an outlet to the door in the corner opposite to G. When the 

 shaft is closed there seems to be a reversal of the currents, under 

 the doors at B and C, so that in the one case the staircase outside 

 is fed by the lecture-room and in the other the reverse is the case. 

 This may account for some of the very large difference between the 

 exhaust and the inlet measurements. 



The effect upon the atmosphere of the room is of course not to 

 be expressed by measurement ; the reports however of some of 

 those who use it seem to shew that the experiment has to a 

 certain extent succeeded. 



In the report of the Parliamentary Commission on warming and 

 ventilation of dwellings (1857), Roscoe gives the amount of air 

 required per person for continuous occupation of a room as from 

 15 to 20 cubic feet per minute. This would require for a lecture- 

 room, occupied by a class of 100 persons, from 90,000 to 120,000 

 cubic feet per hour, so that the exhaust at present operative of 

 41,000 cubic feet is still deficient. 



(3) On the series for e x , log e (1 + x), 

 Hill, M.A. 



(1 + x) m . By M. J. M. 



The object of this paper is to give a proof of the series for 

 log" e (l ± #)> which does not employ the method of indeterminate 

 coefficients nor the method of limits. 



The necessary work nearly completes a proof of the Binomial 

 Theorem which does not involve the principle of permanence of 

 equivalent forms. 



