30 Mr. T. H. Blakesley on a Geometrical Determination 



majority of compounds at present rest upon a most uncertain 

 basis : the constitution of the paraffins, of the benzenes, and 

 of the haloid compounds and alcohols derived from the hydro- 

 carbons of these series, may be regarded as determined with 

 a degree of precision almost amounting to certainty ; but in 

 the vast majority of other cases we have as yet no secure 

 method of arriving at conclusions which in any sense 

 approach finality. There can be little doubt that in framing 

 our modern conceptions of valency, we have been too much 

 influenced by the graphic symbols which have been so widely 

 made use of. In the future it will be necessary to attach a 

 more liberal interpretation to the facts, and it may be hoped 

 that it will some day be possible also to take into account 

 differences depending on the relation of the different forms 

 of matter to the pervading medium. 



IV. On a Geometrical Determination of the Conditions of 

 Maximum Efficiency in the case of the Transmission of Poicer 

 by means of Alternating Electric Currents. By Thomas H. 

 Blakesley, M.A* 



1. ^l^HIS paper treats the above problem as a particular 

 -■- application of the method of representing Combinations 

 of Electromotive Forces possessing a simple Harmonic Law of 

 Change, already given by the author more than three years 

 ago, and detailed in a series of papers published during 1885 

 in the ' Electrician.'' 



It was then pointed out that, though with two constant 

 electromotive forces acting in a simple circuit the transmission 

 efficiency does not exceed the ratio of the smaller to the larger, 

 yet with alternating electromotive forces [denominated by 

 their maximum values] the efficiency may exceed this ratio, 

 owing to the self-induction of the circuit, and to the possibility 

 of varying the interval of time at which the phases of one 

 electromotive force may follow the corresponding phases of 

 the other. 



It is here proposed to show how the particular interval of 

 time which will give the maximum efficiency may be geome- 

 trically determined, and what the value of that maximum 

 efficiency is for two given electromotive forces undergoing har- 

 monic repetition in the same given period, in a simple circuit 

 possessing a known resistance and a known coefficient of self- 



* Conunuiiicated by the Physical Society : read November 12, 1887. 



