450 Mr. T. Muir on the first Extension of the term Area 



mentioned is one of my most firm convictions. Even now 

 several of such applications begin to foreshadow themselves, by 

 which the electromagnet, as a source of electricity, is destined 

 hereafter to live in the lives of the millions of mankind when 

 the memory of its origin, except with the curious and the learned, 

 shall be forgotten. 



LVII. The first Extension of the term Area to the case of an 

 Autotomic Plane Circuit. By Thomas Muir, M.A., Assistant 

 to the Professor of Mathematics in Glasgow University** 



IN this country mathematicians know of the use of the word 

 area as applied to an autotomic plane circuit through 

 De Morgan's paper " On the Extension of the word Area " in 

 the ' Cambridge and Dublin Mathematical Journal' for 1850, 

 and a paper consequent upon this by Sir William Thomson, 

 " On the Potential of a Closed Galvanic Circuit of any Form." 

 The use may be shortly yet accurately explained thus : — The 

 course followed in tracing the circuit is, first of all, carefully 

 marked by means of arrow-heads; the area (in the ordinary 

 sense) of each cell is then taken a certain number of times, viz. 

 the number of times the circuit is crossed from right to left 

 diminished by the number of times it is crossed from left to 

 right in coming in the plane from a point wholly outside the 

 circuit to any point within the cell in question ; and the sum of 

 these products is the area of the circuit. 



This extended meaning being invaluable in the generalization 

 of geometrical theorems, the question of its first publication 

 becomes a matter of some importance in the history of mathe- 

 matics. De Morgan probably considered himself pioneer in the 

 matter ; he says, in the publication above cited, " no such ex- 

 tension of the word has been made that I ever met with/' The 

 object of the present notice is to direct attention in correction of 

 this to a paper by Alb. Ludov. Fried. Meisterf in the ' Gottingen 

 Commentaries' for 1769-70, entitled "De Genesi Figurarum Pla- 

 narum et inde pendentibus earum Affectionibus," which contains 

 almost all that even yet can be said on the subject. 



The paper, which is well arranged and bears marks of careful 

 preparation, extends to thirty-seven pages quarto, and is illus- 

 trated by nine large plates containing in all about fifty separate 

 figures. After a preface of four pages and a short introductory 



* Communicated by the Author, 



t A. L. F. Meister"(born 1724, died 1788) was Professor of Philosophy 

 in Gottingen, and the author of memoirs on a variety of subjects — optics, 

 hydrodynamics, military instruction, the Egyptian pyramids, &c. 



