OP ARTS AND SCIENCES. 421 



of a cyclic operation are explicitly and separately considered. Altlioiigh 

 my results were in a large measure such as had previously been de- 

 monstrated by other methods, yet, as I readily obtained those which 

 ■were to me before unknown, or but vaguely known, I was confirmed 

 in my belief in the suitableness of the method adopted. 



*' A distinguished German physicist has said, — if my memory serves 

 me aright, — that it is the oilice of theoretical investigation to give the 

 form in which the results of experiment may be expressed. In the 

 present case we are led to certain functions which play the principal 

 part in determining the behavior of matter in respect to chemical equi- 

 librium. The forms of these functions, however, remain to be deter- 

 mined by experiment, and here we meet the greatest difficulties, and 

 find an inexhaustible field of labor. In most cases, probably, we must 

 content ourselves at first with finding out what we can about these 

 functions without expecting to arrive immediately at complete expres- 

 sions of them. Only in the simplest case, that of gases, have I been 

 able to write the equation expressing such a function for a body of va- 

 riable composition, and here the equation only holds with a degree of 

 approximation corresponding to the approach of the gas to the state 

 which we call perfect. 



*' Gratefully acknowledging the very favorable view which you have 

 taken of my effiarta, I remain, gentlemen, very truly yours, 



"J. AViLLARD GiBBS. 

 "New Haven, Jan. 10, 1881." 



The following papers were presented : — 



"Discovery of Palaeolithic Flint Implements in Upper 

 Eg3'pt." By Henry W. Haynes. 



" On Telegraphing across Bodies of Water without the Use 

 of a Cable." By John Trowbridge. 



" Anticipation of the Lissajous Curves." By Joseph Lov- 

 ering. 



Dr. William Everett presented the following suggested 

 emendation of Shakespeare : — 



*' Hamlet, Act I. Sc. 4. 



" ' The dram of eale 

 Doth all the noble substance of a doubt 

 To his own scandal.' 



" Every reader of Shakespeare has been puzzled by these words ; 

 and every critical student of him knows that they are the crux of 



