National Academy of Sciences. 



machine In so far that it not only follows out a reg-ilar 

 sequence as the result of its construction, but it is able 

 to follow out the principle of the game when modified 

 by the varying and unexpected moves of its antagonist. 

 Tlic manner in which this is done is briefly as follows : 

 The opponent to the automaton makes the rirst move in 

 the inline, and in so doing causes a curtain cylinder or 

 equivalent device to change, its position. Tins, from the 

 construction of the apparatus, causes the automaton to 

 make that play which the proper sequence of the same 

 requires, and at the same time moves the corresponding 

 cylinder into position. The next play of the opponent 

 moves the third cylinder, and the combination of the 

 three cylinders determines the action of the automaton 

 for the fourth; and .so on throughout the sequence. If the 

 player plays perfectly, the game will be drawn, as the 

 automacou's play is mathematically correct. If the op- 

 ponent makes a mistake, the automaton, by a simple do- 

 viee, takes advantage of it, and makes such a play as to 

 win the game. Illustrations were then given on the 

 blackboard, showing that there were three general con- 

 ditions of the problem, the third being much more com- 

 plicated than the other two. 



The application of this mechanism to a game of this 

 kind is intended to illustrate its character, and to show 

 that its addition to apparatus for registering physical 

 phenomena, or for performing geometrical or mathe- 

 matical operations, may enable such mechanical de- 

 vices to have a use much more extended than hereto- 

 fore. 



The paper of Prof. Rogers excited much interest, 

 and the practicable character of the proposed autom- 

 aton was very clearly demonstrated. Prof. Hil- 

 gard inquired how many pieces of machinery were 

 necessary. Mr. Rogers said that in the first of the 

 three cases involved by the problem, there were 18 

 levers required ; in the second case, 32; in the third, 

 48. As many cylinders were required as there are 

 units in the game; as many levers as there are com- 

 binations. To economize machinery, the board it- 

 self turned round a half or more. 



Prof. Hilgard asked whether we do not really 

 think very much as the automaton acts whether 

 the mental process was not similar to the mechani- 

 cal. Prof. Henry said that the question was trans- 

 cendental iu its character. Mr. Rogers mentioned 

 that several solitaire games could be played by an 

 automaton, and that the machinery lor this was very 

 simple, but it had not the same interest as a machine 

 which could take advantage of an opponent's mis- 

 takes. 



Three papers by Prof. A. M. Mayer of the Stevens 

 Institute of Technology , Hoboken.in the absence of 

 their author, were read by the Secretary of the 

 Academy. 



FUNCTIONS AND MECHANISM OF AUDITION. 



BY PROF. A. M. MAYER. 



This paper was entitled Suggestions as to 

 the Fuuciions of the Spiral Sea Ire of the Cochlea, lead- 

 ing to an Hypothesis of the Mechanism of Audition. 

 It opened by a reference to the paucity of investigations 

 on the form and functions of Ihe cochlea, and mentioned 

 as ttie principal if not the only contribution to the sub- 

 ject the statements and suggestions of Dr. J. W. Draper 

 in his work on physiology in 1853. Prof. Mayer dissents, 

 however, from the view taken by Dr. Draper respecting 

 the action of the auditory apparatus, bating his 



8 



on a measurement of the wave-lengths of the a<v 

 sumed vibrations and a comparison of those lengths 

 with the lengths of the spiral scalas which were believe I 

 by Dr. Draper to bo the subjects of these vibration-. 

 *"rof. Mayer shows that the seals are too short to fulllll 

 the requirement. 



Prof. Mayer's paper then gives a careful, detailed, 

 technical review of the anatomy of the ear. I' then 

 undertakes to show that t'. significance of these ana- 

 tomical relations is to brirg tie sound vibrations to act 

 with the greatest advantage on the co-vibrating parts 

 of the ear, and to cause these parts to make one-half as 

 many vibrations in a given time as the tympanic or 

 basiolar membranes. This is demonstrated by an ex- 

 tended review of the functions and possibilities of dif- 

 ferent portions of the auditory apparatus. In the course 

 of this train of argument Prof. Mayer advances the view 

 that what are known as the hair-cell cords, having 

 swellings in the middle of their lengths which cause 

 chem to act like loaded strings, are probably so consti- 

 tuted that eack hair-cell cord is adapted to co-vibrato 

 with only one special sound. He mentions, referrintr to 

 one of his own discoveries reported in 'IHE TIUCUNE 

 last October, that these hair-cell cords are placed m 

 reference to the pulses striking them, somewhat in the 

 relation which the external fibrils of the musketo bear to 

 a wave-surface to which their lengths are perpendicular. 

 If his view be correct, these cords bear to the nieuihran 

 to wbich they are attached, the same relation as 

 stretched strings bear to the vibrating tuning-forks iu 

 Melde's experiments, and therefore a corl in the dus 

 tus of the ear will vibrate only half as often in a second 

 as the basilar membrane to which it is fastened. 



Prof. Mayer waa able to illustrate this theory by an 

 apparatus devised for the purpose. But perhaps the 

 most couvinciugexpanment in support of the hypothesis 

 was this a tuuing fork held near the eir causes a sen- 

 sation corresponding to the designated pitch of the fork. 

 But the vibrations of this fork can bo seu^; to the inner 

 ear through the bones of the head. Now if we first hold 

 the fork near to tho ear and note its pitch, and then 

 press it firmly against the temporal bone, we per- 

 ceive a marked difference; we hear the simple sound 

 of the fork accompanied by its octave. By a va- 

 riety of modifications this effect was clearly brought 

 out, the sound communicated only to the internal ear 

 always having the higher octave of the folk singing 

 along with its usual note. If the external ear be now 

 closed, the higher octave sounds as loud as the original 

 note. Prof. Mayer has the testimony of an accomplished 

 musician to the success of this remarkable experiment. 



DURATION OF THE SENSATION OF SOUND. 



BT PROF. A. M. MAYER. 



This paper was headed Abstract of a Re- 

 search in the determination of the Law connecting the 

 pitch of a sound with the duration of its residual sensa- 

 tion, and on the determination of the numbers of beata 

 throughout the ran ire of musical sounds which pro- 

 duce the most dissonant sensations; with applications 

 of these laws to the fundamental facts of musical har- 

 mony, and to various phenomena in the physiology 

 of audition. Prof. Mayer unva the particulars of a se- 

 ries of experiemonts by which it was ascertained what 

 must be tiie frequency of successive sounds to have them 

 blend indistingui.shably together. Worked out mathe- 

 matically, the data indicated that the residual sensation 

 only occupied one flve-hnudredth of a second in tho case 

 of 40,000 vibrations per second; but in tho case of 40 



