58 T. BRAILSFORD ROBERTSON. 



The existence of the lower limit is evident from a consideration 



of the equation 



au 

 t=- + fi, 



r(n -f 7') 



for since b has a negative sign, when 



;/ b 



v(ii -+- v} a 



then the time of one beat is zero, and for still lower values of 

 // [r(// + ?')] the time of one beat would be negative, which is, of 

 course, impossible. The equation 



u_ _b 



r(n + ?) a ' 



therefore gives us a theoretical lower limit, in this case 562 x io~ 5 . 

 Before this, however, as the experiment with LiNO 3 shows, the 

 beats begin to fuse - - for the beats take a certain time to traverse 

 the heart, and this interval may be greater than that between the 

 beginnings of two beats. The upper limit is possibly the expres- 

 sion of the fact that ions must reach the minimum number neces- 

 sary to displace those in combination with the proteids (the 

 " threshold-number ") before they have time to diffuse away 

 through the tissue. Before this point, however, irregularities 

 appear, as in the last two experiments in the table above. The 

 beats soon stop in these extreme solutions. Thus in KC1 or in 

 20 c.c. A T 10 NaCl -f 30 c.c. N/io KC1 the beats are only sustained 

 for about 5 minutes at 21 -in the latter solution the value of 

 n [?/( // + ?'j] is 706.9, and we notice that it is just about at this 

 value of iil\T.>(u -f ?>)] that irregularities begin to appear in the 

 value of the constant a. Hence the limits for CcriodapJinia are 

 probably 570 x io~ 5 and 700 x \or : \ Any solution in which 

 U/[T'(II + 7')] lies between these values, and which does not 

 contain any substance forming irreversible proteid compounds, 

 should sustain the heart-beat in this organism - - solutions hav- 

 ing values of /[?'(// + 7')] falling outside these limits could not 

 sustain the heart-beat. 



10. By mixing a solution having a value of it/[v(n + t>)] below 

 the lower limit for the rhythmically contracting tissue in question 



