1870.] Mr. A. H. Garrod on the Sphygmograph Trace. 



353 



Again, in fig. 2, the ratios are : — 



1 s 3-8 



: 3775 

 : 3-8 

 : 3-825 



with an average of 1 : 3*8. 



Calling the rate of the pulse #, and the number of times the first part 

 is contained in the whole beat y, xy equals the number of times that the 



first part is contained in a minute, and — equals the part of a minute 



xy . 



occupied by the first part of each pulse-beat. 



From several observations, it was found that xy increases with x, not 

 directly as it, but as its cube root, consequently the following equation 

 finds xy in terms of #, 



xy=k \/x, 

 k being a constant, equal to 47 (about). 



For instance, in fig. 1, #=137, y= 1*7443 ; 

 and in fig. 2, #=44, 2/ = 3*8 ; 



and 137x 17443 = 238-9691, 



44x3-8=167-2; 

 and 238-9691 : 167_^: : 1*43 : 1, 



and |/137: ^44:: 



= 5-155: 3-54:: 1-456:1, 

 which shows that in these individual cases xy varies, within the limits of 

 experimental error, as the cube root of #. 



If this statement of the ratio of the first part of the trace to the whole 

 beat is a correct one, a knowledge of the rapidity of the pulse alone is 

 sufficient to enable the length of the first part to be found by multiplying 

 the cube root of the rapidity by the constant quantity 47. 



Thus, supposing the pulse beats 64 times in a minute, the cube root of 

 '64 being 4, 4x47=188, and the length of the first part of the beat 

 ought to be yj^ of a minute. In one case with # = 64, xy was found to 

 be 185*75, and in another with #=63-5, xy= 181 77, both numbers which 

 agree closely with the requirements of the equation. 



With #=140, and therefore ^# = 5-2, 



5-2x47=244*4; 



and therefore the first part=Yi- 4 — of a minute; in a pulse of that 

 rapidity xy was found =242*9. 



To save the trouble of extracting the cube root for any rapidity, these 

 facts have been thrown into a coordinate form in the accompanying Table, 

 and the observations on which the formula is based are represented by 

 dots on their proper coordinates, the calculated curve, with &=47, being 

 represented by a continuous line. 



Since the above equation was worked out, a great many other observa- 



