III. CENTRIFUGATION 83 



In the system utilized in the vacuum ultracentrifuge already de- 

 scribed (89), an opaque strip or bar is substituted for the inclined 

 slit, so that the deviations of light are indicated by the lateral dis- 

 placement of a dark band against a bright background. Measure- 

 ments are taken from both edges of the band and averaged. Ex- 

 amples of sedimentation photographs obtained with such an arrange- 

 ment may be seen in Figures 5 and 7. 



C. MATHEMATICAL THEORY 



1. Sedimentation Constant 



Consider a monodisperse suspension sedimenting in a centrifuge 

 having an angular velocity of w radians per second. If at time t, the 

 boundary is at a distance x from the axis of rotation, the sedimenta- 

 tion velocity is dx/dt. The velocity per unit field of force, being a 

 characteristic constant for the sedimenting material, is called the 

 sedimentation constant (1) and is denoted by s. Thus: 



dx 1 .^ V 



dt (jo^x 



Sedimentation constants are usually given in S or Svedberg units, 

 i.e., in units of centimeters per second per unit field of force multiplied 

 by 10^^ Thus, for hemoglobin s = 4.4 X 10"^^ cm./sec./dyne/g. = 

 4.4aS. It is often required to correct a value of the constant from one 

 set of conditions (subscript 1) to some other set (subscript 2). Since 

 sedimentation rate varies directly as the net centrifugal pull on the 

 particle and inversely as the resisting force : 



771(0- - P2) /„>, 



S2 = Si — K^J 



mW — pi) 



where -q represents viscosity of the medium and a and p represent, 

 respectively, the densities of particle and medium. It is important 

 to note that this factor corrects for changes in -q and p only and is not 

 sufficient unless it can be assumed that these are the only factors con- 

 tributing appreciab y to the change in rate. To permit direct com- 

 parison of sedimentation constants, this assumption usually is made 

 and the values reduced to standard conditions equivalent to water at 

 20°C. Thus, if the subscript 20 refers to water at this temperature, 

 the corrected constant (1) is: 



