In recent papers Bing (1) and Williams (2) have proposed formulae which these authors believe to be more accurate than the original "standard" and "maximum" clearance equations of M6ller, McIntosh, and Van Slyke (3,4), in expressing the effects of urine volume flow on the urea clearance in human subjects. Both Bing and Williams base their formulae on the data of M6ller et al (3).The essential test of accuracy of such a formula is the consistency with which it permits one to calculate, from clearances shown by a subject with widely varying urine flows, the clearance that he would show with a given constant urine flow. Neither Williams nor Bing has applied such a test. In the present paper it is applied to compare their formulae with the original equations of Miller et al, with data from both normal and nephritic subjects. The theoretically derived equation of Dole (5), which was apparently overlooked by both Williams and Bing, is also included in the comparison, and tentative conclusions are drawn concerning permeability changes in the renal tubules in chronic nephritis.CLEARANCE FORMULAE Maximum and standard clearance formulae of Austin et al (6), and M6ller et al (3). Simultaneous observations of urea excretion rates, urine volumes, and blood urea concentrations made by Austin et al (6) and by MBller, et al (3) showed that the urea clearance, defined as the volume of blood containing the amount of urea excreted in 1 minute, was but little affected by urine flow changes in normal human subjects when the flow (per 1.73 sq. m. body area) exceeded an "augmentation limit" which was usually about 2 cc. per minute, but that when the urine flow fell below this limit the urea clearance fell with the urine flow, the clearance then becoming proportional approximately to the square root of the flow. Chesley (7,8) confirmed the square root rule for urine flows down to about 0.35 cc. per minute, but found that when extreme dehydration reduced urine flow below this rate, further reduction in flow was accompanied by a more rapid fall in urea clearance, which then fell in direct proportion to the urine flow, rather than to its square root.The above empirically observed effects of urine volume on the urea clearance in the 3 respective urine flow ranges are expressed by Equations 1, 2 and 3, in which C. represents the clearance calculated as UVIB, for any urine volume flow V (in cc. per minute), and U and B indicate the concentrations of urea in urine and blood respectively. When V exceeds the augmentation limit of about 2:1. C, = Cm = constant for each subject.Cm is the "maximum clearance" of M6ller et al (3), and averages 75 for normal adults.' When V is between the augmentation limit and 0.5 cc.per minute:2. C, = C, fV- 3. C. = Rm X V. Rm is a constant, the maximum U/B ratio attainable by decreasing urine flow to its minimum. The average normal value of Rm is about 75. (In nephritis the value of Rm may fall to 3 or 4 (9) and be reached with urine volumes above 1 cc. per minute [see Table IV is made by using as V corrected, t...