10 ME. L. OWEN OK THE [vol. lxxix,, 



estimate of the productiveness of any area, and, within certain 

 limits, to forecast the colour, specific gravity, vesicularity, factor 

 of saturation by water, texture, and percentage of minor con- 

 stituents. 



(9) The planes give the impression that, since their formation, 

 they have been tilted on an east-north-east to west-south-west 

 axis to the extent of 0° 17'. The effect of such a tilt would be to 

 raise the north-north-western part of the island about 30 feet. It 

 is this part that is girt by a raised beach which reaches a maximum 

 of 30 feet above the present sea-level. Further, the inclination of 

 the isophosphatic planes is equal and parallel to that of the plat- 

 forms in the coral under the phosphate, to which reference has 

 already been made. 



(10) The formula co-ordinating the analyses is expressed as 

 follows : — 



Percentage of Ca 3 P 2 O d at any point X 

 =80 + 0-04 (height of X above sea-level in feet) 

 -0-04 XA' feet, tan 0° 17', 1 



where AB is the line of intersection between the 80 per cent, 

 datum-plane and sea-level, and XA' is the horizontal distance of 

 the point X from that line. 



1 This formula gives, for all bulk samples, a value closely approximating 

 to that obtained by actual analysis, the difference usually being less than 0'2. 

 per cent. : that is, within the experimental error of an analysis carried out 

 under commercial conditions. The theoretical derivation of the formula is as 

 follows : — Let the figure given below (fig. 3) represent a section of the island 



Kir. 3. 



cut by a plane at right angles to sea-level and the 80 per cent, datum-plane. 

 A' is the point of intersection of the trace of the datum-plane with sea-level, 

 X is the point at which it is required to determine the percentage of tricalcium 

 phosphate, XX' A' and XYA' are right angles. 



It is assumed that the percentage of tricalcium phosphate is a function of 

 the distance of X from the datum-plane, and the formula will therefore be 

 of the type : -Ca 3 P 2 O d per cent. = 80 + (/)XY. 



By analysis in the field it was found that /=0 - 04 when XY is" measured in 

 feet. Hence Ca 3 P 2 O s per cent. = 80 + 0-04 (XY feet). Now, as X"XY is a very 

 small angle (17'), XX" may be taken as equal to XY, without introducing 

 sensible error, therefore : — 



Ca 3 P 2 O d per cent. = 80 + 0*04 (XX" feet) 



= 80+0-04 (XX' feet-X"X' feet) 

 = 80 + 0-04 (height of X above sea-level in feet-A'X'' 

 tan TAX'). 



