Appendix 3 FORMULAE USED FOR COMPUTING FUTURE LEVELS OF Sr® ON U. K. SOIL Model 1: The future programme is such that the mean rate of deposition of Sr*° maintains the value it has had over the past three years (2.3 mc/km’/year). The meanrate of fallout of Sr°° between May 1954 and May 1957 has been 2.3 mc/km?/year, and the cumulative level in May 1957, including pre-1954 material, was 7.5 mc/km?. In the detailed model we can make an allowance for this pre-1954 sr*° by supposing that the mean depo- sition rate of Sr®° has been 2.3 mc/km?/year since January ist, 1954. The level on the groundat any time t (years) since that date is then given by Xg where: Xp = *3 (1 — et) where A is the decay constant of Sr*” i.e. X, (me/km?) = 92 (1 — e705) (1) The equilibrium value of X, on this model is 92 mc/km?. Model 2: Firing is presumed to cease in mid-1957. The one unknown factor in this case is the fraction of the stratospheric reservoir deposited per year. ‘ In the most recent complete year of measurement (May 1956 to May 1957) the amount of sr*° deposited at Milford Haven was 2.55 me/km? and hence the effective stratospheric reservoir, on the assumption that a fraction Am of stored Sr®? is deposited annually, is given by: Xs = 2.55/Am (2) If firing be presumed to have ceased in mid-1957, the value of the ground level concentration t years later will be: Xp = T.5e7At + nee (1—e7AmtjenAt m (3) X, has a maximum value given by: 7.5 Am + 2.55 Xg(max) = + (12 + hm) ) g-aT at a time T given by the equation: “hm = (7.5 Am + 2.55) (5) 2.55(A + Am) Thus if the deposition rate is 12% per year, Am ~ 0.12 and the ground level concentration will go through a maximum value of 17.7 me/km? in 1969. Maximum values for other values of Ay, may be calculated from equations (4) and (5). The rate of deposition at a time t after mid-1957 is given by the expression 2.55 e -OtAm)t Thus if Am = 0.12 the rate of deposition will fall by a factor of 2 every five years. Model 3: Future test programme such that the amountof sr*° generated per three-year period is equal to that created between Spring 1954 and Spring 1957. The total deposited between May 1954 and May 1957 was 6.9 mc/km? at a meanrate of 2.3 mc/km?/year. If, as before, we assume that a fraction Am of the stratospheric reservoir 247 a