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two methods of dealing with the debt of £96,000. In the first place, the Government might pay to the Fund 3-| per cent, interest on the debt, together with a sinking fund which would redeem it in thirty-five years. It happens that 5 per cent, per annum would exactly cover the interest and sinking fund for that period, making an annual payment of £4,800 —£3,360 for interest and £1,440 sinking fund. As I understand, however, that it is desired to know the lowest annual amount necessary, I can only suggest that the debt should be taken over by the Government for an unlimited period, £3,360 being paid annually to the Fund as interest; this would be the lowest that could be paid to maintain the Fund in a sound condition. 6. If the latter suggestion should be adopted, it would be necessary to provide an annual sum of £11,820 —of course, increasing with the increase of the Force. I would, however, point out that, in practice, there would be receipts from various sources, which cannot be calculated, that would go towards lessening the annual amount paid by the Government, as follows :—■ (1.) Some officers will doubtless prefer to remain on service drawing full pay after they have become entitled to pensions. It is obviously impossible to make any estimate, but a considerable saving will probably be effected in this direction. (2.) In paragraphs 11 and 12 (page 7) of the Commissioner's Eeport it is provided that there shall be returned to officers resigning or dismissed certain proportions only of their total deductions, whereas my estimates provide for the return of the whole of the deductions in these cases. The balance would go to diminish the annual payment by the Government. (3.) The miscellaneous sources of income which it is proposed should go to the Fund (page 5, Commissioner's Eeport), would properly go to the Government if the whole liability were taken over as proposed. 7. It is impossible to calculate the benefit No. 7 (page 6, Commissioner's Eeport), as the allowances are indefinite, being anything up to three-fifths of the pay; but I assume that they will be granted with discretion and a due regard for the condition of the Fund. 8. It will be understood that it is absolutely necessary, in order to maintain the Fund in a sound condition, that the whole of the accrued funds belonging to it shall be invested to earn not less than 3f per cent, interest. Any additional interest that may be earned could go either to the credit of the Fund or to diminish the annual payment by the Government. 9. Finally, I may say that I consider the Fund should be investigated periodically, not less than every five years, as it is not possible to estimate some of the proposed benefits with great exactness, and, although I have made my estimates with care, only the test of actual experience will show whether the payments are too large or too small. I am satisfied, however, that the divergency will not be sufficiently great to interfere with the successful progress of the Fund on the lines laid down. Morris Fox, Actuary.

The Commissioner of Police to the Commissioner of Insurance. Sir, — Police Provident Fund. 4th September, 1899. By direction of the Eight Hon. the Premier, I have the honour to enclose you herewith returns giving—-(1) the ages, length of service, and rates of pay of the members of the Force; and (2) number of men retired from the Force on compassionate allowance during the ten years ended 31st ultimo, giving their ages and length of service at the time of retirement; and to request that you will be good enough to obtain and submit a report from the Actuary of your department, stating the lowest probable annual amount required to maintain a fund under which men can be retired on the lines given in my last annual report, except that the age for voluntary retirement is to be sixty years instead of fifty-five, and the amount of retiring-allowance to be one-sixtieth of average salary for each year's service instead of one-fiftieth. In making the calculations it is requested that no provision whatever be made for management or other similar expenses, the whole of the amount to be provided, and any interest that may accrue therefrom is to go absolutely for the payment of retiring-allowance. I have, &c, J. B. Tunbridge, Commissioner of Police. The Commissioner, Government Life Insurance Department, Wellington.

Memorandum for the Eight Hon. the Peemieb. Police Department, Wellington, Ist September, 1899. Eβ Attached Beport of the Government Insurance Actuary on the Proposed Police Provident Fundi In submitting this memorandum I desire to state that in presuming to criticise the deductions arrived at by the Actuary I realise that, being a laic in matters of this kind, my remarks will perhaps not receive the consideration they would if emanating from a professional source, and consequently I approach the matter with some diffidence. I will, as far as possible, deal with the Actuary's remarks seriatim. Paragraph 1: Needs no comment from me. Paragraph 2: (1.) The Actuary assumes the accumulated capital of the Fund will not earn more than 3J per cent, interest. I find in the annual report of his own department for the past year that the accumulated capital has earned £4 13s. lid. per cent. I therefore think the Actuary has placed the probable earnings of the capital of this Fund at too low a figure. (2.) The Actuary states, inter alia, as an argument against my suggestion that policemen are not noted for longevity, that the available mortality statistics of policemen indicate that their mortality is at least as good as that of doctors, lawyers, merchants, bankers, architects, and surveyors.