Immediately upon the passage of this act, the Adjutant General shall ascertain the individuals who are veterans as defined in section two,¹ and as to each veteran the number of months of service as defined in sections three and four² for which he or she is entitled to receive compensation, and his decisions shall be final and not subject to review by any court or by any other officer. In all cases, not within the express purview of this act, the decision of the Adjutant General as to payment or nonpayment of compensation or eligibility therefor shall be in all things final.