MATHEMATICAL HOWLERS 835P. 444,1. 6 from the bottom. The first steps towards numberfields were taken earlier. Gauss worked in this direction.P. 487. It should have been noted that where biographicalnotices are given the first page number following an author^name refers to this. Hence the numbers which follow an authorsname are not always arranged in order.P. 4j94. Instead of 'Emsh' write 'Emch.'P. 501. After Kowalevski, Madame, delete the last 436.P. 502. Insert the name of H. Lebesgue. Most of the refer-ences after the name of V. A. Lebesgue relate to the work ofH. Lebesgue.P. 503. Delete 360 after the name McClintock.P. 505. Under the word 'Number' add the number 267after 'quadratic reciprocity.'P. 507. Instead of 'Peterson' write 'Petersen.'The number of these marginal suggestions may appear large,especial y since it does not claim to be a complete list of desirablemodifications. In view of the great variety of subjects treatedand the vast amount of material which had to be consideredit was only to be expected that private copies could be greatlyimproved by the addition of numerous marginal notes. Many ofthe notes here suggested can be very much abbreviated beforethey are entered.SOME MATHEMATICAL HOWLERS.Question: Substitute the roots obtained in the equation and explainthe failure of some of them to satisfy the equation.Answer: Plus or minus the square root of seven will not satisfy theequations (sic) for an unknown quantity equalling a radical sign willnever satisfy an equation.Question: Write down and prove the formula for the sum of n termsof the series a, a+^ a-^-2d, etc.Answer 1: The formula for n terms of a series is a aT^r^ I=~dSince the last number in a series of n terms cannot be found, the lastterm must be dropped out and the sum would increase indefinitely asthe terms are gradually increased.Answer 2: a+a+(n-l) d S. First, you start with the difference,n2d, which is the progression one step. The next consideration is thenumber of steps and this is one less than the number of terms, to wit:(n1). Multiply (n-1) by d and you get the progress. Take theprogress and add it to the first term and this will carry you to the lastterm. Take the first term and the last term, add them together anddivide by two. This will give you the average term. If this is theaverage (or one term, multiply it by the number of terms and this willgive the sum.