=Arithmetic.=--Although arithmetical ability depends upon special aptitude, and a child may be quite intelligent though backward in arithmetic, the tests here chosen are so elementary, and the ignorance one tolerates is so great, that failure is of serious significance. We follow here the directions of M. Vaney, who has taken the trouble to simplify them at our request. All the questions in arithmetic ought to be dictated. This may even be done collectively. It is essential not to interpose to ask the child what operation is to be done. Such help would make the work much too easy, and indeed that is the very problem which has to be solved in the very exact and carefully considered form in which it has been stated. It is the problem rather than the operation which requires intelligence. Moreover, it will be noted that the difficulty of our mode of expression is calculated. The words _subtract_, _take away_, _remain_, ought not to be replaced by synonyms, and still less should they be explained. Even when, as often happens, the child makes a mistake in the first problem (for example, 19-6 = 12), he must not be allowed to stop there; his mistake might be due to carelessness. One must always try the higher problems until one obtains a clear demonstration that the child is incapable of solving them. M. Vaney has suggested a scale of marking for these sums. It enables one to take into account slight differences by the aid of a system of points. Here it is: _Correction of Sums._ _First Sum_ (1 point).--1 point for correct answer (_vide_ p. 54). _Second Sum_ (2 points).--1 point for subtraction; 1 point for correct answer. _Third Sum_ (3 points).--1 point for 604 correctly written; 1 point for subtraction; 1 point for correct answer. _Fourth Sum_ (4 points).--2 points for correct division (1 if wrong); 2 points for the remainder (1 if obtained by long division). _Fifth Sum_ (5 points).--2 points for the subtraction (1 if answer wrong); 3 points for correct division (2 if it is wrong). _Sixth Sum_ (6 points).--A dressmaker buys 8 yards of velvet at 9s. 6d. a yard and 25 yards of cloth; she pays for the whole £6. Find the price of the cloth per yard. 2 points for the price of the velvet; 2 points for the price of the cloth (1 for subtraction, if answer wrong); 2 points for price of cloth per yard (1 for division if answer wrong). _Seventh Sum_ (7 points).--A merchant mixed 25 pints of wine at 2s. a pint with 60 pints at 2s. 6d. a pint; at how much per pint must he sell the mixture in order to gain 55s.? etc. This scale enables us to determine by the total number of points obtained the level of the child in arithmetic, and at the same time we find out what sums can be done by the pupils of each age. This is shown in the table. RESULTS OF ARITHMETIC TESTS IN AN ELEMENTARY SCHOOL IN PARIS.