We are in receipt of the tenth annual report of the above institution, which shows it to be in full and successful operation. The report discusses the history of the institution from its origin in the liberality of its founder to the present time, during which it has conferred inestimable benefits upon the young mechanics and others through its system of free night classes, its schools of art and telegraphy for women, its musical department, its reading room and library, and its popular lectures upon scientific subjects. The trustees state that " Far better and larger results would have been produced if the pupils who have been admitted to the institution had been better trained in the ordinary rudiments of a common-school education, namely, reading, writing, and arithmetic, a good knowledge of which is essential for any higher progress. By far the larger number of applicants have been ignorant of arithmetic beyond its simplest elements, showing that the existing night schools maintained by the public authorities, valuable as they unquestionably are for the primary education of the foreign element in our midst, are not so organized and conducted as to give a thorough knowledge of arithmetic, without which it is vain to attempt a mathematical course or to make any scientific progress. The trustees have therefore considered the propriety of establishing a training or prepatatory school for the young men, over sixteen years of age, who must necessarily be refused admission to our classes in consequence of their ignorance of arithmetic. Such a school is required, but it is surely the duty of the Board of Education to establish it, and the trustees have decided to make a formal representation of the facts to the new Board of Education, in the hope that such a school for adults will be opened in October next for the reception of the pupils who must be refused admission to our classes in consequence of want of preparation. The necessity for such a school is made apparent by the fact that during the last ten years not more than one third of the pupils admitted to the mathematical department have remained until the close of the term, and that the progress of those who were qualified has been seriously interfered with by the sifting out of those who could not go on. " The trustees are the more earnest in calling attention to this lack of elementary preparation, because it has been found to be the most serious obstacle to the scientific and technical education of a very large proportion of the young men of New York engaged in mechanical pursuits. " A brief statement of the results of thefree night classes of the year just closed will confirm these observations: The total number admitted in Mathematics is...................... 482 " " remaining at the end of the term is............ 109 " " admitted in Natural Philosophy................ 276 " " remaining at the end of the term____.'.....58 ' " admitted in Elementary Chemistry............. 97 " " remaining at tne end of the term.............. 22 " " admitted in Applied Chemistry................. 35 " " remaining at the end of the term............... 21 " " admitted in Free-Hand Drawing.................182 ' " remaining at the end oftlieterm..............332 " " admitted in Architectural Drawing........... 16 " " remaining at the end of the term............. 53 " admitted in Mechanical Drawing............... 160 " " remaining at the end of the term............... 83 " Whence it appears that in the night schools of Science and Art 1,757 pupils in all were admitted during the term Which has. just closed, of which only 678 remained at the close. Of course some-of this falling off is due to the migratory nature of the working class s, but it will be observed that the loss is greatest in those branches which require good mathematical preparation, and the experience of t. ach-ers in their intercourse with the pupils all goes to show that the chief obstacle to progress and a far larger measure of BUCC3SS in imparting a technical education is the total want Of preparation in the ordinary rules of arithmetic." We will add, in this fconneotion, that Wm. S. Plympton has been appointed Professor of NatuAl Philosophy and Mechanism to this Institution, and delivered his inaugural address on the 30th October. These lectures will be continued in the Mechanical Lecture Boom every evening of the week except Saturday and Sunday, at 7| P. M. Free to all.