Haupt.] **«*U [Nov. 21, 



point of view, and hence unless it be symmetrical with reference to a point 

 in space, as a sphere, the line of apparent contour will be different to each. 

 The magnitude will also appear larger or smaller according to the distance 

 of the observer from the object. Thus, if a circular disk be held up before 

 an assembly it will appear circular only to that person at the end of its 

 axis, while to those in the plane of the disk it will appear to be a straight 

 line, and to all others the ellipses of which the line and circle are the limits, 

 thus verifying the aphorism of the poet Longfellow, when he says, 

 " And things are not what they seem." 



With projections, however, the case is different, as, if understood at all, 

 they can only convey one impression to the reader. But it must be con- 

 fessed that they are no more intelligible without a knowledge of the prin- 

 ciples upon which they were constructed than is a printed work to one 

 ignorant of letters. 



The principles of projections are, however, as simple as those of element- 

 ary geometry, upon which they are based, and can be readily compre- 

 hended by the pupils in our public schools. And a knowledge of these 

 principles would enable many of them to work much more intelligently in 

 the various trades in which they may thereafter become apprentices. 



The application which may be made of such information is very ex- 

 tended. As a disciplinary study it is one of the first order, developing the 

 conceptive faculties and enabling one to grasp an idea readily. It has its 

 application in' nearly all manufactured articles and in all constructions and 

 designs, in wood, iron, stone, clay, or other materials. It is used con- 

 stantly by the engineer, architect, builder, pattern-maker, iron or sheet 

 metal-worker, stair-builder, stone-cutter, designer, and a host of others. 

 It is the basis of all perspective drawings which are generally made by rule 

 and without reason, and is essential to a correct interpretation of all sug- 

 gestions relating to constructions of any kind. It is used to explain and 

 reinforce verbal language, and should be so used whenever possible. 



One of the most important applications of graphical language must not 

 be overlooked. To the statistician as well as merchant it is valuable as 

 furnishing at a glance information which if expressed in a mass of figures 

 would be unintelligible. It cannot be surpassed as a method of exhibiting 

 rapidly the distribution of population, of products, of poverty or wealth, of 

 crime or morality, of vital, or in fact any statistics which may be expressed 

 numerically. To the physicist it is also particularly useful in investiga- 

 tions into the properties of molecular or mass physics, and enables him to 

 discover almost immediately the laws governing the motions of matter. 



Fluctuations of prices, in the market values of daily commodities, may 

 be more intelligently expressed by this means than any other and can be 

 compared at a glance. In short, the number of intelligent and eminently 

 practical applications that may he made of projections is almost limitless. 



Its introduction would supplant a certain amount of mnemonical by 

 rational and manual development, and would thus be a relief to a system 

 already overtaxed with memorizing. 



