LOGIC. 



laws and properties that make up any one science 

 varies with the nature of the phenomena included 

 in it. Hence, the cultivation of each confers a 

 distinct and separate discipline on the intellectual 

 faculties. Astronomy, for example, carries to the 

 highest perfection the two processes of observation 

 and deduction. In no other science have the 

 means and devices of accurate observation been 

 so much improved ; and, on the other hand, as all 

 the phenomena can be deduced from the ultimate 

 laws of mechanics, combined with the law of 

 gravitation, with the most complete numerical 

 accuracy, the science affords a perfect instance of 

 the deductive method of arriving at truths. If we 

 pass from Astronomy to terrestrial Physics, in- 

 cluding the laws of solid, liquid, and gas, heat, 

 mechanics, hydrostatics, optics, electricity, &c., 

 we find ourselves in the domain of experiment, 

 which is entirely inadmissible in the celestial 

 physics ; and the cultivation of the experimental 

 devices, of excluding and including known causes 

 and circumstances, is in the highest degree prac- 

 ticable. For the last two centuries, Physics has 

 been the great field of experimental research ; and 

 it may be said that the art of accurate experi- 

 menting was first acquired in this field, although 

 it has since been extended to other branches. 

 The experiments that decided the weight and 

 pressure of the atmosphere, Newton's experiments 

 on light, the researches of Dr Black on latent 

 heat, and the very extensive experimental inquiries 

 that have been made within the last seventy years 

 on Electricity, may be alluded to as illustrious not 

 only in the history of Physics, but in the progress 

 of the human reason. Chemistry is, like Physics, a 

 highly experimental science, but its distinguishing 

 feature is its having to provide for a classification 

 of the materials of the globe according to their 

 composition. As it shews that the earth consists of 

 about sixty simple substances, which have almost 

 an infinite capacity of combining into compounds, 

 it has to ascertain the circumstances attending on 

 all combinations and decompositions, and to make 

 a regular classification of all the resulting bodies 

 according to the simples that make them up. For 

 this it has to invent a grand system of nomen- 

 clature and arrangement, such as is not required 

 to the same extent in any other science, but is not 

 without its use, apart from the immediate purposes 

 of chemistry. The science of Life requires, as its 

 peculiar auxiliary, a system of classification by 

 genera and species, and carries this device to its 

 utmost perfection. In like manner the sciences 

 of Mind and Society have their peculiarities of 

 method, or their special contributions to the 

 logical cultivation of the human intellect. The 

 lessons that all the leading sciences agree in culti- 

 vating are the supremacy of reason over sense 

 and instinct, and the necessity of bringing all 

 assertions to the test of rigorous proof. We shall 

 now advert to the fundamental sciences, with the 

 view of bringing prominently forward the peculiar- 

 ities of the classes of phenomena which they 

 severally include : 



The science of Mathematics is divided into two 

 great branches the one Abstract, including Arith- 

 metic, Algebra, and the higher or transcendental 

 Analysis ; the other is called Concrete, and takes 

 in Geometry and General Mechanics. The Ab- 

 stract branches consider number and quantity in 

 general without reference to any special things 



numbered or quantitatively estimated. The Con- 

 crete branches refer to peculiar kinds of quantity : 

 the one, Geometry, referring to space and the 

 forms of things occupying space ; and the other, 

 General Mechanics, being devoted to motion and 

 the things necessary for expressing motion 

 namely, space and time. Mathematics proper, 

 however, is usually considered to terminate with 

 Geometry. 



Arithmetic reposes upon the ten figures and the 

 decimal notation. Without inventing names for 

 the successive numbers, and adopting some prin- 

 ciple for expressing shortly and systematically 

 the higher sums, no nation could ever progress 

 in arithmetical calculation, or in the arts and 

 sciences where it is much required. The chief 

 business of Arithmetic comes to be the reducing 

 of all possible combinations of numbers to one 

 universal form, or to the gradations of units, tens, 

 hundreds, &c. Thus the multiplication table, 

 which contains the fundamental laws of the 

 science, merely serves to shew how to reduce 



a product of any two numbers to a product 

 where ten shall be one of the factors. ' Nine 

 times seven are sixty-three,' means that if a 

 row of seven be taken nine times, the sum-total 

 will be the same as six rows of ten and three over. 

 When all products are reduced to the one decimal 

 scale, their comparison among themselves be- 

 comes much more easy than if they were kept 

 in all variety of scales. If we wish to compare 

 nine times six with eleven times five, we find it 

 most convenient to bring both into products of 

 tens, by making the one fifty-four, and the other 

 fifty-five. 



Algebra is a higher process than Arithmetic, 

 and has been defined the reduction of equations. 

 Its main peculiarity lies in putting two different 

 complex expressions that are equal over against 

 one another, and then in operating upon the two 

 by adding, subtracting, &c. the same things from 

 both, so as still to preserve the equality, and at 

 the same time to bring the equation to son 

 simple form that will give the value of a single 

 ingredient of the original expression. Thus, an 

 easy question in Algebra would be to rind a 

 number which, when added to its square, would 

 give 56 Here an equation would be formed by 

 putting 56 on one side, and on the other an ex- 

 pression of a number added to its square, the 

 number being represented by a letter such as x 

 and the business would then be to operate ( 

 this equation till it is reduced to another having or 

 one side only the representative of the number 

 itself, in which case the other side would give the 

 actual number in arithmetical figures. The higher 

 analysis was invented by Newton and Leibnitz 

 to solve such questions as computing the areas 

 and circumferences of curved surfaces, and 

 spaces and times of accelerated and retarded 



m0 Geom'etry treats of the laws and properties of 

 lines, surfaces, and solids, straight or curved. 

 It has two branches Special and General Geo- 

 metry : the one is exemplified in Euclid, who 

 treats each figure by itself in succession, as in 

 triangles, circles, &c. General Geometry treats 

 wholS classes of figures at once by stating them 

 in Algebraical Language. 



General or Rational Mechanics lays down tJ 

 first principles or laws of motion, and applu 



