VOL. XLII.3 PHILOSOPHICAL TRANSACTIONS. QQj 



viz. by giving to the foot, tiiat enters into the arm of the chair, a cylindrical 

 shape, by which means it can turn all manner of ways; so that if the luxation 

 be forwards, we need only turn the extremity of the lever accordingly, lower- 

 ing it at the same time enough to make the necessary extension and elevation; 

 by this turn of the extremity of the lever forward, the head of the bone is of 

 necessity carried backward, and replaced into its cavity. It is easily conceived, 

 that we must go to work in the opposite way when the luxation is backward, 

 and so on as for the rest ; all according to the directions of the surgeon placed 

 at the articulation, who is to be attentive to examine the state of the parts, 

 and to order in what direction, and how much is necessary to be done. 



Continuation of the Account of a Treatise of Fluxions, &c. Book 2. By Colin 

 Maclaurin, F. R. S* N" 469, p. 403. 



In the first book, the author described the method of fluxions, and its appli- 

 cation to problems of different kinds, without making use of any particular 

 signs or characters, by geometrical demonstrations, that its evidence might ap- 

 pear in the most simple and plain form. In the second book, he treats of the 

 method of computation, or the algebraic part ; to the facility, conciseness, and 

 great extent of which, the improvements that have been made by this method 

 are in great measure to be ascribed. In order to obtain these advantages, it was 

 necessary to admit various symbols into the algebra; but the number and com- 

 plication of those signs must occasion some obscurity in this art, unless care be 

 taken to define their use and import clearly, with the nature of the several 

 operations. An example of this is given by an illustration of one of the first 

 rules in algebra. As it is the nature of quantity to be capable of augmentation 

 and diminution, so addition and subtraction are the primary operations in the 

 sciences that treat of it. The positive sign implies an increment, or a quantity 

 to be added. The negative sign implies a decrement, or quantity to be sub 

 tracted; and these serve to keep in our view what elements enter into the com- 

 position of quantities, and in which manner, whether as increments or decre- 

 ments. It is the same thing to subtract a decrement as to add an equal incre- 

 ment. As the multiplication of a quantity by a positive number implies a re- 

 peated addition of the quantity, so the multiplication by a negative number 

 implies a repeated subtraction: and hence to multiply a negative quantity, or 

 decrement, by a negative number, is to subtract the decrement as often as there 

 are units in this number, and therefore is equivalent to adding the equal incre- 

 ment the same number of times; or, when a negative quantity is multiplied by 



• See the beginning of this account, N" 46'8, p. 6"32 of thit vol. 

 4Q 2 



