Lodge Of Benevolence.

LODGE OF BENEVOLENCE .

him step by step . In this slig ht sketch a few of his rules are given ; for this glorious branch of science is of immense importance to calculators , and many useful systems have been lost and afterwards revived fluxions ; to finding fluxions from given curves in

. Murdoch was well acquainted with Sir Isaac Newton ' s philosophy , as well as that of Leibnitz ; he considered tlie former to be certainly the inventor effluxions ; he maintained that a differential has been , mid still is , by many called a fluxionancl a fluxion a differential—yet it is an abuse ; and the contents and centre of By following by his exp and made

, of terms ; a fluxion has no relation to a differential , nor a differential to a fluxion . The principles upon which the methods are founded , show them to he . very different , notthe of investigation in each be the adequate notion forming a true years for his the fundamental

way same , and that both centre in the same conclusion . Nov can the differential method perform what the fltixionary method can . The excellency of the fluxionary method is far above the diflerential . fluxions ; and the solution of mathematics , in the phenomena

The Late Dr. Mackey, Sec. Gen. 33°,&C., &C.

THE LATE DR . MACKEY , SEC . GEN . 33° , & C ., & C .

this way is not generated by an opposition of points , or differentials , but by the motion or flux of a point : and the velocity of a generating point in the first moment of its formation , or generation , is called a fluxion . In forming magnitudes after the differential way , we conceive them as made poise , hanging at both ends of a globe , bar , to liave Second lobe to

an , so disposed as to produce a magnitude of a given form ; that these parts are to each other as the magnitudes of ivhich the } ' are differentials ; and that one infinitely small part or differential must be infinitely great , with respect to another diflerential , or infinitely small part ; but by fluxion , or the g given density velocity it is and in the to find tho curvilinear

of flowing , we proportion of magnitudes , one to another , from the celerities of the motion by which they are generated . This most certainly is the purest abstracted way of reasoning . Our considering the different degrees of magnitude , as arising from an increasing series of mutations of velocity , is much more , simple and less perplexed than the other way ; -r , . Belli

the operations founded on fluxions must be more clear , accurate , and convincing , than those that are founded on the diflerential calculus . There is great difference operations—when tities Again , how space enclosed tote : and , how oscillation of

a m quan are rejected because they really vanish ; and when they are rejected , because they are infinitely small : the hitter method , which is tho differential , must leave the mind in ambiguity and confusionaud cannot in many cases come up to the line P , A , M circle F , A , There were that

. It is a very great error , then , to call differentials fluxions ; and quite wrong to begin with the differential method in order to learn the law , or manner of flowing . Mr . Martin Murdoch's system of teaching ivas this : —He first taught arithmetictrigonometrygeometryalgebratho two latter describe any nothing , and cision , Iho bewildered in does nofc know

, , , ; branches , first in all their parts and improvements , the methods of series , doctrine of proportions , nature of logarithms , mechanics , and laws of motion ; from thence he proceeded to the pure doctrine of fluxions , and afc last looked into the differential calculus ; and lie declared it would how can the idea of , such Mr . Murdoch speculations the method The operation

be lost labour for any person to attempt them who was unacquainted wifch these procognita . When he turned to fluxions , the first thing he did was to instruct the pupil in the arithmetic of exponents , the nature of powers , and the manner of their generation ; he next went to the doctrine of infinite series , and then to the manner generate , or successivel y certainly a well as a the difference the effect

of generating mathematical quantities . This generation of quantities was the first step into fluxions , and he so simply explained the nature of them in this operation , that the scholar was able to form a jmt idea of a first fluxion , though thought by many to be incomprehensible . He proceeded from thence to -the notation and algorithm of first the cause . he can or things relating arising states . The knowled

Masonic History And Historians.

MASONIC HISTORY AND HISTORIANS .

finding secondthirdetc . fluxions ; tlie

of exponential quantities , and the fluents ; to their uses in drawing tangents to the areas of spaces , the values of surfaces , of solids , their percussion and oscillation ,

. his plan , this clever master made the pupil happily understand and work with ease ; find no more difficulty in conceiving an of a nascent or evanescent quantitthan in

y , idea of a mathematical point . He gave two pupils to acquire an aptitude to understand principles and operations at all relative to could then investigate , and not only give

most general and useful problems in the likewise solve several problems that occur of nature . arc ; some of his difficult questionswhichby

, , answered immediately : — . —He requested in the first place to be intime of a body ' s descending through an arch found : and if ten hundred weight avoirdu-

The British Association At York.

THE BRITISH ASSOCIATION AT YORK .

same effect '" ! . —How long , and how far , ought a given by its comparative weight in a medium of a without resistance , to acquire the greatest capable of in descending ivith the same wei ght ,

medium , with resistance : and , how are we of a solid formed by the rotation of this , A , C , D . The general equation expressing curves : — m

n a — X x x" ) yz j TO rt " the centre of to be found of the

gravity an hyperbola and its asymp- r- -7 are we to find the centre of \ ^ y S sphei * e revolving about the j—" 7 f tangent , to the generating \ p / \ ^ in the point A as an axis ? a

some learned men of his time would not allow which continues for no time at all can possibly at all : its effect , they say , is absolutely instead of satisfying reason with truth and prefaculties are quite confounded , lost , and fluxions . A velocityor fluxionis at best he

, , what—whether something or nothing : and lay hold on , or form any accurate abstract subtile fleeting thing . answered—Disputants may jierplex with dee ]} confound with mysterious disquisitions , but fluxions has no dependence on such things . not what any single abstract velocity can assertbut what continual and

e cause may produce a variable effect , as cause a permanent and constant effect ; can only be—that the continual variation of be proportioned to the continual variation of method of fluxion therefore is true whether

conceive the nature and manner of several to them , though he had no idea of perpetually and magnitudes in nascent or evanescent ge-of-such things is not essential to fluxions