,TOR. 



PROGRESSION, 



prnrtoni. '"it i thrown open to ban-inters. nlUmicyii, ami 

 . i-, 6, aIoenlpw 



> practise inthecourt of Admiralty. Thus the practice 

 fa th* UvUincoUry and matrimonial hiuunm of the Eocleuastioal 

 emiru and that of the court of Admiralty U no longer confined to the 

 advocates and procton of Doctor*' Common*. Marriage lioenoea are 

 obtained through the medium of procton: they prepare the affidavit 

 P^n^mln. the particular* required to enable partial to be married 

 without tin- publication uf bannn. The 5 Geo. II. c. 18, . 2, pro- 

 hi Wta practicing procton from being juatiee* <if the peace. But they 

 are exempt from nerving on jurim. or being made paruh offloen, as 

 churchwarden!, Ac. The tenn " proctor " is also applied to those of the 

 clergy, who are (elected by tin ii brother clergy to represent them in 

 convocation [CONVOCATION]. For the practice of the Ecclesiastical 

 courts, we COURTS, ECCLESIASTICAL. 



The two procton in the universities of Oxford and Cambridge are 

 nominated by each college in rotation from among the resident 

 nsnHiti of art*. They hold office for a year ; they each have two pro- 

 proctors. Their office is of great dignity and importance ; they rank 

 after the vice-chancellor. Their duties are to preserve order and 

 discipline among the under-graduates, and to aid the authorities in all 

 their important functions. 



ntnCl'UATOK, a manager or agent, whence the word pr. 

 formed. 



A Roman procurator was a person apiinted by another to conduct 

 a cause for him. and it n jniifd no particular word* to constitute n 

 procurator. A man might commence a suit as a procurator, without 

 showing his authority; but he was obliged to produce it befon- tin- 

 judges came to a decision, or to enter into security that the plaintiff 

 would abide by his acts. (Gaius, iv. 84.) 



Coder the Empire the governor of a province was, in certain cases, 

 called a Procurator, or Procurator Ctcsari*. Sometimes this Procurator 

 had not the government of a province, but only managed affairs of 

 revenue (re fisci). [PROVINCIA.] 



Solicitors in Scotland who practise in the courts of the Sheriffs, are 

 usually called Procurators; and in judgments the courts generally 

 recite the hearing of the Procurators of the partien. 



Procurator Pitcal, in Scotland, is the term used to denote the public 

 prosecutor. 



TKOCYON. [Smius and Pnocrox.] 



PRODUCT, a term really equivalent to result, but used only when 

 the result is the one obtained by the multiplication of two or more 

 quantities. 



PKOFAXEXKSS. [BtASPHEirr.] 



PROFIT, one of the three ports into which all that is derived from 

 the soil by labour and capital is distributed, the other two being wages 

 and rent : from these three sources arise all the revenues of the com- 

 munity. Profit is therefore the surplus which remains to the capitalist 

 after he has been reimbursed for the wages advanced and the capital 

 expended during the process of production. To obtain this surplus is 

 the only object for which capital is employed. 



Profits have a tendency to fall to the same level in all branches of 

 industry; for if the ratio of profit in proportion to the capital em- 

 ployed be greater in one than in another, more capital will be directed 

 to that which affords the highest profit ; and the powers of production 

 being increased, the supply is greater, prices fall, and the equilibrium 

 of profit is restored. A distinction must however be made between 

 real and apparent profit. When the employment of capital is attended 

 with extraordinary risk, profits are nominally high ; but after deduct- 

 ing the locses to which it is exposed, the real profits tend to the same 

 level a* the ordinary rate. The case is similar in occupations of a 

 disagreeable or agreeable nature, the pleasantness of the latter counter- 

 balancing the low rate of profit A wholesale merchant and a retail 

 trader both dealing in the same commodities may appear to obtain 

 different rate* of profit ; but in the latter case wages are confounded 

 with profit*, and when they ore properly distinguished, the apparent 

 disproportion is diminished. Unless we reduce profits from their 

 apparent to their real value, there is no truth in the maxim that the 

 nte of profit is uniform in the same country at the same time. 



The natural tendency of profit* (whether arising from capital em- 

 ployed in agriculture or in manufactures) i* to decline as the neccs- 

 iitio. of the population render it necessary to have recourse to inferior 

 oils. Happily, improvement* in machinery and in the art of agri- 

 culture, better combinations of labour and capital, and greater freedom 

 of commerce, are calculated to arrest this retrograde movement ; and 

 to such sources of relief every highly advanced country must look as a 

 mean* of *u*taining its prosperity ; for whatever diminishes the neces- 

 sity of railing food from the poorer soils, tend* to maintain the nte of 

 profit. 



Two other causes have great influence upon the rate of profit, 

 namely, wage, t^ taxation. A rise in wage* will diminish profit*, 

 lie** industry becomes more productive ; but if the latter take place, 

 may rise at the came time, either in the same or in different pro- 

 portions according to circumstance*. 



Taxation will diminish profit*, unlcm wages fall or industry become 



Taxes on profit*, when they fall alike upon all 



engaged in productive industry, are pud by the ownen of 



t*fn*i, no have not the power of charging the tax upon consumers. 



.-.in* of accumulation an> diminiiOiisI win n tin- profit* of 

 certain classes of tradan ore tiX'-d. and they would ' -olve* 



to other occupations not taxed, unless they could charge the consumers 

 with the tax : the tax therefore fall* Upon the consumer*. 



The competition of capitalist* alao act* in reducing the nte of profit, 

 though this ha* been denied by some writer*. Capitalists who have 

 accumulated at the old nte of profit are content with a new invest- 

 in. nt producing a lower nte, instead of consuming their savings un- 



:Vf ly. 



PBOONOSEB (in Medicine) is the opinion funned rfispectii 

 probable future event* of any disease, as. for example, whether it will 

 terminate in recovery or in death, how long it is likely to continue, 

 what other rlisosioi may be expected to arise in its course, what an- th.- 

 chances of relapse, and what those of some permanent injury of struc- 

 ture or function Wing produced by the morbid processes. 



ru>i;i:i:s<|i >N. A M.THM of numben following any lawahould be 

 called a progression, but the word i* usually restricted to two sorts of 

 progreafflon, which are called, but by no means correctly, arithmetical 

 and geometrical : the analogic* pointed out in UKCTANULE give the 

 origin of these term*. 



An arithmrtiral progrtaion i* one in which the terms continually 

 increase or diminish equally, including, as an extreme case, that in 

 which they do not increase or diminish at all. Thus 



7, 7, 7, 7, Ac. 



1", '.'1, 9, 84, Ac. 



7, 8, 9, 10, Ac. 

 2, 31, 44, 5J, Ac. 



are set* of terms in arithmetical progression. The following proposi- 

 tion contains the principal part of their theory : 



If a be the first term of an arithmetical progression, and Aa the 

 difference between any two terms (negative, if the terms diminish) ; 

 and if a. be the nth term from and after a txdtuire, and I. the sum 

 of n terms, we have 



a, = a + n Ad ; 

 1 

 I. = no + n jjj Ao, 



From these two equations between a, n, a, , Aa, and *, , any three of 

 these being given, the other two can be found, subject however to 

 this restriction, that the problem is unmeaning when n is not a whole 

 number, whether it be given or found. These theorems are only the 

 simplest case of a more general pair, in which, taking any series, and 

 supposing neither the differences nor the differences of the differences, 

 Ac., to be equal, an expression is given for any term of a series, or for 

 the sum of n terms, which frequently gives definite forms in the place 

 of indefinite ones. Calculate, as in the article DIFFERENCE, the value 

 of A, A s a, Ac., from a, a,, a,, Ac., and let 



,= 



n 1 n 2 



', Ac. 



Then 



a, = a + n, Ao -(- n t 6"a + n s A'a + , Ac. 

 . = n,a + n a Ao + n,A-a + 4 A'o + , Ac. 



Thus in the series 1 + 5 + 17 + 43 + 89 + 161 + Ac,, the law of 



terms is undiscoverablo at first sight, we shall, by what the 



beginner may, till he knows better, call an accidental circumstance, 



discover both the law of the terms and that of their sum, as 



follows : 



5 



17 



8 







H : o , 



43 20 I 



26 6 



89 

 161 



72 



0=1, Aa = 4, A'o = 8, 

 Aa = 6, A<a = 0, A'o = 0, 

 Ac. 



a, = 1 -r 4n, + 8, + 6n, = n> ^ 



. 'n( + l)<2. 



(n 



6 



Thus the seventh term (the sixth after 1, n = 6) is 6 3 + 7', or 265, 

 and the sum of 6 terms (make n = 6 in the second formula, in which 

 remember that is the sum of n terms, not of n terms after o) is 

 (4.6.5)* + J.6.7.13, or 316, which may easily be verified. [St)M.] 



The apparently accidental circumstance above alluded to, is the 

 vanishing of all the differences of a from and after the fourth. But it 

 i* to be observed, that the series was originally constructed so as to 

 make all differences vanish after the fourth, and that the preceding 

 theorem will never change indefinite into definite formula;, except 

 when all differences after a certain one vanish. The rule i, when a, is 

 an algebraically rational and integral function of i of the Border, 

 that is, of the form in' +{!-' + , Ac., all differences after the .pth 

 vanish, and then only. 



utric.al Proyreuion is when the terms of a series increase or 

 diminish by the use of the saute multiplier, whole or fractional, 

 including, on an extreme case, that in which the multiplier is unity. 



