## Exp Sentence Examples

- 173; National Antarctic
**Exp**., Nat. **Exp**. Fund Publications - Sir C. Warren, Jerusalem, Memoir (1884); Clermont-Ganneau, Archaeol.**Exp**., 1878.- 198; Du Moncel,
**Exp**. de l'Elect., ii. **Exp**.) reveals his many-sided intellectual interests and ready sympathies.**Exp**. Gen.- Sec., elastic vinculum and
**Exp**.sec.,**expansor**secundariorum; Pt.br and Pt.lg, short and long propatagial muscles; Tri, triceps. **Exp**.sec. From Newton's by permission of A.**Exp**. et gen.**Exp**. to Syria (1904).- =
**exp**,udl where**exp**denotes (by the rule over**exp**) that the multiplication of operators is symbolic as in Taylor's theorem. - 1890, p. 490) that
**exp**(mldl +m2d2+m3d3+...) =**exp**(Midi +M2d2+M3d3+...), where now the multiplications on the dexter denote successive operations, provided that pp t**exp**(MiE+M2 2+M3E3+...) +mlH+m2V+m3S3+..., being an undetermined algebraic quantity. - Hence we derive the particular cases 1 1
**expel**' =**exp**(d1 -2d2+5d3 - ...);**exp**/ld 1 =**exp**(Ad1p2d2 +/13d3 - ...), and we can**express**D. - =
**exp**{(siox+Solt') - s20 x 2+ 2siixy+S02y2)+ï¿½ï¿½ï¿½}, and thence derive the formula? - - If, in the identity 1 (1 +anx = 1+aiox+aoly+a20x 2 +allxy+a02y 2 +..., we multiply each side by (I -ï¿½-P.x+vy), the right-hand side becomes 1 +(aio+1.1 ') x +(a ol+ v) y +...+(a p4+/ 1a P-1,4+ va Pr4-1) xPyq - - ...; hence any rational integral function of the coefficients an, say f (al °, aol, ...) =f
**exp**(ï¿½dlo+vdol)f d a P-1,4, dot = dapg The rule over**exp**will serve to denote that i udio+ vdo h is to be raised to the various powers symbolically as in Taylor's theorem. - 1
**exp**(Adlo + vdol) = (1+/oD10+ v Doi +..ï¿½+ VQ +.ï¿½.)f; now, since the introduction of the new quantities 1.1., v results in the addition to the function (plglp2g2p3g3...) of the new terms A PI Pg1 (p 2q2 p 3g3ï¿½ï¿½ï¿½) +/ AP2Pg2 (p 1 g 1P343 ...)+/ Z3vg3 (p l g i p 2 g 2 ...)+ ï¿½, we find DP141(plqip2q2p3q3ï¿½ï¿½ï¿½) = (p 2 q 2 p 3 q 3ï¿½ï¿½ï¿½), and thence D P141 D P242 D P343 ï¿½ï¿½. - From the above D p4 is an operator of order pq, but it is convenient for some purposes to obtain its
**expression**in the form of a number of terms, each of which denotes pq successive linear operations: to accomplish this write d ars and note the general result**exp**(mlodlo+moldol +... - Where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation
**exp**(M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities. - And the result is thus
**exp**(Mdlo+vdol) = {ï¿½die+vdol- 2 (ï¿½ 2 d2 +2ï¿½vd11+ v2d02)+...{ =1 +,D10+vD01+... - 4 Faraday,
**Exp**. Res. - Faraday,
**Exp**. Res. - 3
**Exp**. Res., iii. - The best modern determinations of the value of K for gaseous oxygen agree very fairly well with that given by Faraday in 18J3 (
**Exp**. Res. - Throughout his researches Faraday paid special regard to the medium as the true seat of magnetic action, being to a large extent guided by his pregnant conception of " lines of force," or of induction, which he considered to be " closed curves passing in one part of the course through, the magnet to which they belong, and in the other part through space," always tending to shorten themselves, and repelling one another when they were side by side (
**Exp**. Res. - Above and below this sea, from Borsippa to Kufa, extend the famous Chaldaean marshes, where Alexander was nearly lost (Arrian,
**Exp**. Al. **Exp**. (2) (1891), ix.**Exp**. Fund, 1904, pp. 58-64, and the Builder, Feb.- One of these contained the first inti ation of the achievement with which his name is most wid ly associated, for it was in a paper read before the British Association at Cork in 1843, and entitled "The Calorific Effects of i agneto-electricity and the Mechanical Value of Heat," that he xpressed the conviction that whenever mechanical force is
**exp**° nded an exact equivalent of heat is always obtained. - Schlomilch defines these functions as the coefficients of the power of t in the
**expansion**of**exp**2p(t - t1). - The
**exponential**function,**exp**x, may be defined as the inverse of the logarithm: thus x =**exp**y if y= log x. - As y tends towards co,
**exp**y tends towards co more rapidly than any power of y. - Hansen (Die Cirripedien der Plankton-
**Exp**., 1899, p. 53) argues that various nauplii of a type not previously described may probably be referred to this group or family. - 544) that an intelligible theory can be given which leads to the form j(OX) = c i /{
**exp**(c 2 /A9) - I }, a form which agrees in a satisfactory way with all the**experi**ments. - Plankt.-
**Exp**. ii. **Exp**. ii.**Exp**. p. lxxxv.), which, though penned in extreme old age, may be taken as trustworthy.**Exp**.), but also from unmistakable hints in the account of the life and work of his author prefixed to the translation on its appearance.**Exp**. Fund, Memoirs, iii.- The
**exponential**function possesses the properties (i.)**exp**(x+y) =**exp**x X**exp**y. - D x
**exp**x =**exp**x. - (iii.)
**exp**x = I -f-x+x 2 /2 ! - From (i.) and (ii.) it may be deduced that
**exp**x= (I !