transformable 
transformable (trans-for'ma-bl), n. [< trans- 
form + -able.] Capable of being transformed. 
H. Spencer, Prin. of Psyehol., $47. 
transformancet (trans-for'maus), . [< trans- 
form + -<mce.~\ A transformation; a semblance; 
a disguise. 
Take such a transformance as you may be sure will keep 
you from discovery. Chapman, May-Day, ii. 4. 
transformation (trans-for-ma'shon), w. [< P. 
transformation = Sp. transformation, trasfor- 
macion = Pg. transformayao = It. transforma- 
ziour, traxformasione, < LL. transformatio(n-), a 
change of shape, < L. transformnre, change the 
shape of: see transform. ] 1 . The act or opera- 
tion of transforming, or the state of being trans- 
formed ; a change in form, appearance, nature, 
disposition, condition, or the like. 
Transformation of apostate man 
From fool to wise, from earthly to divine, 
Is work for Him that made him. 
Coirper, Task, v. 695. 
The transformation of barren rock into life-supporting 
soil takes countless ages. 
H. Spencer, Social Statics, p. 378. 
2. In biol., metamorphosis, in any sense; es- 
pecially, the metamorphosis of those organisms 
which undergo obvious and great changes of 
form, as that of insects in passing from the 
larval to the imaginal state. Metamorphosis is the 
more frequent technical term. By some zoologists trans- 
formation is restricted to the series of changes which 
Danais archippus, ideal figures, showing transformation : a, larva 
suspended; 6, pupa forming with larva-skin still attached ; c, the 
same, showing manner of withdrawing from larva-skin. 
every germ undergoes in completing the embryonic con- 
dition, as those observed within the egg ; while meta- 
morphosis, according to the same authorities, designates 
the alterations which are undergone after exclusion from 
the egg, and which alter extensively the general form and 
mode of life of the individual. But this distinction of 
the synonymous words is seldom maintained. See meta- 
morphosis, 2, 4, and compare transform-ism. 
3. The change of one metal into another; trans- 
mutation of metals, according to the alchemists. 
4. In math., a passage in the imagination 
from one figure or expression to another differ- 
ent in form but equal in quantity. Thus, the vol- 
ume of an oblique prism is ascertained by a transforma- 
tion of it into a right prism of equal volume. Especially 
(a) The passage from one algebraical expression to an- 
other in other terms. (6) The passage from one equation 
to another expressive of the same relation, by substitute 
ing for the independent variables it involves their val- 
ues in terms of another set of such variables equal in 
number to the old ones. This is called a transformation 
of the equation; but when this defines a locus, and one 
set of coordinates is substituted for another, it is inaccu- 
rately but universally called a transformation of the coor- 
dinates, (c) A correspondence. If in the transformation 
of coordinates the new coordinates are conceived to be 
measured in a different space or locus in quo, a projection 
or correspondence has taken place, and this, being still 
called a transformation, gives rise to such phrases as a trans- 
formation between two planes. Thus, if in the equation of 
a conic we substitute x = I/a;', y = l/y', z = 1/z', we effect a 
transformation of the equation. This may be regarded as 
signifying a mere transformation of coordinates; but if 
x', \f, 2 are conceived to be coordinates of a correspond- 
ing point in the same or another plane, and measured 
similarly to x, y, z, we have a transformation between the 
planes, which transforms the conic into a uuicursal quar- 
tic. The whole analytical theory being identical under 
the two interpretations, the word transformation has been 
unadvisedly transferred from one application to the other. 
5. Inpathol., a morbid change in a part, which 
consists in the conversion of its texture into 
one which is natural to some other part, as 
when soft parts are converted into cartilage or 
bone. Such transformation is generally a de- 
generative or retrograde metamorphosis. 6. 
In physiol., the change which takes place in 
the component parts of the blood during its 
passage from the minute arteries through the 
capillary system of vessels into the radicles of 
the venous system. There are three kinds of 
change, designated by the terms intussnsi'iji- 
tion, apposition, and secretion. 7. In physics, 
change from solid to liquid or from liquid to gas- 
eous state, or the converse. This change usually 
results merely from change of temperature or pressure, or 
both, without any alteration in the atomic constitution of 
the bodies concerned, as the change of water into steam. 
6430 
8f. The shape to which some person or thing 
has been transformed. 
If it should come to the ear of the court how I have 
been transformed, and how my transformation has been 
washed and cudgelled, they would melt me out of my fat 
drop by drop. Shak., M. W. of W., iv. 5. 98. 
Arguesian transformation, a transformation between 
two spaces where the relation between the two sets of 
point- or line-coordinates is denned by the equations 
xx' = yy' ~ 2Z 1 = ?0'. Every surface will thus be trans- 
formed into a surface having the edges of the tetrahedron 
of reference as nodal lines. Backlund's transforma- 
tion, a transformation between two pseudospherical sur- 
faces having equal negative curvature. Bilinear trans- 
formation, a transformation denned by a lineoliuear 
equation. Biquadratic transformation, n transfor- 
mation by substituting for one set of variables others 
that are biquadratic functions of them. Blrational 
transformation, a transformation where the variables 
of each of the two seta are rational functions of those of 
the other set. When the variables are homogeneous co- 
ordinates, and the transformation is not linear, there is a 
certain nodal locus whose correspondence is indetermi- 
nate. Caseous or cheesy transformation. See case- 
ous. Cremona transformation, a birational transfor- 
mation between two planes. Every curve in one plane 
is transformed into a curve of the same deficiency in the 
other plane, and there are certain nodal points through 
which all such curves pass, having certain lines as mul- 
tiple tangents. Cubic transformation, a transforma- 
tion by substituting for one set of variables others that 
are cubic functions of them. Degree of a transforma- 
tion. See the quotation. 
When the points of a space S have a (1, 1) correspon- 
dence with those of another space 8 in such a manner that 
the planes and the right lines of s correspond to surfaces 
F of m th order, and to curves C of the nth order in the 
former space S, I say that the transformation of s into S 
is of the mth degree, and that the inverse transformation 
is of the n th degree. Cremona. 
Determinant of a linear transformation. See de- 
terminant. Hessian transformation, a transforma- 
tion of a ternary quantic, obtained by substituting for 
the homogeneous variables the umbra; A,, A 2 , A 3 , which 
are such that A,A!, A^g, etc., are the minors of the 
Hessian of the quantic. Homographic transforma- 
tion, (a) A transformation between two planes or spaces 
such that the point-coordinates in one correspond to 
tangential coordinates in the other. (6) A transforma- 
tion by means of a lineolinear equation connecting the 
old variable with the new one. Such a transformation 
is called homographic because it does not alter the 
value of an anharmonic ratio. Imaginary trans- 
formation. See imaginary. Infinitesimal trans- 
formation, a transformation in which the variables are 
increased by infinitesimal amounts. The infinitesimal 
transformation f, TJ is that which results from the sub- 
stitution of x + f( for x and y + eij for y, where e is in- 
finitesimal. If this substitution can be made in a differ- 
ential equation by virtue of that equation, the equation 
is said to admit the infinitesimal transformation (, ij. 
Landen's transformation [named after its discover- 
er, the English mathematician John Landen (1719-90)], a 
transformation of an elliptic integral of the first species 
by which its modulus is changed from i to the arithmet- 
ico-geometrical mean of ft' and unity. Lie's transfor- 
mation, a transformation in which to all the lines tan- 
gent to one surface at each point correspond all the spheres 
tangent to another surface at a corresponding point. 
Linear transformation, a transformation by means of 
a system of equations giving the values of the old varia- 
bles as linear functions of the new. Line-point trans- 
formation, a transformation in which lines correspond 
to points. Modular transformation of an elliptic 
integral. See modular. Modulus of a linear trans- 
formation. See modulus. Order of a transforma- 
tion. Same as degree of a transformation. Orthogo- 
nal transformation, a linear transformation in which 
the sum of the squares of the variables remains un- 
changed. Polar transformation, (a) A transforma- 
tion in which two variables r and are replaced by two 
others r 1 and ff, by means of the equations = mff, 
log r = m log r 1 . The geometrical effect is that of pass- 
ing from the stereographic to Lagrange's map-projection 
(which see, under projection), (b) A transformation by 
means of polar triangles in spherical trigonometry. 
Quadratic or quadrlc transformation, a transforma- 
tion in which each of the old variables is a quadratic 
function of the new ones; especially, a quadratic Cre- 
mona transformation where to a right line in either of 
two planes corresponds a conic in the other, with three 
nodal points. Rational transformation. See ration- 
al. Reciprocal transformation, a transformation by 
means of the equations x : y : z = x, 1 : y t l : 2, 1 . 
Transformation by symmetric functions, a trans- 
formation of an equation by substituting for the variable 
a rational function of the roots by means of the properties 
of symmetric functions. Transformation of energy. 
See correlation of energies, under energy. Tschirnhau- 
sen transformation, the expression of any rational func- 
tion of an unknown by means of a given algebraic equa- 
tion in that unknown, as an integral function of a de- 
gree less than that of the given equation. Unimodular 
transformation. See unimodvlar. =Syn. See trans- 
form, v. t. 
transformation-scene ( trans - f 6r - ma ' shon - 
sen), n. Theat., a scene which changes in 
sight of the audience ; specifically, a gorgeous 
scene at the conclusion of the burlesque of a 
pantomime, in which the principal characters 
are supposed to be transformed into the chief 
actors in the immediately following harlequin- 
ade. 
transformative (trans-for'ma-tiv), a. [< L. 
transformatus, pp. of transformare, transform 
(see transform), + -we.] Having power or a 
tendency to transform. 
transfund 
transfprmator (traus-for'ma-tor), w. [< NTj. 
tranxformator, <L. transformare, transform: see 
transform.] In elect., same as transformer. 
transformer (trans-for'mer), . One who or 
that which transforms. The alternate-current trans- 
former, which is the one most extensively used in elec- 
tricity, is an apparatus similar to an induction-coil, con- 
sisting of two coils of insulated wire wound on an iron 
core for the purpose of furnishing, by means of a current 
of small quantity and high potential in one circuit, a cur- 
rent of large quantity and low potential in another cir- 
cuit. One of the coils, called the primary, of comparative- 
ly high resistance and large number of turns, is included 
in the high-potential circuit, while the other is included 
in the low-potential circuit. The mechanical transformer 
consists of a motor driven by a high-potential current, 
combined with a dynamo driven by this motor, and fur- 
nishing a current of potential and quantity adapted to the 
circumstances where it is to be used. This form is appli- 
cable to direct as well as to alternating currents. 
transformism (trans-for'mi/m), n. [< trans- 
form + -i/tm.] In biol., the fact or the doc- 
trine of such modification of specific charac- 
ters in any organism as suffices to change one 
species into a different species, whether im- 
mediately or in the course of time ; transmu- 
tation of species (see transmutation, 1 (c)). The 
term has nothing to do with the transformation or meta- 
morphosis which any organism may undergo in the course 
of its individual life-cycle. It has attached to some ex- 
treme views of the natural possibilities of transmutation, 
as of a plant into an animal, a horsehair into a hairworm, 
and the like nothing of this sort being known as a fact 
in nature. But in the scientific conception of the term, 
transformism, like transmutation in its biological sense, 
is simply the doctrine of descent with modification on ac- 
cepted principles of evolution, and, so understood, com- 
mands the assent of nearly all biologists. See Darwinism, 
evolution, 2 (a), selection, 3, species, 5, transmutation, 1 (c), 
and transpeciation. 
On the other hand, we may suppose that crayfishes have 
resulted from the modification of some other form of liv- 
ing matter ; and - this is what, to borrow a useful word 
from the French language, is known as transformism. 
Huxley, Crayfish, p. 318. 
transformist (trans-fpr'mist), n. [< transform 
+ -ist.] A believer in or an advocate of the 
doctrine of transformism, in any sense. 
Agardh . . . was a little too earnest a transformist, and 
believed that certain algee could become animals. 
Pop. Sri. Mo., XXXVIII. 257. 
transformistic(trans-fr-mis'tik), a. f_< trans- 
formist + -ic.~\ Pertaining to transformism or 
to transformists. 
In the chapter on the first appearance of man, the va- 
rious transformistic theories are passed in review. 
Nature, XXXV. 389. 
transfreightt. v. i. A corrupt form of transfrete. 
Waterhouse, Apology (1653), p. 52. (Latham.) 
transfretationt (trans-fre-ta'shon), n. [< L. 
transfretatio(n-), crossing over a strait, < trans- 
fretare, cross over a strait: see transfrete."] The 
act of passing over a strait or narrow sea. 
She had a rough Passage in her Transf relation to Dover 
Castle. IloweU, Letters, I. iv. 22. 
transfretet (trans-fret'), r. i. [Also, corrupt- 
ly, transfreight; < OF. transfreter = Sp. trans- 
fretar, ^ L. transfretare, cross over a strait, 
convey over a strait, < trans, over, -I- fretum, a 
strait: see frith 2 .] To pass over a strait or 
narrow sea. 
Shortely after that kyng Henry had taryed a convenient 
space, he transfreted and arryved at Dover, and so came to 
his maner of Grenewiche. Hull, Hen. VII., an. 7. 
transfrontal (trans-fron'tal), o. [< L. trans, 
across, + fron(t-)s, front: see frontal.] Trav- 
ersing the frontal lobe of the brain : specify- 
ing certain fissures of that lobe. Suck's Hand- 
book of Med. Sciences, VIII. 152. 
transfrontier (traus-fron'ter), a. [< trans- + 
frontier.] Beyond the frontier, or of or per- 
taining to what is beyond the frontier : as, the 
transfrontier tribes (that is, usually, the tribes 
beyond the frontier of the Anglo-Indian em- 
pire). 
Of the new maps, 4,062 were published during the year, 
and heavy demands continue to be made for transfrontier 
maps, and maps of Upper Burmah. Science, XIV. 216. 
transfuge (trans'fiVj), . [< F. transfuge = Sp. 
trdnsfuga, trdnsfugo, trdsfuija, trdsfugo = Pg. It. 
tranxfiuja, < L. transfuga, a deserter, < transfu- 
gere, desert, flee over to the other side, < trans, 
over, + fugere, flee : see fugitive.] A deserter, 
in the military sense. 
The protection of deserters and transfuges is the invari- 
able rule of every service in the world. 
Lord Stanhope, To George Ticknor, May 12, 1855. 
transfugitiye (trans-fu'ji-tiv), . [< trans-, 
over, + fugitive. Ct.triiiisfiige.] Same as trans- 
fniir. Eclectic Rev. (Worcester.) 
transfund (trans-fund'), v. t. [=Sp. Pg. tniits- 
finiflir = It. traiixfoiitlcre, < L. tramtfundere, 
pour out from one vessel into another, < trans, 
