Proteins in Food Processing 2nd Edition Rickey Y. Yada
Proteins in Food Processing 2nd Edition Rickey Y. Yada
Proteins in Food Processing 2nd Edition Rickey Y. Yada
Proteins in Food Processing 2nd Edition Rickey Y. Yada
Proteins in Food Processing 2nd Edition Rickey Y. Yada
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Proteins in FoodProcessing 2nd Edition Rickey Y. Yada
Digital Instant Download
Author(s): Rickey Y. Yada
ISBN(s): 9780081007228, 0081007221
Edition: 2
File Details: PDF, 21.44 MB
Year: 2017
Language: english
Woodhead Publishing Seriesin Food Science,
Technology and Nutrition
Proteins in Food
Processing
Second Edition
Edited by
Rickey Y. Yada
An imprint of Elsevier
Contents
List of contributorsxi
Preface xv
1 Properties of proteins in food systems: An introduction 1
E.C.Y. Li-Chan, I.M.E. Lacroix
1.1 Introduction 1
1.2 Structural properties of proteins 3
1.3 Factors affecting properties of proteins in food systems 12
1.4 Future trends 18
1.5 Sources of useful information 20
References 20
2 Impact of processing on the chemistry and functionality of
food proteins 27
A.N.A. Aryee, D. Agyei, C.C. Udenigwe
2.1 Introduction 27
2.2 Structure and chemistry of food proteins 28
2.3 Functionality of food protein 30
2.4 Effect of processing on food protein functionality 34
2.5 Effect of process-induced protein modifications on chemosensory
properties of food 40
2.6 Conclusion 42
References 42
Further reading 45
Part One Sources of proteins 47
3 The caseins: Structure, stability, and functionality 49
T. Huppertz, P.F. Fox, A.L. Kelly
3.1 Introduction 49
3.2 Chemistry of caseins 50
3.3 Casein interactions 62
3.4 Casein-mineral interactions 64
3.5 Casein micelles 65
3.6 Stability of casein micelles 69
3.7 Casein-based ingredients 74
12.
viContents
3.8 Conclusions andfuture perspectives 79
References 79
4 Whey proteins 93
A. Kilara, M.N. Vaghela
4.1 Introduction: What are whey proteins? Sources of whey (acid, sweet) 93
4.2 Analytical methods for determining protein content 94
4.3 Structure of whey proteins 98
4.4 Functional properties of whey proteins 102
4.5 Improving functionality of whey proteins in foods:
Physical processes and enzymatic modification 109
4.6 Future trends 117
References 118
Further reading 126
5 Muscle proteins 127
Y.L. Xiong
5.1 Introduction 127
5.2 Structure of muscle proteins 127
5.3 Endogenous proteases 130
5.4 Muscle protein functionality 132
5.5 Prepared muscle proteins as functional ingredients 139
5.6 Future trends 143
5.7 Sources of further information 143
References 144
6 Soy as a food ingredient 149
K. Nishinari, Y. Fang, T. Nagano, S. Guo, R. Wang
6.1 Introduction 149
6.2 Structure of soybean proteins 151
6.3 Gels and gelling of soy proteins 156
6.4 Emulsification of soy proteins 163
6.5 How to improve the functionality and processability 169
6.6 Applications 171
6.7 Conclusion 177
References 177
Further reading 184
7 Proteins from oil-producing plants 187
S.D. Arntfield
7.1 Introduction 187
7.2 Characteristics of oilseed proteins 187
7.3 Factors limiting protein utilization 191
7.4 Extraction and isolation of proteins 196
7.5 Preparation and use of oilseed protein hydrolysates for
health benefits 202
13.
Contentsvii
7.6 Technofunctional propertiesof proteins 204
7.7 Techniques to improve functional properties 207
7.8 Utilization of oilseed proteins 209
7.9 Future of these proteins 210
References 211
8 Cereals proteins 223
N. Guerrieri, M. Cavaletto
8.1 Introduction 223
8.2 Protein function in the seeds 225
8.3 Protein classifications 229
8.4 Gluten properties 232
8.5 Cereals and pseudocereals proteins in food processing 235
8.6 Future trends 238
Acknowledgements 240
References 240
Further reading 244
9 Seaweed proteins 245
J. Fleurence, M. Morançais, J. Dumay
9.1 Introduction: Seaweed and protein content of seaweed 245
9.2 Composition of seaweed proteins 248
9.3 Algal protein digestibility 250
9.4 Uses of algal proteins in food 255
9.5 Future trends 255
9.6 Sources of further information and advice 258
References 259
10 Insects as an Alternative Protein Source 263
Y. Akhtar, M.B. Isman
10.1 Introduction 263
10.2 History of entomophagy 266
10.3 Nutritional value of insects for human consumption 266
10.4 Amino acids 268
10.5 Dietary energy and fat content 274
10.6 Impact on the environment 277
10.7 Challenges 280
10.8 Conclusion 283
Acknowledgments 283
References 283
Further reading 287
11 Proteins in cultured beef 289
M.J. Post
11.1 Introduction—Why cultured beef? 289
11.2 Technology 290
14.
viiiContents
11.3 Optimizing theproduct 292
11.4 Whole cuts of meat 294
11.5 Road to product development 295
11.6 Summary 296
References 297
Part Two Analyzing and modifying protein 299
12 Food proteins for health and nutrition 301
N. Shang, S. Chaplot, J. Wu
12.1 Introduction 301
12.2 Growing demand for protein and sustainability 302
12.3 Protein intake 303
12.4 Protein quality and its measurement 304
12.5 Bioactivities of proteins 305
12.6 Applications 321
12.7 Safety and legal aspects of protein 323
12.8 Summary 325
References 325
Further reading 336
13 Factors affecting enzyme activity in food processing 337
M.G. Scanlon, A.W. Henrich, J.R. Whitaker
13.1 Introduction 337
13.2 Enzyme types 338
13.3 Parameters affecting enzymatic activity 340
13.4 Endogenous enzymes 349
13.5 Exogenous enzymes 350
13.6 Future trends 360
Acknowledgments 361
References 362
14 Detection and deactivation of allergens in food 367
C.L. Okolie, A.N.A. Aryee, C.C. Udenigwe
14.1 Introduction 367
14.2 Mechanism of food-induced allergic reaction 368
14.3 Detection of food allergens 369
14.4 Food processing and allergenicity 372
14.5 Conclusion 381
References 382
15 Food protein-derived peptides: Production, isolation, and purification 389
R.E. Aluko
15.1 Introduction 389
15.2 Protein sources 389
15.3 Enzymatic hydrolysis of proteins: Basic concepts 396
15.4 Peptide separation and isolation methods 400
15.
Contentsix
15.5 Purification protocols403
15.6 Structural identification and amino acid sequencing 404
15.7 Current uses 404
15.8 Future trends 405
References 406
Further reading 412
16 Modifying seeds to produce proteins 413
S.T. Häkkinen, A.M. Nuutila, A. Ritala
16.1 Introduction 413
16.2 Methods used for seed modification 415
16.3 Applications in seed modification 421
16.4 Future trends 430
16.5 Sources of further information and advice 431
References 431
Part Three Applications 443
17 Seafood proteins 445
M.A. Mazorra-Manzano, J.C. Ramírez-Suárez,
J.M. Moreno-Hernández, R. Pacheco-Aguilar
17.1 Introduction 445
17.2 Nutritional aspects of seafood proteins 446
17.3 Technological and functional aspects of seafood proteins 447
17.4 Seafood processing and its impact on protein quality 450
17.5 Seafood proteins as food ingredients 458
17.6 Recovery of high-value proteins from seafood and its by-products 461
17.7 Proteins used as markers of quality and authenticity in seafood 464
17.8 Future trends 466
References 467
18 Edible films and coatings from proteins 477
A. Chiralt, C. González-Martínez, M. Vargas, L. Atarés
18.1 Introduction 477
18.2 Proteins as film-forming agents 478
18.3 Physical and chemical methods to improve properties of protein films 478
18.4 Active protein films 489
18.5 Final remarks 493
Acknowledgment 493
References 494
Further reading 500
19 Protein gels 501
C.D. Munialo, S.R. Euston, H.H.J. de Jongh
19.1 Introduction 501
19.2 Protein sources 502
16.
xContents
19.3 Gel formationby proteins 504
19.4 Proteins as gelling agent 505
19.5 Mechanical properties of protein gels 506
19.6 Gel properties 508
19.7 Relation between gel morphology and macroscopic responses 514
19.8 Comparison between plant and animal protein gels 515
19.9 Future trends 516
19.9.1 Conclusion 516
References 517
20 Health-related functional value of dairy proteins and peptides 523
B. Miralles, B. Hernández-Ledesma, S. Fernández-Tomé,
L. Amigo, I. Recio
20.1 Introduction 523
20.2 Health benefits of dairy proteins and peptides on metabolic
syndrome 524
20.3 Effects of dairy proteins and peptides on intestinal epithelium 536
20.4 Other effects of dairy proteins and peptides 546
20.5 Conclusions and future challenges 550
References 552
21 The use of immobilized enzymes to improve functionality 569
N.S. Hettiarachchy, D.J. Feliz, J.S. Edwards, R. Horax
21.1 General overview about enzymes and immobilized enzymes 569
21.2 Enzyme immobilization methods: Descriptions, benefits,
and drawbacks 577
21.3 Usage of immobilized enzymes in food production,
medicine, and other fields 581
21.4 The use of immobilized enzymes either in producing proteins,
carbohydrates, or lipids; or utilizing proteins, carbohydrates,
or lipids as the matrix, support, or carrier 586
21.5 Other important applications of immobilized enzymes 588
21.6 The practice of cell immobilization 589
21.7 Potential and developing applications of immobilized enzymes 590
References 590
Further reading 597
22 Impact of proteins on food color 599
P.L. Dawson, J.C. Acton
22.1 Introduction 599
22.2 Role of proteins in color 606
22.3 Improving protein functionality in color control 620
22.4 Applications to maintain color quality 622
22.5 Future trends 632
References 632
Further reading 638
Index 639
17.
List of contributors
J.C.Acton Clemson University, Clemson, SC, United States
D. Agyei University of Otago, Dunedin, New Zealand
Y. Akhtar University of British Columbia; DE Labs Inc., Vancouver, BC, Canada
R.E. Aluko University of Manitoba, Winnipeg, MB, Canada
L. Amigo Institute of Food Science Research, CIAL (CSIC-UAM), Madrid, Spain
S.D. Arntfield University of Manitoba, Winnipeg, MB, Canada
A.N.A. Aryee Delaware State University, Dover, DE, United States
L. Atarés Universitat Politècnica de València, Valencia, Spain
M. Cavaletto University of Piemonte Orientale, Vercelli, Italy
S. Chaplot University of Alberta, Edmonton, AB, Canada
A. Chiralt Universitat Politècnica de València, Valencia, Spain
P.L. Dawson Clemson University, Clemson, SC, United States
H.H.J. de Jongh ProtIn Consultancy, Zeist, The Netherlands
J. Dumay University of Nantes, Nantes, France
J.S. Edwards University of Arkansas, Fayetteville, AR, United States
S.R. Euston Heriot-Watt University, Edinburgh, United Kingdom
Y. Fang Hubei University of Technology, Wuhan, China
D.J. Feliz Independent Food Scientist Consultant, Baltimore, MD, United States
S. Fernández-Tomé Institute of Food Science Research, CIAL (CSIC-UAM), Madrid,
Spain
18.
xii List ofcontributors
J. Fleurence University of Nantes, Nantes, France
P.F. Fox University College, Cork, Ireland
C. González-Martínez Universitat Politècnica de València, Valencia, Spain
N. Guerrieri Institute of Ecosystem Study, CNR-ISE, Verbania, Italy
S. Guo China Agricultural University, Beijing, China
S.T. Häkkinen VTT Technical Research Centre of Finland Ltd, Espoo, Finland
A.W. Henrich CSM Bakery Solutions, Bingen am Rhein Germany
B. Hernández-Ledesma Institute of Food Science Research, CIAL (CSIC-UAM),
Madrid, Spain
N.S. Hettiarachchy University of Arkansas, Fayetteville, AR, United States
R. Horax University of Arkansas, Fayetteville, AR, United States
T. Huppertz NIZO, Ede, The Netherlands
M.B. Isman University of British Columbia, Vancouver, BC, Canada
A.L. Kelly University College, Cork, Ireland
A. Kilaraa
Arun Kilara Worldwide, Chapel Hill, NC, United States
I.M.E. Lacroix The University of British Columbia, Vancouver, BC, Canada
E.C.Y. Li-Chan The University of British Columbia, Vancouver, BC, Canada
M.A. Mazorra-Manzano Research Center for Food and Development (CIAD),
Hermosillo Sonora, Mexico
B. Miralles Institute of Food Science Research, CIAL (CSIC-UAM), Madrid, Spain
M. Morançais University of Nantes, Nantes, France
J.M. Moreno-Hernández National Institute in Forestry, Agriculture and Livestock
(INIFAP), Culiacan Sinaloa, Mexico
a
Deceased.
19.
List of contributorsxiii
C.D. Munialo Heriot-Watt University, Edinburgh, United Kingdom
T. Nagano Kawasaki University of Medical Welfare, Okayama, Japan
K. Nishinari Hubei University of Technology, Wuhan, China
A.M. Nuutila VTT Technical Research Centre of Finland Ltd, Espoo, Finland
C.L. Okolie Dalhousie University, Truro, NS, Canada
R. Pacheco-Aguilar Research Center for Food and Development (CIAD), Hermosillo
Sonora, Mexico
M.J. Post Maastricht University; MosaMeat B.V., Maastricht, The Netherlands
J.C.Ramírez-SuárezResearchCenterforFoodandDevelopment(CIAD),Hermosillo
Sonora, Mexico
I. Recio Institute of Food Science Research, CIAL (CSIC-UAM), Madrid, Spain
A. Ritala VTT Technical Research Centre of Finland Ltd, Espoo, Finland
M.G. Scanlon University of Manitoba, Winnipeg, MB, Canada
N. Shang University of Alberta, Edmonton, AB, Canada
C.C. Udenigwe University of Ottawa, Ottawa, ON, Canada
M.N. Vaghela Nestle Development Center, Solon, OH, United States
M. Vargas Universitat Politècnica de València, Valencia, Spain
R. Wang China Agricultural University, Beijing, China
J.R. Whitaker Deceased
J. Wu University of Alberta, Edmonton, AB, Canada
Y.L. Xiong University of Kentucky, Lexington, KY, United States
Preface
As one ofthe major components of food, proteins not only play a vital role in their
nutritional quality but also to the physicochemical, sensory, health aspects, and utili-
zation. Proteins in food processing, 2nd edition is an update of the 1st edition and re-
views the mounting body of research on understanding protein structure, and existing
and emerging sources as multifunctional ingredients for the food industry.
The book is comprised of two introductory chapters followed by three parts. The
two introductory chapters outline the basic properties of proteins in food systems and
the impact of processing on their chemistry and functionality. Part 1 discusses both ex-
isting and emerging sources of proteins, for example, insect and cultured beef. Part 2
illustrates the analysis and modification of proteins, and included chapters on pro-
teins for health and nutrition, factors affecting enzyme activity, allergens in food, food
protein-derived peptides, and the modification of seeds to produce proteins. The book
concludes with Part 3 devoted to the application of proteins as well as those examining
their modification, health impact, and contribution to color.
Rickey Y. Yada
University of British Columbia, Vancouver, BC, Canada
2 Proteins inFood Processing
milk, and eggs as well as food products such as bread and cheese. Interactions of pro-
teins with other components are exemplified in protein-starch interactions observed
during dough processing and baking, protein-hydrocolloid interactions in dairy prod-
ucts, protein-fat interactions in comminuted meat emulsions, mayonnaise and cheese,
protein-water as well as protein-protein matrix interactions in fish surimi gels, yogurt,
and cheese (Lluch et al., 2001).
With this complexity in mind, this chapter first describes the basic chemical and
physical properties of proteins and their amino acid building blocks. It then provides
an overview of the factors that can influence the properties of proteins in food systems
and highlights the current trends in food protein research.
Table 1.1 Total protein content of some foods and beveragesa
Food productb
Protein (g/100g)
Almonds [12061] 21.15
Almond milk, sweetened, vanilla flavor [14016] 0.42
Apples, raw, with skin [09003] 0.26
Bananas, raw [09040] 1.09
Beef, grass-fed, strip steaks, lean only, raw [13000] 23.07
Bread, white [18069] 8.85
Broccoli, raw [11090] 2.82
Cheese, cheddar [01009] 22.87
Cheese, feta [01019] 14.21
Chicken, breast, skinless, boneless, meat only, raw [05062] 22.50
Chocolate, dark, 70%–85% cacao solids [19904] 7.79
Corn flakes, cereals, ready-to-eat [08020] 7.50
Egg, whole, raw [01123] 12.56
Ice creams, vanilla [19095] 3.50
Lentils, raw [16069] 24.63
Milk, whole, 3.25% milkfat, with added vitamin D [01077] 3.15
Oranges, raw, navels [09202] 0.91
Pasta, whole-wheat, dry [20124] 13.87
Potatoes, russet, flesh and skin, raw [11353] 2.14
Quinoa, uncooked [20035] 14.12
Rice, white, glutinous, unenriched, uncooked [20054] 6.81
Salmon, Atlantic, wild, raw [15076] 19.84
Soymilk, original and vanilla, with added calcium, vitamins A and D
[16139]
2.60
Tofu, raw, firm, prepared with calcium sulfate [16426] 17.27
Tuna, light, canned in water, drained solids [15121] 19.44
Yogurt, plain, low fat [01117] 5.25
Yogurt, Greek, plain, nonfat [01256] 10.19
a
The information in this table was obtained from the US Department of Agriculture, Agricultural Research Service,
Nutrient Data Laboratory. USDA National Nutrient Database for Standard Reference (Release 28. Released September
2015, slightly revised May 2016). Available from: https://ndb.nal.usda.gov/ndb/ (24 January 2017).
b
Numbers in square brackets are the NDB numbers (the 5-digit Nutrient Databank number that identifies each
food item).
25.
Properties of proteinsin food systems: An introduction3
1.2
Structural properties of proteins
1.2.1
Amino acids commonly found in proteins
It is commonly recognized that 20 amino acids form the building blocks of most pro
teins, being linked by peptide (amide) bonds formed between α-amino and α-carboxylic
acid groups of neighboring amino acids in the polypeptide sequence. As shown in
Fig. 1.1, 19 of these 20 amino acids have the general structure of H2NCαH(R)CO2H,
differing only in R, which is referred to as the side chain, while the 20th amino acid
is in fact an “imino” acid, in which the side chain is bonded to the nitrogen atom.
With the exception of the amino acid glycine, in which the side chain is a hydrogen
atom, the α-carbon atom exhibits chirality. Typically, only the L-form of the amino
acids is found in proteins, being incorporated through the transcription and trans
lation machinery of the cell. The D-enantiomers of amino acids are present in a few
peptides, including some found in the cell walls of bacteria (Nelson and Cox, 2005).
Readers interested in learning about the discovery of these amino acids are referred to
Belitz et al. (2009).
Table 1.2 shows the three-letter abbreviations and single-letter symbols as well as
some key properties of the 20 amino acids commonly found in food proteins. These
amino acids can be grouped in five main classes based on their side chain type: aro-
matic (Phe, Trp, Tyr), nonpolar, aliphatic (Ala, Gly, Ile, Leu, Met, Pro, Val), polar, un-
charged (Asn, Cys, Gln, Ser, Thr), positively charged (Arg, His, Lys), and negatively
charged (Asp, Glu) (Table 1.2). This classification, however, should not be considered
absolute since some amino acids, particularly Gly, His, and Cys, do not fit perfectly
into a specific group. Moreover, as noted above, two of the amino acids are unique in
being achiral (Gly) or an imino rather than amino acid (Pro).
The two amino acid residues occurring at greatest frequency in proteins possess
aliphatic side chains (10.3% and 8.1% for Leu and Ala, respectively), while Gly is
the third most frequently occurring amino acid at 7.2% (Jordan et al., 2005). With the
exception of His, more than 80%–90% of the positively and negatively charged amino
acid residues in proteins usually locate such that they are primarily exposed to the
solvent (Bordo and Argos, 1991; Leibniz Institute on Aging—Fritz Lipmann Institute,
2016a). Similarly, amino acid residues with polar side chains (Ser, Thr, Asn, Gln) as
well as Pro are also primarily accessible to the solvent. Conversely, with the exception
of Tyr, which contains an aromatic phenolic group, less than 50% of the aliphatic
and aromatic groups have solvent-exposed areas greater than 30Å. Nevertheless, only
40%–50% of aliphatic and aromatic residues would be considered to be “buried,”
with solvent-exposed areas of less than 10Å. These observations indicate that while
charged residues are almost always located near the surface or solvent-accessible re-
gions of protein molecules, the converse cannot be assumed for nonpolar aliphatic or
aromatic residues, probably due to insufficient capacity in the interior of the molecule.
Thus, both charged and hydrophobic groups reside at the surface or solvent-accessible
regions of protein molecules, whereas charged groups are found much less frequently
in the buried interior of protein molecules. In fact, it has been reported that approx-
imately 58% of the average solvent-accessible surface or “exterior” of monomeric
304 The Elementsof Perspective Join A E. Then, by the
second Corollary of Problem II., a e is a horizontal line. Draw t v
parallel to a E, cutting the sight-line in v. .'.v is the vanishing-point of
a e. Corolla? thC constructions of Problem II. and its second Then by
Problem II. a b is the line A B drawn in perspective ; and by its
Corollary a e is the line A E drawn in perspective. From v erect
perpendicular v p, and produce a b to cut it in P. Join T P, and from e
draw / parallel to A E, and cutting A T in f. S Now in triangles EBl
and AET,as^ is parallel to E B and c /to A E ; — e b : ef : : E B : A E.
But T v is also parallel to A E and P v to e b. Therefore also in the
triangles apv and a V T, e b : e f : : p v : v T. Therefore PV:vt::eb:ae.
And, by construction, angle T v p= angle A E B. Therefore the
triangles T v p, a e b, are similar; and T P is parallel to A B.
28.
Appendix 305 Nowthe construction in this problem is
entirely general for any inclined line A B, and a horizontal line A E in
the same vertical plane with it. So that if we find the vanishing-point
of A E in v, and from v erect a vertical V P, and from T draw T P
parallel to A B, cutting v P in P, P will be the vanishing-point of A B,
and (by the same proof as that given at page 226.) of all lines
parallel to it. Next, to find the dividing-point of the inclined line. Fig.
77. I remove some unnecessary lines from the last figure and repeat
it here, Fig. 77., adding the measuring-line a M, that the student
may observe its position with respect to the other lines before I
remove any more of them. Now if the line A B in this diagram
represented the length of the line A B in reality (as A B does in Figs.
10. and 1 1.), we should only have to proceed to modify Corollary
III. of Problem 1 1, to this new construction. We shall see presently
that A B does not represent the actual length of the inclined line A B
in nature, nevertheless we shall first proceed as if it did, and modify
our result afterwards.
30.
306 The Elementsof Perspective In Fig. 77. draw a d
parallel to A B, cutting B T in d. Therefore a d is the sight-magnitude
of A B, as a R is of A B in Fig. 11. Remove again from the figure all
lines except P v, v T, P T, a b, a d, and the measuring-line. Set off on
the measuring-line a ?n equal to a d. Draw P Q parallel to a m, and
through bdraw m Q, cutting P Q in Q. Then, by the proof already
given in pages 230. and 303., P Q = P T. Therefore if P is the
vanishing-point of an inclined line A B, and Q P is a horizontal line
drawn through it, make P Q equal to p T, and a m on the measuring-
line equal to the sightmagnitude of the line A B in the diagram, and
the line joining m Q will cut a P in b. We have now, therefore, to
consider what relation the length of the line A B in this diagram, Fig.
77., has to the length of the line A B in reality. Now the line A E in
Fig. 77. represents the length of a e in reality. But the angle A E B,
Fig. 77., and the corresponding angle
32.
Appendix 307 inall the constructions of the earlier
problems, is in reality a right angle, though in the diagram
necessarily represented as obtuse. Therefore, if from E we draw E C,
as in Fig. 79., at right angles to A E, make E C = E B, and join A c, A
c will be the real length of the line A B. Now, therefore, if instead of
a m in Fig. 78., we take the real length of A B, that real length will
be to a m as A C to A B in Fig. 79. And then, if the line drawn to the
measuring-line P Q is still to cut a P in 6, it is evident that the line P
Q must be shortened in the same ratio that a m was shortened ; and
the true G- ?9dividing-point will be Q' in Fig. 80., fixed so that Q' p
shall be to Q P as a in is to a m ; a m representing the real length of
A B. But a m is therefore to a m as A C is to A B in Fig. 79. Therefore
P Q' must be to P Q as A C is to A B. But P Q equals P T (Fig. 78.) ;
and P v is to v T (in Fig. 78.) as B E is to A E (Fig. 79.). Hence we
have only to substitute P v for E C, and v T for A E, in Fig. 79 . and
the resulting diagonal A C will be the required length of P Q'. It will
be seen that the construction given in the text
34.
308 The Elementsof Perspective (Fig. 46.) is the simplest
means of obtaining this magnitude, for v D in Fig. 46. (or v M in Fig.
I5.) = v T by construction in Problem IV. It should, however, be
observed, that the distance P D or P x, in Fig. 46., may be laid on
the sight-line of the inclined plane itself, if the measuring-line be
drawn parallel to that sight-line. And thus any form may be drawn
on an inclined plane as conveniently as on a horizontal one, with the
single exception of the radiation of the verticals, which have a
vanishing-point, as shown in Problem XX.
35.
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INDEX TO ELEMENTS OF DRAWING Aerial Perspective,
139 Art, coarse, its inferiority, 14 ; not perfect if depending on visible
lines, 81 ; excellence of, dependent on expression of the individuality
of natural objects, 99 ; of painting, in what it consists, 4 (note)
Artists, list of those whose works are to be studied, 195-201
Background, to be drawn exactly as seen, 45 Banks, their beauty, 89
Bewick, 199 Black, rightly to be made conspicuous, '33. 134 Blake,
199 Body-colour drawing, 1 17-120 Boldness, not to be aimed at by
the beginner, 29, 141 Books, what to read, 202-204 Boughs,
ramification of, 73 ; individuality of, 169 ; limitation of, 169 Branches,
structure of, 164 Bridge, ideal construction of, 153, 154 Caraco,
conventionalism of, 102 Chiaroscuro, the masters of, 57 ; its
importance in water painting, 106 Clouds, best introduction to
drawing of, 38 ; 109, 1 10 ; mistakes of ordinary artists in drawing,
no; their sculptured form, no, in ; how to sketch the lighter wreaths
of, in ; as drawn by Turner, Titian and Tiutoret, 112 Colour, cause of,
4 (note) ; smooth, how to produce, 5-7 ; depth of, represented by
depth of shade, 19 , relation of, to shade, 24, 25 ; scales of, how to
prepare, 24, 25 ; cast back by objects in reflected light, 33 ; of
water, 107, 108 ; relativeness of, 113; importance of, in comparison
with form, 115 ; relative merits of transparent and opaque n 7-120;
gradations in, 126-128 ; how obtained, 120 ff.; in nature, 123, 133,
136 ; colour power a sign of mental health, 136 ; its relation to form,
137 ; how expressive of distances, 137-139 ; how best to obtain
harmony of, 186 Composition, 141 ff ; law of principality, 144-147 ;
of repetition, 147-150 ; of continuity, 150-155; of curvature, 155-161
; of radiation, 161-173 ; of contrast, 173-179 ; of interchange, 170-
180 ; of consistency, 180-183 ; of harmony, 183-193 Confusion. See
Nature Consistency, law of, 180-183 Continuity, law of, 150-155
Contrast, law of, 173-179 Coreggio, 117, 176 Cracks or fissures, how
expressible, 3L 32, 35 Cruikshank, his etchings, 58, 187, see
Appendix Curvature, law of, 155-161 Curves, of shore, necessity of
right drawing of, 105 ; necessary of, to good composition, 157
36.
Detail, cannot beexpressed in drawing as it is in reality, 44 Distance,
how expressed by colour, 137-139 Drapery, difficulty of drawing, 37
Drawing, good, an abstract of natural facts, 183 Durer, his perfection
of chiaroscuro, 57, 59. 64, 66 Economy of execution, as shown in the
work of great masters, 61 Engraving, more difficult than common
drawing, 56 Execution, how to distinguish that of the great masters,
61 ; habit of, opposed to true drawing of detail, 99 Eye, innocence
of, 3 (note) ; how to obtain accuracy of, 8, 9 Flatness, nowhere
found in the natural world, 27 ; tendency towards in fine drawing
and painting, 44 Foliage, important element in effect of, 52 ; in the
works of Harding, 92, 93 ; radiation and enclosure of, 93 ; as drawn
by Turner, 101 ; by Titian, 102 Foreground, bad in all engravings, 56
Form, perception of, 3 (note) ; expression of, on what it depends, 10
; refinement of, difficulty of obtaining, 29; how expresseJ by Nature,
31 ; 309
37.
3io Index moregained by drawing of, than labouring at
texture, 36 ; expressed by colour, 36 ; how expressed by great
artists, 43 ; vital facts of, 70 ff. ; absoluteness of, 113; disguised by
colour, 137 Freedom, error of aiming at, 9 French art, 184 (note)
Gainsborough, his foliage, 96 Gradation of colour, difficulty of
obtaining evenness of, 29 ; roundness and projection expressed by,
36 ; how to obtain, 40-42, 120 ff. ; in Nature, 126 ; beauty of, 127 ;
universality of law of, 133 Ground-surface, linear expression of, 109
Hand, lightness of, required for shading, 8 Harding, J. D., foliage by,
92 ; its excellences and shortcomings, 90 Harmony, law of, 183-193
; how best obtained, 186 Hunt, Holman, 116 Hunt, William, 42, 132
I.vitation, to be aimed at as far as possible, 60 India-.ubber, use of,
8 (note), 12 Individuality of natural objects as opposed to general
law, 95, 96, 97 ; excellence of art dependent on expression of, 99 ;
of boughs, 169 Inimitableness of natural objects, 52, 69
Interchange, law of, 179-1S0 Landscape drawing, three main laws to
be considered in regard to, 95, 96 Leaves, how to draw, 45 ff. ;
foreshortening of, 46 ; lustre of, 51 ; causes of form of, being altered
and hidden, 52 ; structure of, 92, 93 ; individual caprice of, as
opposed to general law, 94 ; radiation of, 162 Leech, woodcuts of, in
Punch, 58 Lewis, John, n6, see Appendix Light, reflected, 33 ;
receives colour from objects from which cast, 33 ; neutrality of, 33
Lines, difficulty of drawing them well slowly, 9 ; straight, great
draughtsmen unable to draw, 15, 16 (note) ; rules for direction of,
59, 60 ; Straight, used for shading, 61 ; leading or governing,
importance of, 70 ; two kinds of harmonies of, 161 Lustre, of leaves,
51 ; a defect in painting, 118 Memoranda, usefulness of, 85, 86
Mulready, 116 Mystery of foliage, 66 ; of other natural objects, 96,
100 ; as shown by Turner, 101 Natural objects, inimitableness of, 52
; mystery concealing, 96 Nature, character of confusion of, 47, 48 ;
how to express, 49 ff., 66-68 ; mystery of 96 ; colours in, 123, 133,
136 ; gradation of colours in, 126 ; symmetry in, 149 Neutrality of
reflected light, 33 Outline, more or less interrupted in good work, 62
; false and true, 62, 63 ; for what purposes to be used, 64 ; to what
objects to be confined, 65 Painting, technical powers of, 3 (note) ;
38.
art of, inwhat it consists, 4 (note) Paper, colour and quality to be
used, 110 Patterns, drawing of, good exercise for gaining perception
of tint, etc., 37. 38 . Perspective, aerial, 139 Perugino, Madonna of,
150 Pigments to be used in water-colour drawing, 116 ff. Power, only
gained by care, 29 Preciousness of colour, how obtained, 135 .
Precision, less danger for amateurs in, than in vagueness, 58
Principality, law of, 144-147 Projection, expressed by gradation, 36 ;
impossible to show, 44 ; deceptively produced by partial
exaggeration of shadow, 44 Prout. his St. Nicholas, 172; his
principles of composition, 180, see Appendix Radiation, of foliage, 93
; lawof, 161173 ; beauty of groups of form dependent on, 170
Raphael, his hesd of Angel ; 63, his ' St. Catherine, 82 ; his
Disputa, 146 Reflection, law of, 106 ; colour of, 107, 108
Rembrandt, his precision of line, 57 ; his perfection in chiaroscuro,
57 Repetition, law of, 147-150 Rethel, 58, see Appendix Retsch, 62,
200 Richter, 58 ; illustrations by, 187, see Appendix
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Index 3ii Rivers, general character of, 152 Rossetti, 116,
see Appendix Roundness, drawing dependent on power of
representing, 27 ; expressed by gradation, 36 Salvator Rosa, his
foliage, 96 Scales of colour, how to prepare, 24, 25 ; principle
underlying 26 Shade, gradation of, with pen, 10-T2 ; with pencil, 12-
14 depth of.colour represented by depth of, 19 ; good work more
or less touched with, 62 Shadow, generally darker than dark side of
object, 34-35 ; impossibility of getting all the gradations of, seen in
Nature, 43 ; value lent to objects by their, 86 ; colouring of, 134^
Shore, curves of, 105 ; perspective of, 107 Sight, keenness of,
required for shading, 8 Sketching from Nature, what to choose, and
what to avoid for subject, 87-91 Sky, difficulty of drawing, as
compared to earth subject, 109, no; inimitable brilliancy of, 123
Solids, illuminated, how generally seen, 32, 33 ; colour of, 34 Stone,
how to draw a, 26, 29, 32 ; colours of, ro7 Subjects, most suitable
for drawing, 87 ff. Surface, lustrous, expression of, 38 ; how
expressed by Rethel and Richter, 58 ; softness of, of trees, 103
Symmetry in Nature, 149 Texture, chief points to study in the
drawing of, 38 ; how expressed by Leech, 58 Tinting, 8r ; unity of,
with line, 82 Tintoret, 9 (note) ; drawing of clouds by, ri2 ; 118. 172
Titian, 47 ; drawing of foliage by, 102 ; ofrloudsby, 112; 146, 172
Translucency, beauty of, ri8 (note) Transparent colour drawing, 117 ;
relative merits of, as compared with body colour drawing, 1 17 ff.
Trees, boughs of, dark against the sky, 17 ; how to learn to draw,
17-T9 ; further study of, 45 ; structure of, 71-73 ; their softness of
surface, 103 ; good and bad drawing of, '59 I perfect type of
structure, 162, 163 ; four great laws of structure, r68, 160 Turner,
drawings by, 53, 54, 74, 77, 78, ioi, 146, 147, 148, rsr, 156, 172,
177, 189, 190 ; foliage, clouds, moonlight by, 55 ; his use of shadow,
85 : mystery of nature expressed by, 101 ; drawing of clouds by, 112
; his colours, 116 ; his gradation of colour, r28 Unity, organic, of
natural objects, 95 Vagueness, to be avoided by amateurs. 58
Vegetable form, radiation of, 162 ; expression of four great laws by,
40.
168 Velasquez, 134Veronese, 9 (note), 118, 125, 126, 146, 172
Water, reflections in, 104 ; necessity of careful drawing of lines of
disturbance on surface of, 104, 105 ; colour of, 107, 108 Water-
colour drawing, how to mix and lay on a flat tint, 20-23 ! a gradated
one, 23-24 ; gradated scales of colour, 24,23; materials to be used
for, 116 tt.: processes by which gradation and other characters are
to be obtained, 120 ff. White, preciousness of, 133 White objects,
how to treat, 44 ; how treated by Veronese and Titian, 44 ; by
Turner, 44 (note) Wilson, his drawing of trees, 73
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