Fire- AvS A :^^- ^c Science s^^iv-^: ^y^^i^-v- LIBRARY OF THE University of California. GIFT OF .6r'ivcs\. cL,..\jj^\)sAli;ioux, Class Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/fireratingasscieOOdeanrich Fire-Rating As a Science Fire-Rating As a Science BY A. F. DEAN "Get your Principles right, then 'tis a mere matter of Detail'^ -—NAPOLEON BONAPARTE '» I9OI PUBLISHED BY J. M. MURPHY 928 NEW YORK LIFE BUILDING CHICAGO HGr qtB^ ■P H Copyrighted 1901 BY A. F. DEAN €f)t ILti'ktsiibt Ifress R.R. DONNELLEY & SONS COMPANY CHICAGO THIS BOOK IS DEDICATED TO AMOS J. HARDING IN GRATEFUL REMEMBRANCE OP A FRIENDSHIP OF TWO-SCORE YEARS. 227491 CONTENTS PART I PRINCIPLES What Is Science? Natural Laws Defined The Relativity of Knowledge Symbols . . . - - Standards - - The Law of Rhythm Law of the Wave of Fire Destruction PAGE 3 17 19 24 29 32 37 PART II DETAIL The Evolution of Procedure in Fire-Rating • - -47 The Formula of the Rating Function ... 56 The Individual Rate ------- 60 Basis Tariffs ..-.--- 63 Classification in General - - - - - - 68 The Individual Classification List - - - - 73 Uniform and Combined Classification - - - - 78 Class Differentiation ...... 81 Rate Standard - - - - - - - - 83 What Shall the Standard Be? ... - 86 The Establishment of Cost Estimates - - - - 89 Relations Between National and State Tariffs of Cost Estimates -------- 91 The Comity of Fire Insurance ----- 94 The Law of Relation Between Net Underwriting Profit AND Class Cost Waves ----- 100 The Relations of Fire Insurance to Chance and Proba- bilities -------- 103 Metropolitan Conflagrations - - - - - 112 The Personal Equation - - - - - - ii4 National Loss Waves in the Light of the Diagram - - 118 State Loss Waves in the Light of the Diagram - - 131 Dead Reckoning ------- 189 vii vm Contents Drift and Leeway Summary The Transition NoTA Bene Conclusion PAGE 193 196 200 205 208 APPENDIX External Exposures Introductory There has been no time within the memory of the present generation when fire rates in the United States have agreed among themselves, or when they have not been in a state of chronic clash with everything else; no time when they have not been a bone of contention between fire insurance and the public, and a chip on the shoulder between underwriter and underwriter. It is a time-honored adage that no truth ever collides with another truth, and without the unreasonable assumption that everything else is at all times in the wrong, it is impossible to conceive that a thing could collide at so many points with so many other things, were there not something fundamentally untrue in its compo- sition. Fire underwriters are a busy tribe. Too deeply engrossed in the immense and constantly accumulating details of their business to generalize upon the methods of reasoning they employ, and too busy to heed the generalizations of others, they have allowed the spirit of adventure to elbow the spirit of research into the background. Instead of trying to solve a mathematical equation by earnest study, they have permitted it to be dragged by con- flicting interests into the arena of popular discussion where, as might be expected, with one hundred and fifty million dollars of annual spoils in sight, the voice of truth has been drowned out by a jargon of discordant opinion; one clamoring that fire-rating is a science, another that it is not and never can be, another, that it is of no consequence whether it is or is not, so long as it furnishes salaries, dividends, and commissions. Meanwhile, if their lives depended upon it, not one of the disputants could furnish an intelligent definition of science. To determine the real relation between fire-rating and science* is the problem of problems in fire insurance. The final solution of this problem is pregnant with fate to the future of the industry, for upon this solution depends whether it shall ultimately take its X Introductory place among the honored social forces of the future, or forever remain one of the discredited manifestations of civilization which are endured because they cannot be cured. If fire-rating can be made a science, there is but one right thing to do, and that is to make it a science at any cost. If fire insurance as a whole is an activity of two distinct parts, one, the selling of indemnity, commercialistic, the other, the measurement of fire hazard, scientific, it is a duty to separate these parts, for they have little in common. Like the masculine and feminine temperaments, yoked together in matrimony, it is their fate to go through life viewing things from different stand- points, but obligated by a life contract to co-operate. Domestic harmony between this ill-assorted pair can be established only through a plain understanding as to mutual rights and obliga- tions. Commercialism means expediency — compromise, while science makes no compromise and bows not to expediency. The boundaries between these parts may, at times, be indefinite, but if fire-rating ever becomes a science, its boundaries must be made so plain that they cannot be questioned and then preserved invio- late. In its domain as a science, there should be room for the undisturbed search for truth, as, in the outlying territory of commercialism, there should be all necessary latitude and longi- tude demanded by the universal quest for profit in all legitimate ways. To mark off and maintain the boundaries between science and commercialism in the dual nature of fire insurance, will be to quiet the present confusion of tongues and ideas and establish a permanent entente cordiale. In a burst of common sense, the venerable Bede once said, "Either then show why a thing is so, or a purpose wherefore it is so, or else cease to declare it so." Even unto the present day, this is good advice to fire underwriters, for it is idle to waste further time in asserting that schedule rating is, or is not a science, without a definite idea of what constitutes science. With this end in view, the first part of this book is devoted to a study of fundamental principles so far as these principles have any bearing upon the problem of fire-rating. There can be no intelligent study of the subject without a preliminary study of the principles on which all science is founded. Introductory xi If we cannot make fire-rating conform to these eternal verities, it will be time to admit that it is something which, by its nature, is forever doomed to remain outside the domain of science. If, on the other hand, these verities reveal that fire-rating is not, by nature, the lawless thing it has been allowed to become, and in the face of this revelation we fail to make it conform to these verities, we stand answerable at the bar of public opinion to explain whether our omission is due to incompetency, indiffer- ence, or wilful intent. This is the trilemma that confronts fire underwriters to-day in many important states where schedule- rating has been placed under the ban. This investigation is based upon the hypothesis that public intelligence of the twentieth century will not outlaw science in fire-rating, when we have found it and are prepared to prove the fact, and that, if we ever find it, we must first interrogate science itself. The interrogation pursued in the following pages, crude and imperfect as it may be, elicits answers by no means Delphic — answers which point out in clear and unmistakable language not only what to do but how to do it, and while these answers disclose many startling departures from scientific principles in our rating procedure, they are full of encouragement in showing that the transition to right methods involves no violent organic upheaval of existing system, such as it is, that it entails no hardship to the industry, or to the public. In the chapters devoted to pure science the author has simply aimed to state generalizations which constitute working hypoth- eses in modern scientific thought, and while the explanatory illustrations may be original, the principles stated are the com- mon property of science. The conclusions reached from these principles are open to all fair criticism. The spirit of science is no less earnest to detect fallacy than in its search for truth. If shown to be wrong in his conclusions, the author will be consoled by the fact that the temple of science is surrounded by the debris of discarded hypotheses which have served as scaf- folding in its erection, and he will at least indulge in the hope that his labors may not be without value in stimulating other and abler investigators to pursue the quest for truth with equal faith- fulness and better success. xii Introductory The subject of fire-rating is certainly not less arid to the author than to others who have a far greater financial interest in it. It offers neither moneyed reward nor glory; on the contrary any discussion that hews to the line of truth for truth's sake, may confidently be expected to elicit some unfriendly criticism. In spite of these facts, the subject, unattractive as it is, has for years claimed many a leisure hour which certainly for himself, and possibly for others, might have been more profitably spent in needed recreation. With this brief confession, the author dis- burdens himself of his long, self-imposed task, with a heart grateful, not that it is well done, but that it is finally done. PART I PRINCIPLES What is Science? It is the object of this investigation to determine whether the measurement of fire hazard, commonly known as fire-rating, conforms, or can be made to conform, to a standard known as science ; and with this end in view it becomes necessary at the outset to reach a correct understanding of what constitutes science. In the light of existing definitions, we are justified in regard- ing science as a body of systematized and organized knowledge. As all knowledge exists in the mind alone, science, as a part of knowledge, cannot exist outside of mind; and if we would under- stand what creates the difference between scientific knowledge and ordinary knowledge, it will be necessary to turn our atten- tion to mental processes.* It is a startling conclusion to reach at the very outset, that a word which we use every day to describe an indefinite nexus of relations as wide as the universe is the name of something that exists only in the mind; but it is a conclusion which cannot be avoided. The word "science," derived from the Latin verb scio (I know), in its primary sense means knowing, or knowledge. It has finally come to mean a certain kind of knowledge, which, for the purposes of the following investigation, it is necessary to define in order that we may learn wherein it differs from ordinary knowledge. An eminent scientist was once asked what caused the vowel qualities in speech. After many years of investigation, he proved to the world that what is known as tone-color is caused by the shape of atmospheric waves. At an early stage in his investiga- tion he adopted this inference as his working hypothesis, but he spent eight years in accumulating proof of his inference before he gave it out to the world as a scientific generalization. The *" Science is a purely mental existence, and must therefore conform to the laws of that which formed it. Science is in the mind, and not in the things, and the properties of the mind are therefore all-important."— Principles of Science, Jevons. 4 ' ''* ** *•'*• *••' Firc^ Rating as a Science mental processes which demonstrated the brief fact he announced were scientific, and the fact itself may be said to constitute a molecule in the body of organized knowledge called science. A natural inference from this fact was, that like atmospheric waves would produce like effects, and that if these waves could be re-created, the original sounds would be reproduced. Other investigators had discovered the peculiar properties of the dia- phragm in relation to sound-waves. Others had shown that electricity was a species of wave motion, and the way was thus paved for another kind of scientist, known as the inventor. One inventor soon perfected an ingenious apparatus, through which sound-waves converted into electrical waves were transported to some distant point, and reconverted into the original sound- waves, and in this way the human voice could be sent out through space for an unlimited distance. Another inventor devised an apparatus through which a vibrating diaphragm traced its move- ments on a revolving cylinder of wax, which would reimpart the wave back to the atmosphere at any time in the future. This apparatus is called the phonograph, an instrument which utilizes the original generalization in its time relations as the telephone utilizes it in its space relations. This historically true recital shows that the long inductive process which revealed a scientific truth, and the deductive processes which utilized it in its space and time relations, occurred in the mind alone. All waves have doubtless had the quality of shape ever since the morning stars sang together. The fact itself existed millions of years before man or his mind had been created, and science simply converted this fact into knowledge, through a long chain of accurate reason- ing. The telephone and phonograph, born of this knowledge, are not science, but the products of science. These facts show that science exists only in the mind, and that it is necessary to know something of the mind itself and its modes if we would learn what creates the difference between scientific and popular knowledge. As the body receives food and sorts it out into life-giving elements, so the mind receives impressions and sorts them out into elements of thought and knowledge. To feel and know are the twin functions of intelligence. Things outside of the mind What is Science? 5 cause sensations in the mind. Like things cause like sensations, and unlike things unlike sensations. The feeling mind is able to detect the likeness in these sensations and group or classify like with like, and store these groups away in an orderly array in the memory, in about the same way as in a mercantile establishment a shipment of mixed merchandise is sorted and arranged on the shelves with like merchandise. If a sensation has never been felt before, neither the feeling nor the thinking mind can do any- thing with it except to put it among the miscellaneous stored impressions in the memory until another similar sensation is felt, when the feeling mind is apt to note the resemblance and classify the new sensation with the old, as the beginning of a classified group, and as each succeeding sensation with similar character- istics is received, it is automatically classed with this group. The thinking mind occupies itself with establishing relations among these sensations; and the oftener a given sensation is received, the better the mind is able to determine the nature and extent of its relations, just as the merchant becomes more familiar with each class of goods he deals in in proportion as he becomes, through constant handling, more familiar with its relations to his trade. The feeling mind does not think, nor does the thinking mind feel — they simply co-operate with each other, each in its own way. The feeling mind classifies sensations intuitively. The thinking mind never ceases "during business hours" to ponder over these sensations, and establish their relations as grouped by the feeling mind. In fact, it is about as difficult for the thinking mind not to ponder over relations while it is awake as it is for the eyes not to see while open. As experience develops the thinking mind, it begins to establish relations among relations — to square and cube relations, as it were — and these relations, primary, secondary, and tertiary, are formulated into concepts and ideas, and relations again established among these concepts and ideas; and as these relations become more and more complex and wider in scope, they become less and less definite; in other words, more abstract, just as in a large mercantile establishment the clerk in charge of a counter may know the contents, quality, and price of the goods on every shelf and in every box in his charge, while the department head has simply a general idea of 6 Fire-Rating as a Science the stock on hand in his department, and the proprietor, knowing little or nothing of details, has a comprehensive knowledge of the business as a whole. This analogy may be considered crude, but the mind has been compared by many eminent authorities to a sorting and relation- ing machine; and by general consent it is admitted by every modern psychological authority that the brain, as an organism in its most general functional aspect, is concerned solely with classifying and establishing relations — that all thinking is rela- tioning, and that all knowledge consists of establishing relations of each thing or group of things with as many things or groups of things as our perceptive and reasoning faculties are able to establish in proportion to individual intelligence and experience. It is obvious that science, as a body of organized knowledge, is in like manner built upon conceptual relations. It is important that this fact should be carefully noted, because if fire-rating is or is to become a science, it cannot differ from other science by ignoring relations. On the contrary, the greater the number and the more exact the relations it is able to establish, the nearer it will approximate to science. It is obvious that the relations established by the reasoning faculties are relations among sensations which, themselves, are simply interpretations of changes in our consciousness called feelings, which are generated primarily by things outside of mind, and secondarily by the interaction of parts within the mind itself. But sensations themselves, as well as the mental faculties which sort and arrange them, are modified by the per- sonal equation found in each individual, and further modified in each individual by temporary bodily conditions. The same tem- perature is warm to the Esquimau and cold to the Hottentot, and it may be cold to the same person at one time and hot at another, according to the rate of circulation of the blood. Again, the temperature may be both hot and cold at the same time to the same individual. If we turn on the hot and cold water faucets in a wash-basin, holding a hand under each while the water is running, when we plunge both hands into the water in the basin it will feel cold to one hand and warm to the other. We soon become oblivious to an odor, or to the ticking or strik- What is Science? 7 ing of a clock. The sense of taste is purely relative; sweets are more sweet after acids and acids more tart after sweets. Light is blinding after darkness arid darkness more dark after light. Every sensation is itself related to bodily conditions or to mental conditions, known as moods, which themselves are logically the results of an interaction between mind and body. These facts show that both the body and the mind are varying criteria with relation to relations and the sensations on which these relations are based. " In all their various kinds and compounds, what we call relations can be to us nothing more than modes in which we are affected by bringing together sensations, or remembered sensations, or both." This universality of relationship is further shown by the structure of language, through which all ideas are exchanged. Every sentence must contain a subject and a predicate, which are related to each other. Every rational proposition must express some relation; or again quoting from the same authority: " It must assert the manner in which two things are related to each other, as resembling or differing, and to what extent, as successive or simul- taneous in time or conjoined in space, and whether invariably so." * The word "rational" indicates a reasonable ratio or relation in a statement compared with known facts. The word '*rate," which indicates the price of fire insurance, is derived from the same root, and in like manner signifies a reasonable relation. " The ascertainment of what a thing is or is not signifies the ascertain- ing of what things it is like or not like — what class it belongs to Likeness of relation is the intuition common to reasoning and classification, and it results in one or the other according as the relations thought of are partial or total Every ratiocinative act is the indirect establishment of a definite relation between two things by a process of establishing a definite relation between two definite relations All reasoning is the indirect establishment of a definite relation between two things."! Admitting that the form of mental activity known as reason- ing has to do exclusively with relations, we find that all words used to denote different kinds of reasoning indicate shades or gradations in the relative certainty of the reasoning process. The words *'guess," "surmise," "hypothesis," "inference," ♦Fallacies, A. Sedgwick. t Principles of Psychology, Herbert Spencer. 8 Fire-Rating as a Science ^'analogy," ''prognostication," "prevision," "prophecy," etc., embrace an ascending scale of certainty or definiteness with regard to undetermined relations, and the word "truth," which is the focus toward which all these words point, signifies finally established relations between or among things. Lest it be thought that too much stress has been laid upon classification and the establishment of relations which constitute the processes that create all knowledge, it is proper to say that a principle is involved which is vital to this inquiry. The extent to which we have ignored classification and relations marks not only how far fire-rating has departed from science, but how far it has departed from the methods inherent in all intelligence. So far no difference has been established between the methods which create science as distinguished from ordinary knowledge. It is admitted that "any department of inquiry where a number of like facts can be collected and systematized may be made into a science"; hence the difference does not exist in the raw material out of which both kinds of knowledge are fashioned. The fact remains, however, that knowledge in general has been immeasurably expanded by science — that civilization has been lifted out of a "bestial, unsocial, perpetually fighting and unfathomably superstitious stage of savagery," and the unaided senses enabled "to explore a universe compared with which the earth is a grain of sand, and to detect the structure of a monad, compared with which a grain of sand is an earth," by the system- atized and organized knowledge known as science. It is further admitted, that, as found in high stages of civili- zation, knowledge in general is largely the result of a slow assimi- lation of science by the people, and that a legitimate contrast between science and common knowledge unaffected by science can be instituted only through a comparison with utter savagery; for even in semi-civilizations we find traces of the effects of science in the use of crude mechanical contrivances and in a certain rude comprehension of fundamental principles. Making all due allowance, however, for the science embodied in popular knowledge as found in high civilizations, there still remains a yawning gulf between the definiteness, accuracy, and reach of science and the vague and limited knowledge of ordinary people. What is Science? 9 This difference exists, notwithstanding the fact that science itself is most ready to admit that it is saturated with error, and that its reasoning processes must still utilize guess, surmise, hypothesis, analogy, and all the lower forms of reasoning, in its unending struggle toward the higher forms of reasoning. Indeed, the strength of science might be said to lie in the fact that its indirect mission is to detect fallacy as the negative side of its real mission to discover truth. As the vast difference between scientific and ordinary knowledge does not arise from any funda- mental difference in reasoning processes, or in the raw material which generates these processes, we must seek the cause of this difference in some fundamental thesis. This thesis consists in the affirmation by science of the uniformity of nature as mani- fested in the laws of mind and matter. Science does not recog- nize that chance can exist. It contends that things outside of mind are obedient to the laws imposed upon them, and that the mind, by being obedient to the laws imposed upon it, can put itself in harmonious relations with things and their relations which exist outside of itself; that the nearer it comes into har- mony with its own laws the better it can establish the complete harmony found only in the relation known as truth.* It should be remembered, however, that this fundamental thesis of science is itself the result of an evolution which began with the first inference that nature was uniform in some specific way. The proof of this uniformity established science to that extent only, and to-day science is evolving with equal gait in proportion as uniformities are established through the discovery of natural laws. Science makes it its business to search out and prove this uniformity in nature, and to describe it for the use and behoof of humanity. In this search it utilizes all forms of reason- ing, but it uses every form as provisional, pending proof. So far as the familiar properties of things are concerned, ordinary knowledge is not only sufficiently correct for practical purposes, but in some respects is more available for immediate use than scientific knowledge. We expect a given effect from a given cause, and our anticipation is verified with sufficient * " Where chance seems to work, it is our deficient faculties which prevent us from recog- nizing the operation of law and design."— Principles of Science, Jevons. lo Fire- Rating as a Science accuracy for every-day purposes. The perceptive and reasoning faculties, through guess, surmise, inference, etc., create skill, expertness, shrewdness, acumen, and other requisites to what the world calls success. But ordinary intelligence does not methodically seek for generalizations except as it imbibes them through maxims, apothegms, epigrams, mottoes, "wise-saws," etc., which constitute a sort of rudimentary body of organized knowledge of half-truths for daily use. Ordinary reasoning is content to infer from repeated experience that bodies fall, with- out seeking to know the law of gravitation, or that water is use- ful for lavatory purposes or extinguishing fire, without seeking to know the laws of hydraulics. It might be said that ordinary intelligence has no conception that uniform laws govern these phenomena, or that such a thing as knowledge of these laws exists. On the other hand, science recognizes that these laws must exist in every manifestation of nature, and it is its acknowledged mission to search out the natural laws which underlie phenomena. At the point where scientific reasoning separates from popular reasoning, science begins carefully to observe things in their relations, and collect facts, with the end in view of grouping these facts into a broader fact which will describe more than one relation, and to extend this general fact into a final generalization which will describe all allied relations and the phenomena result- ing from them. The process which leads up to this generaliza- tion is called inductive reasoning. When a generalization has been tested and verified as true under all circumstances, it becomes an established natural law, and science begins to use this as a means of foretelling what will occur under its con- ditions. The process of reasoning from a generalization of this kind to the results which may be expected to flow from it is called deductive reasoning. It may be said, however, that many sciences have never advanced beyond inductive reasoning, and that in even the most advanced sciences a constant process of induction is maintained along with deduction; for every pro- gressive science, in gathering material for use in formulating new generalizations and broadening its established generalizations as a means of wider and more accurate research, must avail itself What is Science? ii of the entire gamut of reasoning, from the hypothesis which might be called an induction in its incipient stage to the final proof which is the end of all reasoning. The infinitude of relations existing among things has been grouped by science under two heads — relations of quality and relations of quantity; and as either of these may exist simultane- ously or in succession, they are again divisible into relations of coexistence and relations of sequence. All intelligence progresses by imperceptible degrees from automatic or unconscious reasoning into conscious reasoning, which becomes more conscious in proportion to the novelty and complexity of the relations dealt with. This is illustrated by the laborious efforts of the novice in music, compared with the per- formance of the finished artist, which requires little or no con- scious reasoning. In proportion as we learn to do things at first difficult, the necessity for conscious reasoning diminishes. Most of our bodily and mental functions, learned with more or less conscious reasoning in infancy or youth, become seemingly intuitive in the fact that the mind acts with an ease and celerity which defies analysis. This is illustrated in speech, reading, and the simpler arithmetical calculations. For the reasons stated, it is difficult to differentiate purely intuitive processes from reason- ing which is performed so rapidly as to elude consciousness. Among the seemingly intuitive, or at least unconscious, reasoning faculties of the mind is the ability to recognize identity in quality or quantity. Viewed in another way, this ability might be con- strued into an inability to detect differences in either quality or quantity when these differences are so slight as to be indistin- guishable to our perceptive faculties or feelings. Be this as it may, we are able to recognize substantial identity or sameness in quality or quantity seemingly by intuition. Qualitative reason- ing is a lower grade of reasoning than quantitative, and always precedes it in the growth of intelligence; in fact, every act of quantitative reasoning is qualitative in its initial stage, because where differences in quality become measurable, they become quantitative in proportion to their measurability. The measure- ment of quantitative differences is a function of conscious rea- soning, and is one of the chief ends of science, which first 12 Fire-Rating as a Science seeks to know what kind of phenomena will occur, then in what degree.* The story of the primitive farmer who weighed his hog by- balancing a rail across a fence, tying the hog to one end of the rail and a stone to the other, and then guessing at the weight of the stone, will serve to illustrate the advance from qualitative to quantitative reasoning. The farmer, in the absence of any other standard of comparison, selected a stone. f Experiments, let us assume, revealed that other hogs weighed more or less than the stone, but that stone and hog could be made to balance by shift- ing the fulcrum of the rail. The marks on the under side of the rail, occasioned by the friction of repeated weighings, would naturally suggest the existence of some ratio between the relative lengths of the two ends of the rail used as a scale-beam, and this would lead to the inference that by changing the fulcrum a relation would be established between the weight of the stone and the weight of any hog. Finally, the law was established that the numerical relation between the one weight and its arm was equal to the numerical relation between the other arm and its weight. Ingenuity suggested improvements. Graduated weigh- ing-scales were devised and improved, until the descendants of the original fence-rail and stone may be found in every chemist's laboratory to-day, in the delicate balances which will measure the weight of an eyelash. This oft-told tale shows how knowl- edge advances from the qualitative to the quantitative. The hog and the stone had the quality of weight in common, and the problem was to find the relative quantity of weight in each. The notches in the rail revealed the fact that weight was measurable in degrees of quantity. Successive improvements in weighing devices have reduced quantitative measurement of weight into constantly diminishing differences, until in the physicist's scales we see an instrument which will detect extremely minute differ- ences; while the astronomer with his torsion balance is able to weigh the moon or the planet Jupiter. From the farmer's original experiment in ponderation, quantitative measurement of the force ♦"The accurate ascertainment of quantity as well as quality marks the difference between the lower and higher stages of positive knowledge.'' — Principles of Psychology, Herbert Spencer. fThe word "stone " is still used in England for a varying weight, which, according to the thing weighed, may stand for five, eight, fourteen, sixteen, or thirty-two pounds. What is Science? 13 of gravitation, otherwise known as weight, has slowly evolved; but to the farmer's experiment, or some similar reasoning pro- cess, is due the discovery of the fact that gravitation is measur- able, for previous to this experiment, humanity had simply been conscious of the fact that one thing pulled downward harder than another, without the means of knowing how much harder. To-day we have no science of smell, taste, or touch. We know that a thing smells rank or fragrant, but not how much so. We know that a given substance tastes sweet or sour, or that it is hard or soft, smooth or rough, but we have no scale-beam by which we can change these qualities into measurable quantities. " Human knowledge becomes scientific in direct ratio with the measur- ability found in phenomena. Space is measurable, hence the science of geometry. Force and space are measurable, hence statics. Time, force, and space are measurable, hence dynamics. The scale measurement of heat through the thermometer gave birth to thermostatics; and it is the reduction of phenomena to scale measurement that gives to any branch of knowledge its degree of scientific accuracy."* The growth of quantitative reasoning is shown by the inven- tion of money as an instrumentality to measure relations in the abstract quality known as value. As the farmer's experiment was a crude attempt to estimate the weight relations between a specific hog and stone, so it was long possible for men's minds, through a process known as barter, to agree upon the relative value between an ox and a goat, or a sheep and a chicken; but a standard that possessed the same value to all men was needed for measuring the relative value of all things, just as standards were needed to establish relations in the qualities known as weight, heat, time, space, etc., which are now established quantitatively through weighing- scales, thermometer, clock, and yard-stick. This standard, for which at various times and places men have utilized sheep, kine, tobacco, tea, peltry, poultry, and many other things, finally crystallized into money, which has become the world's acknowl- edged instrumentality for measuring relations in value. But men have not yet ceased to quarrel as to whether or not the standard itself ought to possess the abstract quality of value which it ♦Genesis of Science, Herbert Spencer. 14 Fire-Rating as a Science measures. For centuries past, waves of theory as to the true relations of money to value have swept the civilized world, which goes to show how difficult it is for scientific reasoning to con- vince popular reasoning of the true relations existing among things when prejudices have been once aroused. Common knowledge is to some extent quantitative within certain indefinite limits. On the other hand, the most exact quantitative measurements of science do not reach the absolute truth, but only a closer approximation to it. Common knowl- edge knows that to-day is warmer than yesterday — the ther- mometer tells us how many degrees warmer. Common knowledge knows that the days are longer in June than in December — the chronometer tells us the difference in hours, minutes, and sec- onds. Common knowledge knows that one thing is heavier than another — the scales tell us how many pounds and ounces. Still, with the most delicately adjusted thermometers, chronometers, and scales, we are able to establish only an approximation to the actual difference in heat, time, and weight. In the popular conception, a second stands for the ultimate unit of time, but a second is about as far removed from mstan- taneousness as it is from eternity. The extreme violet ray in the spectroscope is caused by 763,000,000,000,000 vibrations in a second. There are 31,536,000 seconds in a year; hence the time consumed by one of the vibrations which produce the familiar color known as violet is to a second as a second is to 24,200,000 years. Lest these figures might be supposed to be but a mere surmise, it is proper to state the curious fact, admitted by all scientists, that the undulations of light, although incon- ceivably rapid and small, admit of more accurate measurement than waves of any other kind. " The most exact sciences have slowly developed an ability to determine quantities not directly measurable or determinable to the unaided senses, by a slow process of growth extending through thousands of years." * While science never ceases to utilize inductive reasoning in its search for more exact and comprehensive generalizations, deductive reasoning and the measurement of quantitative differ- *Genesis of Science, Herbert Spencer. What is Science? 15 ences with increasing nicety constitute the goal toward which every science is striving. All sciences in their beginnings are qualitative, and the first generalization of every science must be empirical. No science, however perfect, may be said to be entirely free from empirical assumptions or unexplained phenomena. Many sciences have had an accidental beginning. A phenomenon which would have been meaningless to ordinary intelligence has been apprehended by scientific intelligence and yoked into the service of humanity. Neither can any science be said to be complete, for every science has occasion, from time to time, to discard or enlarge the generalizations it has outgrown. There is no patent law to protect the proprietary rights of science in the natural laws it discovers. Every scientific generali- zation becomes the common property of mankind as a free gift, and every science is constantly broadening and perfecting its own generalizations through knowledge obtained from the generalizations of other sciences. In this way ''each science has become in turn an art to other sciences." This has been the attitude of science toward humanity, but the attitude of humanity toward science has been an attitude of studied contempt or sullen distrust. When a scientific generali- zation has been crystallized into concrete shape as an invention which can be put to daily use, ordinary intelligence is quick to see the practical benefits, but its attitude toward the generali- zation itself is that of a shying horse toward a newspaper that happens to lie in its road. With ordinary intelligence, '*use is one thing and understanding another." Built up solely of per- sonal experiences, it comprehends abstract truths with such difficulty that it refuses even to make an effort to grasp anything approaching a broad and far-reaching law of nature. It can only understand an abstract truth when reduced to concrete form by illustration. It goes on doing things the way it was taught, and questions the morality of doing otherwise. It cannot imagine better methods, however obvious, than its own. It is loose in reasoning and inexact in statement. Its modesty is shocked in the presence of naked truth, and cold facts give it the shivers. It is quick to jump at conclusions which accord with its precon- 1 6 Fire-Rating as a Science ceived notions, and it is so positive in its belief that it might be said to be a part of its religion not to permit itself to be con- vinced against its will. It cannot deliberate or suspend judg- ment, or balance evidence, or in the least understand how an hypothesis can be framed as a basis for reasoning, pending proof or disproof. It is true that this represents the popular intelli- gence found in the mob, but it is partially true of the higher order of intelligence found among cultivated people. Every individual character has its partial enlightenment, its hilltops of intelligence illumined by the light of knowledge, and its valleys which lie in the eternal shades of ignorance. Our so-called culture is a thing of lights and shades. Most of us are educated into an understanding of the uniformity of natural law in some things, but cannot bring ourselves to believe that this uniformity pervades every manifestation of nature if we will but seek it. Epictetus stated an eternal verity when he said, "Even when full- grown, we appear as children, for a child in music is he who hath not learned music, and in letters one who hath not learned letters, and in life one undisciplined." In fine, it may be stated that science represents a school of thought based upon an abiding faith in the uniformity of nature and nature's laws, a school which has freely yielded up its treas- ures to humanity ; but unfortunately humanity has inherited from its forebears a rooted prejudice against natural laws, which have an irreverent way of toppling over the sacred edifice of popular opinion from time to time; and it is not yet quite safe to one's business reputation, even in the most enlightened business circles, to suggest the utilization of a natural law for business purposes. Natural Laws Defined The difference between scientific and popular knowledge is so largely the result of a systematic search for and utilization of natural laws, that it is important to understand the distinction between these laws and the rules of conduct promulgated through statutes, ordinances, codes, and creeds. Natural laws, so-called, are simply formulae stating an invariable order of coexistence or sequence among phenomena.* These formulae differ from human laws in being descriptive, and not prescriptive. There have been many definitions of natural law, but the following, from the Grammar of Science, by Karl Pearson, professor of applied mathematics and mechan- ics, University College, London, is perhaps the best: "Other laws are valid only for a special community at a special time. The scientific law is valid for all normal human beings, and is unchangeable so long as their perceptive faculties remain at the same stage of develop- ment The discovery of some single statement, some brief formula, from which the whole group of facts is seen to flow, is the work, not of a mere cataloguer, but a man endowed with a creative imagination. The single statement, the brief formula, the few words of which replace in our minds the wide range of relationships between isolated phenomena, is what we term scientific law. Such a law, relieving our memory from the burden of individual sequences, enables us, with the minimum of intellectual fatigue, to grasp a vast complexity of natural or social phenomena When from a sufftcient, if partial, classification of facts a simple principle has been discovered which describes the relationship and sequences of any group, then this principle or law itself generally leads to the discovery of a still wider range of hitherto unregarded phenomena in the same or associated fields "The progress of science lies in the continual discovery of more and more comprehensive formulae, by aid of which we can classify the relation- ships and sequences of more and more extensive groups of phenomena. The earlier formulae are not necessarily wrong. They are what the mathematician would term * first approximations,* in which we neglect certain small quantities. Then we need a widening, not a rejection, of ♦In popular language, the word " phenomenon " signifies something supernatural. In science, the word is used to indicate tne effect produced upon our consciousness by any external agency. 1 8 Fire-Rating as a Science natural law, and the earlier formulae are merely replaced by others, in which briefer language describes more facts." The law of gravitation formulated by Sir Isaac Newton states that, "Any two masses in the universe attract each other with a force which varies according to the inverse square of the dis- tance. " For over two hundred years this law has stood without change as the limit of comprehensive description in the fewest possible words. Speaking of it, Paul du Bois Reymond says: "Here is the limit to our possible knowledge." Yet this law is the result of over two thousand years of evolution, arising, per- haps, in the myth that the sun-god hitched up his steeds every morning and drove across the firmament. Brief as the law of gravitation is, it is surpassed in brevity by other natural laws of equal import. The law of conservation tells us in a few words that there is nothing lost in the universe; that all is change, and not destruction. Nature, like a thrifty housewife, saves every scrap of matter and energy for future use. The perishability of matter was long a favorite theme with moralists, and in theory, at least, it is the causa causorum in fire insurance; but if it were possible to inclose a burning building in an air-tight crucible until consumed, it would be found that the ashes and gases would weigh the same as the original build- ing and contents; in other words, that matter had been changed, but not destroyed. The real destruction by the burning of a building is a destruction of value^ which is a property of matter, hence it is value alone that we insure or can insure. The law of conservation was not formulated until long after fire insurance became a recognized industry. Knowledge of this law in the beginning might have exercised an important influence on the future of the industry, by showing underwriters as well as their patrons, to say nothing of judges, juries, and law-makers, what it is that fire insurance really insures. Perhaps more care might have been taken in wording policies to show that they insured the values existing in things, and not things themselves. How- ever, as fire insurance has never knowingly availed itself of a single scientific generalization, there is no reason to believe that the law of conservation would have received more attention than other natural laws with which its daily functions are even more closely implicated. The Relativity of Knowledge Of the generalizations established by science, that which states that all knowledge is relative has the most immediate and important bearing upon the question before us; for if true, it follows that the problem of fire-rating has to do, not with things themselves, but with their relations. This generalization is so startling in its simplicity of statement, and so far-reaching in its significance, as to be almost appalling to the average mind when first brought to realize its full import. Yet, as stated by Sir William Hamilton, "It is perhaps the truth of all others most harmoniously re-echoed by every philosopher of every school." At the outset, we encounter the unavoidable inference that if all knowledge is relative, each individual mind as a whole must exist as a relation to everything outside of it, and in its analysis as a labyrinth of interrelations among its parts; in other words, the mind might be called an inner universe of related concepts created by an outer universe of related manifestations. "We infer that in all consciousness there must be a subject, or person who is conscious, and an object, or thing of which he is conscious. There can be no consciousness without the union of these two faculties; and in this fact we are met by a relation, for each exists only as it is related to the other The subject is a subject only in so far as it is conscious of an object. The object is an object only so far as it is apprehended by a sub- ject, and the destruction of either is the destruction of consciousness itself." * So far as this life, at least, is concerned, we know that the complex organism known as the mind cannot exist without con- sciousness, for consciousness is to the mind what the vital prin- ciple is to matter. The sensations we experience are primary, undecomposable states of consciousness, and to realize the rela- tivity of knowledge it is only necessary to regard the mind, structurally, as a conscious center in our anatomy where sensa- tions are felt. This conscious spot, or sensorium, is confined * First Principles, Herbert Spencer. 19 20 Fire-Rating as a Science within a narrow dungeon known as the skull, where it receives news from outside through innumerable thread-like fibers known as sensory nerves, which spread out to the surface of the body in five groups. These nerves convey sensations to different spots in the sensorium, through molecular vibrations caused by things of which we become conscious only through these nerve vibra- tions, which create the sensations recognized by us as sight, hearing, touch, taste, and smell. It belongs to psychology to describe how the reasoning faculties sort, classify, and arrange the sensations delivered to the sensorium, and reason out their relations to each other, and store away these reasoned-out rela- tions as mental concepts, and how this stock of stored concepts, with the relations established among them, constitute each indi- vidual intellect. Summed up, the mind of man might be regarded as a lone prisoner in a camera obscura^ isolated from the outer world by impenetrable walls, and dependent for all it knows of things themselves upon the vibrations conveyed to it through thread- like fibers. When these fibers are healthy and well trained, they give us pretty accurate notions of the relations of things^ but of things themselves^ nothing. "Life itself is definable as the con- tinuous adjustment of internal relations to external relations."* This is discouraging to the man who is constitutionally unable to bring himself to believe that he is not always "in the right," though it may be said for his consolation that the rela- tions established by correct reasoning processes in normal minds furnish us with all the information we need in actual life, pro- vided we exercise a reasonable degree of caution in judging of the news received through innumerable and infinitesimal vibra- tions in our wholly unintelligent and often unreliable nerve messengers. " If every act of knowledge is the formation of a relation in conscious- ness parallel to a relation in environment, then the relativity of knowledge is self-evident. Thinking being relationing, no thought can ever express more than relations. And here let us not omit to mark how that to which our intelligence is confined is that with which alone our intelligence is con- cerned. The knowledge within our reach is the only knowledge that could be of service to us. This maintenance of a correspondence between the ♦First Principles, Herbert Spencer. The Relativity of Knowledge 21 internal action and external action, which both constitutes our life at each moment and is the means whereby life is continued through subsequent moments, merely requires that the agencies acting upon us shall be known in their coexistences and sequences, and not that they shall be known in themselves Deep down, then, in the very nature of life, the relativity of knowledge is discernible. The analyses of vital action in general lead not only to the conclusion that things in themselves cannot be known to us, but also to the conclusion that knowledge of them, were it possible, would be useless." * Had the task been imposed upon a finite intelligence to con- struct a being who should be in sentient communication with all things, it is inconceivable how this intelligence could have accomplished its task in any way other than by starting every- thing in the universe in vibration, and then constructing a sen- sorium responsive to every vibration. It is this "one touch of nature" that "makes the whole world kin," and enables us all, Itke Socrates, to say, "I am a citizen of the universe." It would be wrong to infer from the doctrine of the relativity of knowledge that science does not for all practical purposes accept things as real. Indeed, it might be said that modern science owes its very existence to its final acceptance in good faith of the admission that all knowledge is relative. When the long empirical inquiry of speculative philosophy into the nature of noumena, or things themselves, ended in the frank admission that the mind, by its very constitution, could know things only in their manifestations or phenomena, science began to turn its attention to a practical study of the relations among appearances or manifestations of things, and then, for the first time, began to realize that there need be no limits to its aspirations in the investigation of phenomena. It is a maxim of jurisprudence that circumstantial evidence may be the strongest evidence. It might be said that the scien- tist depends entirely upon circumstantial evidence regarding actualities, and through this evidence science is now pouring a flood of light into the dark recesses of the unknown, and rev^eal- ing to humanity for the first time in the world's history truths that are incontrovertible. If we compare the circumstantial evidence on which so-called ♦First Principles, Herbert Spencer. 22 Fire-Rating as a Science truths are established in our courts of law with the evidence on which scientific truths are founded, we find an overwhelming preponderance in favor of the latter. The Scriptures declare that *'all testimony shall be established out of the mouths of two witnesses," but science has five witnesses which corroborate each other in arithmetical ratio. When two of these senses confirm each other, they may be said to constitute the two scriptural witnesses; but memory multiplies these witnesses, for each repetition in experience of a given sense-impression becomes an additional witness. This makes an endless array of corrobo- rating testimony, for the mind groups the relations among these sense-impressions into innumerable concepts. So long as con- cepts clash, there is doubt; when they agree, they establish an unbreakable chain of circumstantial evidence, so long as the laws of mind have not been violated. Add to this array of concepts the sense-impressions of other intelligences formulated into con- cepts, and we have a resistless array of testimony concerning relations which constitutes scientific proof. An ordinary mind is prone to accept the evidence of a single sense on a single occasion ; the scientist, on the contrary, is of all men least given to constructing hard-and-fast rules based upon insufficient evi- dence. While his generalizations are admittedly based upon circumstantial evidence, it is his business to challenge every bit of evidence, until the chain of demonstration is complete, before he admits an established law of nature, and even then he recog- nizes it simply as an hypothesis which has not been disproved. On the other hand, it is wrong to regard a scientist in the light of an ordinary skeptic, for science has its credo as well as the- ology. The faith of the scientist does not end with a mere declaration of belief, for he is the reverent disciple of truth for truth's sake. The foundation of his creed is an abiding faith in certain a priori truths, which are not the result of reasoning, but of intuition. As stated by Aristotle, "The beginning of demonstration can- not be demonstration, nor the beginning of science science; and when there is no other truth, intuition must be the beginning of science." The scientist recognizes as one of the fundamental laws of The Relativity of Knowledge 23 mind that a preliminary hypothesis is as necessary for the mind to reason upon as food is necessary before the stomach can digest. He accepts certain assumptions as a priori which, though in themselves incapable of proof, are the basis of all science, and constitute the things about which science reasons. He believes in a rationally constructed universe of which he as a part is a rational being. He believes in his own existence, and that he is a thinking being, because he can separate himself from his sen- sations and hold them before himself for contemplation. He believes in the existence and validity of the laws of thought as unchangeable and universal, and that to think according to these laws is to think correctly. He assumes that, within the limits of his reasoning faculties, the universe is capable of being under- stood by the application of these laws, as otherwise it would be useless to try to understand anything. He believes that all objects he can reason about are related together as substances and attributes. He believes that every beginning or change of existence has a cause, and that no effect can be thought of apart from its cause. He believes in a universe created with a design, that nature is uniform and consistent with itself, and that the object of science is to study and know that design as manifested to his reasoning faculties. He believes that error cannot exist in things themselves, but only exists in the mind which creates it through a wrong interpretation of the manifestations of actualities. Symbols We have spoken of the mind as a prisoner under sentence of solitary confinement for life, pondering over the reports it receives through its news-bearers, sorting and storing these reports as classified data for the establishment of relations and inferences; and thrice blessed is it when these inferences reveal to it a natural law from which it can forecast with certainty a wide range of relations. But the mind's nerve-messengers, though more or less unreliable, are amazingly active and acute, and every sane mind soon becomes cognizant of other solitary prisoners, like itself, confined in other dungeons of the great prison-house of life, and it begins to try to establish communi- cation with them. This communication is established by means of signs or symbols, which, like the pitiful expedient of the little girl's rag baby, are made to do duty for the real thing; and thus are we "such stuff as dreams are made of," for our symbols are largely words which, unfortunately, are not always as definite as the rag baby. But the exchange of intelligence by means of symbols is about the most continuous and important function of life, and the necessity for this exchange follows us from the cradle to the grave. The simplest exchange of intelligence illustrates the relativity of knowledge, and our utter dependence upon symbols as the only means of intercourse between mind and mind. Let us suppose that the importing house A, in Chicago, tele- graphs its Paris correspondent, B, to cancel a written order en route. A reaches for his desk-telephone, changes the switch- board, and "rings up" the stenographer. The stenographer sees from the switch-board that A is calling her, takes her note-book and records the dispatch in short-hand, then transcribes her notes on a typewriting machine and rings for a messenger, who delivers the message at the telegraph office, where it is ticked off by dots and dashes to New York, then rewritten by the receiving 24 Symbols 25 operator and sent to the cable operator, who repeats the message to Paris by the needle-code of the cable company. At Paris the message is written on a delivery-blank and sent to B, who, on receipt of the dispatch, pulls the cord of his book-keeper's call- bell and tells him in French to cancel A's order. The book- keeper crosses off from his books the entry, and tells the porter in German not to send the goods. An analysis of this every-day transmission of intelligence shows that it is accomplished through a series of symbols converted into vibrations, and of vibrations converted into symbols. A consults his switch-board to find the symbol for his stenog- rapher, and advises her that she is wanted through vibrations imparted by a push-button, which starts an electrical vibration in a wire which sets the stenographer's bell in vibration. This in turn imparts a vibration to the atmosphere which sets the ear- drum of the stenographer in vibration, which starts a vibration in the nerve-messengers, which finally communicate to her senso- rium the news that her bell is ringing. The symbol on the stenographer's switch-board shows her that she is wanted by A, who dictates his message into his desk-telephone through a pro- cess beginning with his rhythmic breathing, which sets his vocal cords in vibration ; this starts the air in vibration, which sets the diaphragm in the telephone in vibration, which in turn sets up an electric vibration in the wire. This starts the diaphragm at the stenographer's end of the telephone into vibration, which imparts the original sound-waves back to the atmosphere, and these start the ear-drum of the stenographer in vibration, which sets her sensory nerves into the complicated vibration necessary to trans- late to her sensorium the original words. If we follow the message "from start to finish," we shall find a long series of waves and symbols through which the intelligence is finally delivered that cancels the order. The vibrations beginning in the breathing apparatus of A, in Chicago, and ending in the sensorium of the German porter at Paris, pass through flesh, blood, nerve and brain tissue, ether, atmosphere, and solid metal as media. The symbols beginning at A's switch-board, and continued through his spoken word symbols, are transmuted into short-hand symbols, then into symbols printed on the type- 26 Fire-Rating as a Science writing machine, then into the dot-and-dash symbols of the telegraph company, then into needle-code symbols, then into written-word symbols in English, then into spoken-word symbols in French, then into a sign symbol made by the book-keeper to show that the order is canceled, and finally into German word symbols spoken to the porter. We have thus a long and complex chain of causation set in play through a variety of symbols borne upon a variety of waves through a variety of media half-way around the world, in order to communicate a simple mental con- cept from one mind to another. This suppositive case not only illustrates the universal use of symbols as a means of exchanging thought, but shows that two minds cannot communicate without an exchange of symbols of some kind. Whether by gesture, facial expression, pictures, signs, words (spoken, written, or printed), or mere sounds, sym- bols constitute the sole means through which thought is trans- ferred from mind to mind. Without these symbols two minds would be as unresponsive to each other as trees, running brooks, or stones; for it is only the poet who finds "tongues in trees," *'books in running brooks," or "sermons in stones.' Every symbol represents a mental concept, and mental con- cepts are created by the relations established by the reasoning faculties from perceptions which are caused by the molecular quiverings in microscopic fibers called nerves.* Hence the knowl- edge of every mind consists of the relations it has been able to establish and label with the symbols by which they may be recog- nized and utilized in the exchange of thought with other minds. It is a significant fact in proof of the relativity of knowledge, that the only sciences which are universally denominated exact, speak through a language composed entirely of arbitrary sym- bols. Mathematics and logic are classed by every authority among the exact sciences, and the reason they are exact lies in the fact that they do not profess to deal with things, but con- fine themselves exclusively to the relations among things. The reasoning process of every mathematical calculation is conducted *" The average thickness of nerve-fiber, as stated by Alexander Bain, is about one six- thousandth of an inch, and at the extremities of the nerves the axis or core divested of its envelope does not exceed one hundred-thousandth of an inch in thickness."— Principles of Science, Jevons. Symbols 27 through symbols, consisting of figures, letters, arbitrary signs, and diagrams, while in logic the syllogism which forms its corner- stone as a science consists in a! mathematical formula of thought- relations. Two thousand years ago Epictetus, in answer to one who offered to resolve him a syllogism, said, "Slave, your syllo- gism is the measuring-rod — it is not the thing measured." Words and symbols may be as widespread as a language, or confined to a small area, as a town, village, or even a single home, for every family has its own words, signs, and gestures which are unintelligible to others, and in like manner every com- mercial house has similar symbols which are understood by its employees alone. Every calling is compelled to manufacture its own word symbols to express mental concepts in every-day use; and as Balzac truly says, "Every trade has its a^-got.'' The value of a thought symbol consists in its capacity to express the most complete mental concept in the most vivid, comprehensive, and definite manner. Before alphabets were invented, all written language consisted of pictures or diagrams. An interesting phase in the evolution of language is to be seen at present in the tendency to revert to ideographic language as a means of expressing thought which cannot be conveyed by words. A long chain of vivid and complicated thought is frequently conveyed by a series of pictures. The renaissance of ideographic language is shown by the marked increase in illustrations found in books, magazines, and daily journals. There is also evidence of an increasing use of the diagram as a means of showing coex- istent and sequential relations which cannot with economy of thought be conveyed by words or figures. As stated by an emi- nent mathematician, "A curve of no great complexity may give the whole history of the variations of value in a troublesome mathematical expression." The daily papers report the markets, foot-ball, base-ball, yachting, and golfing contests, battles, horse- races, and weather records by graphic diagrams, instead of by columns of printed description, as was the custom a few years ago. There is also an increased us of the diagram in socio- logical and economic investigation. The daily papers frequently contain pages of news almost entirely symbolic, outside of regu- lar printed matter, and the symbolic matter is in every case not 28 Fire-Rating as a Science only more brief, comprehensive, and intelligible, but conveys thought that cannot be economically conveyed by printed words. We find the same tendency to an increased use of ideographic symbols in commerce. Comparative diagrams are now recog- nized as a legitimate auxiliary in every branch of commercial activity. As the function of all reasoning is to establish relations of coexistence and sequence, and as a true understanding of these relations constitutes the whole problem of fire-rating, the dia- gram will be utilized in subsequent chapters as a means of showing relations which cannot be shown by ordinary statistics. Standards The Constitution of the United States confers upon Congress the power to coin and regulate the value of money and fix stand- ards of weights and measures. As the coining and regulation of money is to fix standards of value, it follows that the Constitu- tion practically confers upon Congress the authority to fix stand- ards of values, weights, and measures. The power to fix these standards has been inherent in all governments from a time long before the "shekel of the sanctuary" mentioned in the Bible to the present. In Greece and Rome similar standards were main- tained, and Saxon standards were kept at Winchester before the year 950 A. D. At the present time these standards are fixed by all civilized nations, and preserved with a care equaled only by the care of the national treasury. The advantages of world standards are so obvious that during recent years an international congress has established the metric system, and the standards adopted by this congress are now preserved at the International Metric Bureau at Paris, copies being furnished to seventeen nations which participated in the establishment of these stand- ards and contribute to the expense of their maintenance. Again, all civilized governments have agreed in girdling the globe with imaginary lines of latitude and longitude for the com- mon use of humanity, and these lines are simply standards. As before stated, the aim of every science is to establish exact measurement; but when we come to analyze measurement we find it to consist of a comparison of one thing with another, and this comparison is useless unless we know not only what the thing compared with is, quantitatively, but that it is fixed and unchanging — it must be a constant standard. As stated by a well-known authority: " The real beginning of exact knowledge or science lies in measuring, and a faithful observer of nature is always occupied in measurement All measurements are carried out by the use of a standard To meas- 29 30 Fire-Rating as a Science ure any quantity we need another quantity of the same kind There must be something which does not change with regard to its surroundings, or measurements are impossible." * All measurement might be analyzed into measurements of matter, time, space, energy, and motion, and the measurement of phenomena in one of these may be translated to our senses through the phenomena of another. Gravitation, which is a form of energy, and invisible, is translated to the senses through a scale-beam which is visible. Heat and time, which are invisible, are measured by the scale of the thermometer, or by the dial of the clock. In every case measurement is established from a fixed standard that is purely arbitrary. The zero point of the ther- mometer is a standard arbitrarily selected within the boundaries of heat; and so in measuring phenomena of all kinds we must select some point, line, position, or attribute as our standard. These facts constitute another illustration of the relativity of all knowledge, and additional proof that in the problem of fire- rating we can only establish relations, the problem being to make these relations consistent by reference to universally recognized and unchanging standards. The universal necessity for established standards in all meas- urement, which is recognized by every civilized government, confronts us in the measurement of fire destruction. Is it a measurement of time, space, energy, or motion, one or all? Is it a thing to be measured? If so, before we can measure, we must determine what it is, and how the measurement is to be accomplished, and establish standards of comparison that will not change. We know that fire is energy manifesting itself through an intense form of molecular motion in matter, known as combus- tion, and that all motion must be measured with relation to space and time. Hence we have the complicated problem of measuring the destruction of matter by energy manifested as a form of motion through time and space^ and the additional problem of translating our measurement into the language of value^ which itself is meas- ured by a standard known as money. This complex manifesta- tion has evolved a series of ratios in fire insurance which are in ♦Physical Measurement, A. Earle. Standards 3 1 a state of incessant change; and change is motion, hence we cannot avoid the conclusion that the thing we have to measure is motion of some kind. If measured by the methods of science, we must determine the kind of motion, and establish the unchang- ing standards without which it cannot be measured — this is a sine qua non. Note— The universal necessity for standards suggests an interesting qnestion regard- ing tlie present attitude of many statts in their proscription of fire-rating. In a recent con- vention of the American National Association of Chemists, a memorial was formulated, urging Congress to establish authorized national standards for chemical measurements. If fire destruction is a thing to be measured, it would be difficult to draw a line between the rights of chemists and fire underwriters in demanding fixed standards necessary for their measurements. If chemists have a right to demand these standards, fire underwriters seem to have the same logical right to demand standards of underwriting cost in the shape of an authorized national tariff of standard cost relations. The Law of Rhythm The mewling infant must be sung or rocked to sleep. In its wakeful hours it is pacified by dandling, patting, or "trotting." When it begins to "take notice," its first instinct is to pound something. The most acceptable present to a boy is a drum. When he reaches the amatory age, he begins to cultivate poetry, music, and the dance. When man has journeyed over the "ups and downs" of life into the valley of old age, he chews the cud of reflection in his rocking-chair in the chimney-corner. All these things show the human instinct for rhythmic motion. There is not a tribe so barbarous that it does not find recreation in sym- bolic chants, or dances to the pounding of a hollow log or tom-tom. This instinct for rhythm has its roots in a fundamental law of nature which of all others best interprets the poetry of motion in the drama of life. Other natural laws may place us in harmoni- ous relations with space. This puts us in touch with time, from cradle-song to funeral-dirge. As has been shown, all intelligence consists in establishing relations. These must be relations either of coexistence or sequence ; in other words, relations which exist at the same time, or relations which exist in succession. It is impossible for a finite mind to conceive of the first great Cause creating a motion- less universe, a mere picture of still life, for its eternal contem- plation. It is only possible to imagine cosmos as imbued with life, motion, ceaseless change. Had it been the task of a finite mind to start this vast complexity of coexistent relations, suns, planets, moons, comets, asteroids, meteors, nebulae, star-dust, molecules, and atoms in simultaneous motion, and at the same time quicken all animate creation into ceaseless action and reaction, there would, without doubt, have been a speedy "wreck of matter and crush of worlds." Divine wisdom accomplished this task through the laws of 32 The Law of Rhythm ^^ motion, which have but recently crystallized into the generaliza- tion known as the undulatory theory, or law of rhythm. Like the law of gravitation, this generalization is the result of a long period of evolution from more primitive formulae. The discovery by Helmholtz of a third property in tone-waves was the missing link essential to complete the chain of reasoning which evolved the modern law of rhythm. Previous to Helm- holtz's investigations, any one could see that all waves upon water surfaces were more or less irregular, that every wave bore upon its bosom other and smaller waves. Helmholtz discovered the fact that atmospheric waves were corrugated in like manner by the presence of lesser waves, and that these irregularities created the difference between sounds of the same pitch, which in music is known as tone-color. This fact rounded out the final generalization that all waves possess the three qualities of width or amplitude of vibration, rapidity of vibration, and contour. It was found that there is no such thing as an absolutely pure tone unmixed with the presence of other tones, hence no waves of exactly uniform bilateral contour; just as, in mathematics, there is no such thing as an absolute point, straight line, or circle. Action and reaction never exactly repeat themselves; hence no two wave shapes can be mathematically identical. Aside from the presence of minor waves which produce what Helmholtz termed *' upper tones," he found other tones resulting from both the sum of and the difference between two tone-waves, which he designated as summation and differential tones. As stated by Jevons, '*The same phenomena which we find in some kinds of waves may be expected to occur mutatis mutantis in other kinds," whatever the media through which they are transmitted ; though scientists do not seem to have availed them- selves of this suggestive fact as a clew to the mysterious mani- festations of wave-motion, which possibly cause some of the phenomena that furnish the stock in trade of telepathy, the- osophy, hypnotism, spiritualism, voodooism, etc. In a tentative way, science is beginning to investigate these phenomena. The hypothesis of aetheric vibrations proved the kinship among the phenomena of light, heat, electricity, and magnetism, and possibly at some time in the future, aetheric wave 34 Fire-Rating as a Science contours and resultants may furnish a valid hypothesis regarding some of the faint manifestations of vibratory force, which are at present left to the undisputed possession of charlatanism. The final law of rhythm is the joint offspring of the generali- zation that all matter is in ceaseless motion, and of the so-called first law of motion formulated by Galileo more than four hundred years ago. This law stated that a moving body must forever continue in a straight line, with uniform velocity. The process of reasoning which finally developed this simple, and to ordinary intelligence incredible, generalization into the law of rhythm is so clearly stated by Professor Fiske, in his Outlines of Cosmic Philosophy, that I take the liberty of quoting at some length from that work. "As a single moving body in an otherwise empty universe would move forward forever with unvarying velocity in an unvarying direction, so, on the other hand, two or more bodies moving in independent directions and exerting attractive forces upon each other must forever move in directions which rhythmically vary, and with velocities which are rhythmically aug- mented and diminished. Thus the rhythm of motion is a corollary from the persistence of force. Our alternatives are rhythm or invariable velocity in one invariable direction. The latter alternative being excluded by the fact that in the known universe innumerable bodies coexist, it follows that we must adopt the former, and admit that all motion is rhythmical. .... Thus in all cases, whether molar or molecular, the rhythm of motion is necessitated by the fact that in a multiform universe no portion of matter can move uninfluenced by some other portion Forever throughout the length and breadth of cosmos we find periodicity, rise and fall, recur- rence of maxima and minima. This is the law of all motion whatever, whether exemplified by a star rushing through space, or by the leaf which quivers in the breeze, by the stream of blood which courses through the arteries, or by the atom of oxygen that oscillates in harmony with its com- panion atoms of hydrogen in the raindrop. " The forces which are carrying a given portion of matter in a given direction become gradually altered in their distribution and . in their amounts, until the direction of the motion is practically reversed, and whether this given portion of matter be a planet or a molecule, the dynamic principle remains the same. Thus, what we may call the elementary motion going on throughout the world of phenomena, the elementary motion by which the various combinations of which all 'perceptible motions are made up, are all rhythmical or oscillatory Light, heat, electricity, and magnetism are the product of a perpetual trembling or swaying to and fro of the invisible atoms of which visible bodies are composed. .... The Law of Rhythm 35 According to the latest chemical speculations in philosophy, it is because of the synchronous or rhythmical harmony of the oscillatory movements described by these atoms that elementary substances are enabled to com- bine in myriad-fold ways, thus making up the wondrous variety of forms, organic and inorganic, which the earth's surface presents for our con- templation Since the ultimate particles of which science regards the universe as composed are thus perpetually swaying to and fro, in accordance with the law of motion that admits of no exception, we may expect to find that the various aggregations of these particles which constitute perceptible bodies will exhibit a like rhythm, whether comparatively simple or end- lessly compounded in their motions. The law which governs the action of the parts must govern also the action of the whole, no matter how intricately the whole may be compounded. Whether it be in the case of organic or inorganic bodies, of complex or simple aggregates, we must expect to come upon systems of rhythmical movement which will be comparatively simple or endlessly complex, according to the structural complication of the bodies in question." The law of rhythm, born of Galileo's amazingly simple first law of motion, manifests itself throughout the twin universe of mind and matter.* Every functional act of life is rhythmic; we see, hear, taste, touch, and smell through rhythm. We breathe, sleep, eat, digest, act, and think in rhythm. We waver between opinions. Habits and moods are but elongated waves of recur- rency. Poetry, music, and the dance create their emotional effects through rhythm. Every human being is the center and source of countless incoming and outgoing vibrations; and as society is but an aggregation of individual lives, it is subject to the same universal law, as manifested in work, rest, recreation, worship, in waves of political sentiment, religious revivals, epidemics of war, reform, and vice; in social agitations, strikes, revolts, and even in the infrequent upheaval which we designate by the word "revolution" — a word which in its literal sense means a turning around, about, or over. In the light of this law of protean motion, one can realize the simple grandeur of the description of the Father of Light as the one "with whom there is no variableness, neither shadow of turning.'' *•* There was a time when it would have been a reasonable induction that vegetables are motionless, and animals alone endowed with power of locomotion. We are astonished to discover by the microscope that minute plants are, if anything, more active than minute animals. We even find that mineral substances seem to lose their inactive character, and dance about with incessant motion when reduced to sufficiently minute particles, at least when suspended in a non-conducting medium A jet of water appears to be a con- tinuous thread, when it is really a wonderfullv organized succession of small and large drops oscillating in form." — Principles of Science, Jevons. ^6 Fire-Rating as a Science The ocean of human activities is perturbed by waves of inde- scribable complexity, caused by the action and interaction of both physical and psychical influences; hence the ordinary man of affairs trusts to luck, and takes no pains to conceal his con- tempt for the doctrifiaires who venture to suggest the existence of a fundamental law of recurrence in his world of chance and expediency. In spite of this, however, the law of rhythm is slowly but surely coming into recognition as the generalization with which daily human interests are most intimately concerned.* ♦Not a few of the generalizations of modern science were anticipated by the great imaginative thinkers of former ages. In his Phaedo, Plato quotes Socrates as describing the world as a round globe, and the law of-rhythm is referred to in the following language: ' In the universal opposition of all things are there not also two intermediate processes which are ever going on from one to the other and back again? .... If generation were in a straight line only, and there were no compensation or circle in nature— no turn or return into one another, — then you know that all things would at last have the same form, and pass mto the same state," and there would be no more generation of them All things, like the currents in the Euripus, are going up and down in never-ceasing ebb andflow.^^ Law of the Wave of Fire Destruction As the same thing cannot, outside of its own boundaries, exist in two places at once, all motion requires time, hence the rela- tions found in fire destruction, as a mode of motion or change, must be sequential; but it is also a law of nature that motion itself is relative, and can only be measured with reference to something else. As it is material things which are destroyed, or rather changed, by fire, we must assume coexistent -relations among these things in respect to their relative liability to fire, in order to establish measurement of the sequence found in waves of fire destruction. These coexistent relations are purely artificial, established for the purpose of measuring, not fire destruction itself, but the relative hazard of specific things with reference to each other in their common liability to this destruc- tion. These artificial relations established by our tariff system will be referred to later on; in the mean time, we will turn our attention to the sequential relations of fire destruction inherent in it as a mode of motion or change. As an effect of innumerable causes in an orderly universe where change is ceaseless and all-pervading, and where chance cannot exist, fire destruction must be governed by some funda- mental mode of motion susceptible of generalization into a natural law which will state in the fewest words the most comprehensive description of its sequential relations. From all experience we know that this generalization can never embrace all relations, for generalizations themselves are not exempt from the law of change. As the law of rhythm precludes the thought of anything mov- ing forever in an unvarying direction, it is an inevitable inference that fire destruction must occur in waves, and our inquiry must be directed to the law of motion found in these waves. Assuming, for illustration, that the classifying function which begins and accompanies all intelligence has detected a similarity 37 38 Fire-Rating as a Science of hazard in frame mercantile buildings and contents sufficient to justify their being grouped together in a property class, and that experience has shown that out of each one thousand such hazards, unexposed by other hazards, twenty are destroyed by fire each year, this would give an average life to each building of fifty years, or its equivalent, an average destruction each year of one-fiftieth of the value of all ; hence any single building of the thousand would be liable to an average destruction each year of two per cent of its value ; but as losses actually occur, each building is also liable to be totally destroyed any day during the fifty years; or, on the other hand, it may be partially destroyed and repaired several times during the period, the partial losses aggregating the same as a total loss. But the improbability of these partial losses causing an exactly equal amount of de- struction each and every year for fifty successive years would amount to an impossibility. Under the first supposition, the total destruction would cause a loss wave some one year dur- ing the period amounting to the entire value of the prop- erty. This might be described as the possible maximum of the wave, while the remaining forty-nine years, having no loss, would show the possible minimum for the remaining forty-nine years. In other words, the possible wave fluctuation ranges from nothing to the entire value of the property, and it is the possi- bility of this maximum wave, or of intermediate waves of disas- trous proportions, which creates the necessity for fire insurance on the part of the individual property owner. All motion, however, is relative, and can be measured only with relation to some fixed point or line as a standard of com- parison. In the measurement of all waves, we have three relations — their minimum, maximum, and mean; and in the loss wave under consideration these would be : Minimum, no loss. Maximum, total value. Mean, the average annual destruction, which, as has been stated, is two per cent of the value. Stated by ratios, the above would be related to each other as follows : Law of the Wave of Fire Destruction 39 Maximum, one hundred per cent of value. Mean, two per cent of value. Minimum, no per cent of value. Hence, stated by percentages, the wave for each and every building would range from nothing to one hundred per cent of value. If we now turn to the second hypothesis of partial losses, we find the probability of several partial destructions and repairs to building aggregating one hundred per cent of the value of the property. Assuming these partial losses to be During the tenth year i per cent of value. During the twentieth year - 25 per cent of value. During the thirtieth year 3 per cent of value. During the fortieth year i per cent of value. During the fiftieth year 70 per cent of value. Total 100 per cent of value. These losses, aggregating the entire value of the property, cause a wave of destruction which at no time reaches the maxi- mum, with a tendency to leave the minimum ; in other words, the wave shows a tendency to desert the two limit lines and approach the mean line. If we now assume another unexposed building of the same class, with a similar record of partial losses, the improbability of these losses being identical as to time and amount would again be equivalent to an impossibility. The wave limits of these two buildings would show a further tendency to narrow down toward the mean line, and the more unexposed buildings we assume the more the limits or boundaries of the wave line tend to desert the limit lines and approach the mean line; in other words, as the number of separate and unexposed buildings increases, the width of the wave decreases. On the other hand, if we place two of these unexposed build- ings side by side where one fire will destroy both, it is obvious that the average life of each building will be shortened one-half, and as we add one building after another to the group, this aver- age will be steadily reduced, until with the fifty buildings grouped together into one hazard the life of each will be shortened from 40 Fire-Rating as a Science its average of fifty years to one year, and if the buildings should be reinstated after each annual destruction we would have a wave of loss reaching the maximum line each year. From this process of reasoning we are able to establish the formula that the wave of annual fire destruction tends to approach its mean in inverse ratio of the amount of property exposed to a single conflagration to the total value of all property. While meteorological conditions and the diverse motives which constitute moral hazard tend to increase loss waves, both these influences are themselves subject to the law of recurrency found in all wave motion, and if their waves were superimposed upon the physical wave itself, the above generalization would remain true as to the sequential phenomena of loss waves. If it were possible to parcel out all property liable to fire destruction into unexposed hazard units of say one thousand dollars each, including all property in all civilized countries, the wave of fire destruction from all causes, moral and physical, would in all probability approach and remain so close to the mean line as to become inconsequential as a wave; and the same result would probably follow in the territorial area of the United States could we parcel out all property into unexposed hazard units of one hundred dollars each. Hence we would be justified in stat- ing a law of sequence in fire destruction in the following language : Waves of fire destruction tend toward reduced width of vibration in proportion as property is segregated into smaller unexposed values. This law is recognized in one respect by the principle of dis- tributed lines observed by every well-regulated company; but later on we shall find that it is implicated with other and equally important features of fire insurance. As stated by Jevons, "Laws or principle^ which appear to be absurdly simple and evident when first noticed, reappear in the most complicated and mysterious j^rocesses of scientific method." If we turn our attention to the relation of fire insurance, as an industry, to the wave of fire destruction, it is obvious that this wave, as a cause, creates the necessity for the industry as an effect. For a moneyed consideration, fire insurance capital agrees to shield the individual property owner in his relation to Law of the Wave of Fire Destruction 41 the wave of fire destruction. As has been shown, that which compels the property owner to insure is his liability to disastrous waves which destroy the value in his property, in whole or in part. Under the law that these waves are reduced in width of vibration in proportion as hazard is segregated into smaller unexposed values, the fire insurance company, by assuming a limited part (known as its line) of many hazards, reduces the wave of fire destruction with relation to its own liability. It is obvious that if all risk units could be so distributed as to reduce waves of destruction within maxima and minima limits so close together as to be practically identical, the element of risk would be eliminated, and fire insurance could assume each property owner's hazard with the certainty that income and outgo would be practically equal year after year. Were this possible, mutual insurance would supersede stock insurance, for along with the elimination of uncertainty from the industry, profits would disap- pear, and capital be no longer essential to the business. From the facts stated, it becomes manifest that capital is necessitated by waves of fire destruction; that this necessity is in direct pro- portion to the dimensions of these waves, and that the risk is lifted off the shoulders of individuals by insurance capital through its ability to reduce loss waves with relation to itself. It is a legitimate inference that the risk assumed by insurance capital must increase in direct ratio with the width of vibration found in the wave^ of destruction which create the risk, and that the compensation to capital (net underwriting profits) should be commensurate with the width of wave motion found in specific property classes, for this width of vibration creates the risk which capital is paid to assume. Capital is paid to assume risk. This risk is proportionate to width of wave vibration, hence this width truly measures the extent of the service rendered. Whether or not capital secure its adequate wage for this service is deter- mined largely by competitive conditions, but the law that the extent of the service to each property class is in direct ratio with width of vibration in its loss wave remains constant. Aside from the service rendered by capital itself in assuming risk or hazard, the matter of expense must be reckoned with; and encysted in this expense is found another kind of service, 42 Fire-Rating as a Science rendered by agents. The extent of this service is determined, not by the width of class waves, but by the actual labor per- formed. Hence there are two distinct kinds of service rendered, one by capital and one by labor, the extent of each being meas- urable by two distinct standards of comparison. In the past the compensation exacted by capital for its service to specific classes has not been in proportion to width of vibration found in the waves of fire destruction of each class, but in most cases exactly the reverse. Property classes with small waves have been made to pay capital the largest wage ; while classes with the largest waves have either been served gratuitously, or, in many cases, actually bribed by insurance capital for the privilege of assuming their risk. On the other hand, the personal service rendered by agents has been the cause of a twenty years* war over the question whether the laborer was worthy of his hire. This question seems to be in a fair way of settlement upon the basis of service rendered, and when settled upon some uniform scale that will be satisfactory to all interests, it will, for the first time in the history of fire insurance, be possible to deal with expense in its entirety as an unchanging ratio. Fire rates create the underwriting income of the companies as a whole, and necessarily include all items of outgo with an adequate underwriting profit as the wage of capital itself. In the present stage of evolution found in underwriting ethics, the fixing of this wage is beyond quantitative control, except as determined by competition and expediency, and it may be dis- missed from further consideration as being, at present, a per- turbing influence outside the purview of science. With the element of capital's own wage (commonly known as underwriting profit) eliminated, we have remaining the factors of loss and expense, which constitute the actual cost of the indemnity sold by fire insurance. If we assume any constant ratio as a fixed expense, it becomes possible to superimpose this ratio upon the fluctuating wave of fire destruction, and obtain a wave of cost with a contour identical at every point with the wave of loss, but elevated at every point by the ratio added for expense. In this way the problem is reduced to an analysis of coexistent cost Law of the Wave of Fire Destruction 43 relations, and a synthesis of these relations into a tariff system to be used as a standard of measurement. As before shown, measurement is impossible without an arbitrary standard of com- parison, and the thing to be measured must conform to natural laws. It has been shown that the wave of fire destruction is not lawless, but on the tontrary, conforms to the law that width of vibration diminishes in direct ratio with the segregation of hazard into smaller unexposed values. It may be granted that this is an absurdly simple law, but no more simple than other natural laws, and as stated by Jevons, no less likely to "reappear in the most complicated and mysterious processes of scientific method." Summed up, we have a thing to measure, which under the thesis of science cannot be outside the pale of law, and to measure this thing we must have an agreed standard that does not change. PART II DETAIL The Evolution of Procedure in Fire-Rating Fire-rating, as a science, must consist of an accurately veri- fied body of knowledge and an activity based upon this body of organized knowledge, which has for its end the measurement of fire hazard in conformity with the principles established by the science itself. "A science teaches us to know, an art to do. Science gives us prin- ciples, while an art gives us rules. In art, truth is a means to an end. In science, it is an end itself. Historically, art has often preceded science."* The activity of measuring fire hazard based upon this organ- ized body of knowledge might be called an art, and the real question is, whether this activity can be intelligently guided by a basic science consisting of an organized body of knowledge of the phenomena of fire destruction. We have seen from the preceding chapters that all reasoning begins with the establishment of relations, and that these rela- tions are divisible into coexistent and sequential. In fire-rating we must establish not only internal relations in each, but the external relations of each to the other. With this end in view, it is proper to analyze the procedure of fire insurance in establishing its selling price, as evolved by experience and necessity. There is an interesting contrast and resemblance between the evolution of fire-rating and the evolution of gunnery. Gunnery has for its end the concentration of destruction, while fire-rating has for its end the dispersion of destruction. Gunnery seeks to send destruction with the greatest possible certainty to a given spot. Fire-rating seeks to apply relief for destruction by fire with the greatest possible accuracy through the equitable distri- bution of assessed loss over areas of time and space. Gunnery started from the established fact that gunpowder is explosive; fire-rating, from the fact that fire is destructive. From its estab- * Sphere of Science, Hoffman. 47 48 Fire-Rating as a Science lished fact, gunnery provisionally assumed that gunpowder exploded in a tube open at one end would eject a missile; next, that by pointing the tube in a given direction it would send the missile in that direction; next, that the projectile would go farther with a larger charge of powder and the elevation of the open end of the tube ; next, that it would go farther if round than if of irregular shape, and still farther if conical rather than spherical. All these assumptions were qualitative, and the further prog- ress of gunnery as a science demanded quantitative prevision in order to send the projectile as nearly as possible to any given spot within the widest range. It was found that by rifling the gun to impart a circular motion to the projectile it would go straighter, but this circular motion was found to develop a lateral tendency, known as windage. The possibility of quanti- tative reasoning started with the invention of graded sights to measure the exact degree of elevation and deviation in the gun necessary to correct windage and gravitation. Through the investigation of explosives and initial velocity, the gradual evo- lution of a variety of collateral apparatus followed, until it has become possible to send a projectile to any desired point within a radius of fifteen or twenty miles with marvelous accuracy; and out of the original fact that gunpowder is explosive many sciences, or more properly arts, have been evolved. Among these we find the construction of guns, projectiles, range-finders, sighting apparatus, explosives, fortifications, and armored pro- tection. In addition to these allied activities, applied mathe- matics has been pressed into service in the investigation of force and resistance, and in determining the relations between initial velocity and the parabola of two directions, caused by windage, gravitation, etc. During the slow evolution of gunnery and its collateral sciences, it was assumed that a hollow projectile, filled with explosive material, could be made to explode either within a given time or in contact with its target, and that the explosion of the projectile would create greater destruction than a solid projectile. Quantitative prevision paused, however, with this secondary The Evolution of Procedure in Fire- Rating 49 explosion of the shell, and it remains for the future to determine the possibility of ascertaining how many sub-projectiles will be created by this explosion, and in what direction and how far each fragment will go. So, in the problem of fire-rating, starting from the known fact that fire is destructive, we seek to disperse the disaster through assessments on specific property, in proportion to its specific liability to destruction, under the general law of average. By keeping a record for a year we can determine at the end of the year the ratio between receipts and disbursements neces- sary to make good the destruction, and through a comparison of the total amount insured with the total premiums received we are able to determine the average rate for a given period on all property. By similar comparisons we are able to determine the ratios of loss and expense. Experience has further shown that certain species of property have so many points of resemblance that they can be grouped in classes, and that the record of any of these classes, for any given period, will show similar ratios for each class. So far we are able to establish exact measure- ment, from which we are enabled to intelligently determine our selling price for indemnity as a whole, or for any class of which we have kept a separate record. With equal precision we can, by classifying the different grades of fire department protection, or construction of buildings, determine the average for each standard of protection for each character of building; or by keeping a record of any or all of these features we can determine the averages for one or all in any given state. So far our reasoning has potentially the accuracy of mathe- matics. We now reach a secondary degree of accuracy in the specific features of each risk, as found in its methods of lighting, heating, occupancy, structural features, private devices for pre- venting fires, and its exposures from other buildings. It is clearly within the possibilities of statistical science to determine the relative degrees of hazard between lighting a building by candles, coal oil, gas, or electricity, or heating it by open fire- places, stoves, hot air, or steam furnaces, and it would be equally possible to determine the same relations with all the more impor- tant features of structure, occupancy, and exposure, provided it 50 Fire-Rating as a Science were possible to locate in every case the cause of the fire^ but it would require a vast and expensive system of statistics based upon data impossible to obtain, for the reason that the origin of fires is very often unknown. This difficulty has been met by utilizing a system of analysis of the individual risk, through which we estimate by charges and credits the relative hazard of its parts, as far as analyzable. In adopting this plan of avoiding a tremendous expansion of statistics for a comparatively unimportant end, fire insurance has followed the usages of the industrial world and all governments in determining value relations by estimate; hence, as an expedient, it is identical with the expedient adopted from time immemorial by governments and peoples for similar con- ditions. In thus adopting the economic law of common sense instead of searching for obscure and innumerable laws of causa- tion in the effort to obtain more exact relations among unimpor- tant factors, reasonable equity is obtained so long as personal favoritism is abolished, and every man accorded the same charge or credit for the same item of hazard. We now reach a third phase of fire-rating, in the nameless, numberless, and often remote causes of fire which are not only unanalyzable, but often undiscoverable. In this stage, analysis and prevision are as uncertain as in the post-explosion stage of gunnery, in which it is impossible to fore- tell the specific consequences which will result from the bursting of a shell. In this remote region which lies outside the border- land of inductive observation, however, fire underwriting experi- ence has brought forth from the crucible of conference and competition some nuggets of pure metal, by establishing fixed usages which appeal to common intelligence. Mercantile occu- pancies have been analyzed, classed, graded, and valued; the permanent features of industrial processes sorted, estimated, and labeled with their relative hazard value, and the residuum of irreducible slag left in the crucible has been estimated as a whole for each class of property under the name of "basis rate." This basis rate, arbitrarily assumed as the residuum of hazard, after it has been purged of all measurable factors, is the nucleus on which each rate estimate is built, and when so built we have a synthesis of artificial relations between the analyzed and unan- The Evolution of Procedure in Fire-Rating 5 1 alyzed factors of hazard as a sort of' working hypothesis. By a singular reversal of ordinary reasoning methods, these artificial relations established by reasoning purely hypothetical constitute the basis of the ratios on which fire insurance must establish its sequential relations. In ordinary reasoning, the individual rate should come last instead of first, but necessity has compelled a reverse process of reasoning — a good deal like it would be in gunnery if we should begin with the pieces of an exploded shell, and calculate the trajectory of each irregular fragment back to the place it occu- pied in the shell before explosion, then figure the gravity, wind- age, elevation, initial velocity, and all that sort of thing necessary to replace the shell intact in the gun whence it started. This perplexing reversal is, however, a logical necessity imposed upon fire insurance by its relations with policy holders, and the fact does not necessarily render the solution of its problem less accu- rate on that account. It is this blindfolded orientation that creates most of the prevailing skepticism as to the possibility of scientific rating. This confusing necessity of backing into the shafts be- fore we start, originates from the following sequence of usage : The ratios of loss and expense are found by comparing amounts disbursed with aggregate premiums; but this aggregate is com- posed of a large number of premiums from individual risks, and a condition precedent to the collection of these premiums is that there must be a relation established between each individual hazard and its premium satisfactory to the buyer of indemnity. This makes the first act that sets the wheels in motion an esti- mate of the individual premium ; for it is the aggregate of these individual premiums which constitutes the standard that enables us to sight back and determine the relative accuracy of the original assumptions, and the determination of this relative accu- racy enables us to tell not only whether these assumptions were too high or too low, but how much too high or low — in other words, to establish the quantitative reasoning through which we can accurately estimate hazard in dollars and cents. In this reciprocal process, established rates must be made through an endless cycle of reasoning, in which it is as immaterial which comes first as it is in the cycle of causation between the chicken £2 Fire-Rating as a Science which lays the egg and the egg which hatches the chicken. The essential point is that a series of provisional assumptions through an unending process of readjustment tends to become more and more exact, provided we are faithful to the assumptions. An analysis of the procedure of fire-rating, in its present stage of evolution, plainly shows the continuous exercise of the classi- fying faculty common to all intelligence. It shows that normal reasoning processes have been continuously engaged in establish- ing relations, and it shows, further, that these relations are divisible into coexistent and sequential. In the grouping of class hazards, the establishment of standards of fire protection, charges, credits, and basis rates as found in our class schedules, and in the final synthesis of these relations found in our local tariffs, we discover a system of coexistent relations, but in our attempt to modify these relations to meet our constantly shifting experience year after year, we have entirely ignored the essential difference between coexistent and sequential relations, and the fact that one cannot possibly be changed into the other. Up to this point of confusion, fire insurance has progressed by correct methods, literally because it could not help itself; because these methods are inherent in all intelligence, and as impossible to avoid as the physical function of breathing. The trouble begins with the mixing of coexistent and sequen- tial relations. The former, which by their nature are perma- nent, and should be marshaled as an unchanging whole in their necessary progress through sequential relations, have been con- tinuously shuffled because of our inability to differentiate two kinds of relations inherently distinct, the one a group of rela- tions which by nature is fixed and unchangeable, the other a series of relations which by nature must always be in process of change. In its present status, fire-rating as a science might be com- pared with the science of gunnery, as it would be if reasoning had simply amused itself with wagering on the probable trajec- tories of the fragments of exploding shells. We gather up the disjecta membra of provisionally assumed charges and credits, and patch them onto a provisionally assumed nucleus known as a basis rate, and then call this thing of provisionally assumed shreds and patches an individual rate. When a local tariff of The Evolution of Procedure in Fire-Rating ^^ these assumptions has been formulated, it is turned out to the mercy of the elements. Contention within and without is allowed to work its own sweet will in changing artificial relations of coex- istence into relations of sequence, and the structure of artificial relations we have erected with so much travail begins to disinte- grate almost before the paint is dry. This local tariff of indi- vidual rate estimates, constructed with more or less regard to a basis tariff of hypothetical assumptions, is, up to date, the furthest reach of fire-rating as an activity. It would be a work of super- erogation to point out the lamentable results of the arrested development which has checked further growth at the primary stage of reasoning, where we simply recognize coexistent rela- tions in hazard, which we arbitrarily alter, apparently without the slightest conception that in so doing we are essaying the impos- sible task of changing space into time. Viewed as coexistent relations only, there is no lack of inconsistency in our rates, but by constant tinkering with these relations in the attempt to make them sequential we violate a fundamental law of all science. We construct a basis schedule of each state, but cannot show that it bears any logical relation to the schedules of other states. We say that each individual rate is the sum of a basis rate combined with certain charges and credits, but cannot show whether this basis rate is relatively correct when compared with others, nor can we show that the charges and credits which permeate many classes are consistently imposed upon each class. This naive disregard of relations crops out not only in the comparison of every existing basis tariff with other tariffs, but in the comparison of parts of the same tariff with other parts; select- ing for example the following: Illinois State Board Minimum Tariff 1894 Minnesota and Dakota 1895 Southeastern Tariff Association 1895 Indiana Mercantile Schedule 1893 Missouri, Kansas and Nebraska Minimum Tariff 1886 Missouri Minimum Tariff 1894 Illinois Mercantile Schedule 1895 Western Mutual Underwriters' Association Minimum Tariff --1882 New England Insurance Exchange Schedule 1894 Universal Mercantile Schedule 1896 54 Fire-Rating as a Science In the following table* the upper figures show the number of times the same charge appears in all the above tariffs, and the lower figures show the different charges made for the same thing: Awnings, wood, on one-story building, |, fV, gV Boiler in frame boiler-house, H, ^\, ^a, ^, ^i^] J^, f |, /., ^y^, ^^. Shingle roof boiler-house, y^^, j%, |g, ^\j. Shingle roof on brick boiler-house, j%, ^%, ||, ^, ^. Cornice, wood, i, |, j*^, gS^. No casks or pails of water, |, f ~g, J§, ||, i§. Dipping in building, ||, |f, ^-i^. Heating by furnace, i i, j*^, if, /j, ^^, ^3^. Heating by wood stoves, ^, ^%, ^%, ||, i^, ^\„ ^%. Heating by coal or oil stoves, |, f g, if, ^% ||, ^^, ^V Lighting by other than by gas or electricity, |, f^, /^, ||. Lighting by kerosene, standard metal lamps, I, y^, -^^. Lighting by kerosene, glass lamps, y^^, j^g, j^. Lighting by kerosene, lamps filled by daylight only, y^^, 3*^, i^, ^, ^, ^. Ladders, stationary (none), i, ^, y\, ^0, ^V- Planer, each machine, g^^, i^, ^, y\, rfr). Planer, without blowers or conveyors, ^, ^j^, yf^y, jf^. Picker in mill, y^, ^\, s\, f?, rou. rixr- Roof, shingle, f, H, If, H. U. /^. tU- Spittoons, sawdust, i, yV, sS- Shavings vault, wood, ^, ^, y^, y|^. Shavings vault (not cut off), \^, j\, ^^, ^, ^. Shavings vault, standard (cut off), y'^, ^s> ^' Shavings vault, standard (not cut off), ^, ^, ^%. Metal stack through metal roof, |, yV, i^, ^q. Metal stack through shingle roof, with collar, yV, |f. Metal stack through roof or floor (no jacket), 5V, ^^, J4. ts- Metal stack through shingle roof, y%, ^^, ||. Varnishing, y^-, ^\, ||, ^V. A» ih- Watchman and clock (none), |, ^^, ^%, |f, |g, ^, ^\, ^. Watchman (no clock), |, fj, Jf, iV. P^- Woodwork, not whitewashed or painted, ^, |f , j^^, gV One might go on indefinitely pointing out incongruities of this kind in our coexistent relations, and it needs no argument to show that every attempt to cobble these into relations of sequence makes confusion worse confounded. It would be a truism to say that in the face of inconsistencies so glaring, explanation or defense is impossible. The public con- *The author is indebted to the late L. H. Ticknor, Esq., of Peoria, 111., for the above list. The Evolution of Procedure in Fire-Rating 55 tention that rates are made "by guess and begad" is susceptible of proof from the documentary evidence contained in our own tariffs. It matters not that under the leveling force of self-inter- est among brokers, agents, companies, and the public, receipts and disbursements come out almost exactly even, if taken for decade periods; in other words, that indemnity as a whole is practically sold at average cost. Our failure to make a profit does not concern the public, but our failure to maintain reason- ably true rate relations offends the sense of relation which is instinctively the basis of every reasoning process. Even low rates that are inequitable are an offense to common intelligence. The Formula of the Rating Function The undisputed facts cited in the previous chapter are the results of an unreasoning determination to make a system of artificial coexistent relations perform the entire function of meas- uring fire destruction, while we ignore the natural sequential relations found in loss waves, as well as in every other mode of motion. In the past, expediency alone has fixed the price of fire indem- nity. The seller has fought for high prices, and the buyer for low prices, and between these two contending influences rates have been kept in an irregular and spasmodic motion similar to the atmospheric wave known in music as cacophony. Fire destruction, too, like every other motion resulting from contend- ing influences, has created its own wave. We have thus two irregular waves — the loss wave occasioned by the countless ele- ments of fire hazard, and a sort of "rough and tumble" zigzag (which might be dignified by the name of rate wave) caused by the foot-ball tactics of buyers and sellers of indemnity, and further complicated by the arbitrary decisions of an umpire, known as the local agent, who has a stake up on the game. While we know that rates must be constantly changed, we construct our tariffs, in theory at least, on the assumption that we can maintain them permanently at an unvarying level. When contending influences force this level into a r^te wave, it is invariably a cacophonous wave, not in harmonious relations with the wave of fire destruction, because it is largely the product of contending personal motives beyond quantitative analysis. In making rate changes, in obedience to the law of expediency, we not only observe no system, but cannot observe system. At one time we make a so-called percentage change, at another a flat rate, at another a competitive rate, at another a suspended rate, and after a series of these changes has completely obliterated established relations we are again compelled to construct new 56 The Formula of the Rating Function 57 basis tariffs, and re-create hundreds or thousands of local tariffs of coexistent relations, which, before we can place them in the hands of our agents, are fly-blown with the germs of dissolution, because they furnish our only available material for establishing sequential relations. Under such influences, a new departure in rating methods is a crying need, and the first necessity is the fundamental rule of action essential to every scientific activity. This rule must be an accurate definition of the function of fire-rating in its broadest sense as an activity. That fire insurance meets a public need, aside from being a mere means of earning salaries and dividends, must be admitted, else it could not exist. We have been accus- tomed to define this utility as the distribution of fire destruction from the individual to the community, but in this distribution it is necessary to consider something more than the individual, for each property group, community, state, and year may justly claim relief from an excessive burden of fire destruction with the same logic as the individual; and even the nation at large may stagger under the burden of a single year's losses, and justly claim that these losses shall be spread out through a period of years. This makes it an essential part of the duties of fire insur- ance not only to distribute, but to redistribute and re-redistribute, in order to avoid oppressive taxation. While the above definition may answer as a broad statement of the ethical obligations of fire insurance to the community, it is not a definition applicable to the needs of a physical science. If the measurement of fire hazard can be done scientifically we must admit that the activity of fire-rating legitimately belongs to the family of physical sciences, and all physical sciences deal with the properties of waves. What we need is a generalization defining the function of fire-rating as a physical science. An unbiased consideration of the phenomena of fire rates during recent years ought to convince any sane man that in our refusal to permit rate waves to vibrate in harmonious sequence to cost waves we have been floundering about in the vain attempt to adapt an inflexible system to flexible conditions. Like the African who ties up his hair with cotton twine to take the *'kinks"out of it, we have long struggled against nature in the 58 Fire-Rating as a Science attempt to take the kinks out of a thing which stubbornly refuses to remain straight. Our persistent efforts to flatten loss waves into unvarying rate lines have been a long and irritating struggle against the inexorable physical law of rhythm, and our indisposition or inability to recognize this law has caused endless trouble and misunderstandings among ourselves and with the public. If it were possible to conceive of a sea-going vessel so con- structed as to be unresponsive to the wave motion of the ocean, and started on a voyage from New York to Liverpool, we should find it in heavy weather buried half the time under mountains of sea-water, and the other half paddling through space. Could we trace the ordinary motion of sea-going vessels, we should find a profile view of their line of progress to be invariably a modified form of the surface wave. It is as illogical to ignore the neces- sity of rhythm in fire rates as it would be in navigation to ignore the law of wave motion. The ocean surface when relieved from atmospheric disturb- ances settles down to a dead level. This level is the exact mean between the sum of the wave protuberances and hollows, so that in a dead calm the track of the vessel and water surface would be at all times exactly parallel. In the same manner, between any two given points of time there is an average cost of fire underwriting to be found, which is the true mean between the crest and trough of the annual cost wave of each class. It is this average cost which is the real straight-line, the unchanging sea-level, of every property class, and it is this which we should seek to establish as a fixed basis for our coexistent relations, and our rates should be permitted to fluctuate above and below this mean line in intelligently modified waves, as determined by the greater wave found in the annual cost ratio of each class. The ascertainment of the true level of average cost of each class, and the continuous control of the rate wave by reckoning from this as a "base line," constitutes the real problem of estab- lishing sequential relations, and the determination of this base line is as purely a question of statistics, and ought to be as free from contending personal influences, as the establishment of a The Formula of the Rating Function 59 principal meridian in land-surveying, or the determination of a ship's position at sea. It is the object of this inquiry to learn how this average cost for each class may be determined, and how from this as a base, rate waves may be so regulated as to be in harmony with their loss wave, and at the same time be modified into waves of endurable proportions. It is a characteristic of all waves that they become intolerable when the amplitude of vibration exceeds certain limits. Ocean waves beyond a certain magnitude become destructive to sea- going craft. A deafening noise, a blinding light, a withering heat, an intolerable electrical discharge, are one and all results of width of vibration in the media through which they are prop- agated. The well-known generalization, that the intensity of all wave motion increases in proportion to the square of the amplitude of vibration, might be said to apply not only to matter but to mind and its concerns, for violent change is destructive to all human in- terests. Wide fluctuations in values create commercial panics, and in lesser degree wide fluctuations in fire rates are intolerable to the community. This universal characteristic of wave motion leads us to the unavoidable inference that // is the true function of fire-rating in its broadest aspect to transmute annual cost waves into rate waves modified into proportions that will be endurable to property interests. This is the fundamental rule from which fire-rating as a physical science must start. Can this be done consistently with the description of scientific reasoning set forth in the opening chapters? In order to answer this question, it will first be necessary to take up the individual rate as a synthesis of coexistent relations. The Individual Rate The individual rate as a cause and effect, as the a and the x of the rating equation, is a standing paradox. In the beginning it seems that relative difference of hazard was recognized to the extent that it was assumed that a frame building was twice as hazardous as one of brick or stone, hence it should pay twice the rate, but it was necessary to postulate a rate for each frame and brick, bearing the relation of two to one. On the basis of these postulated class rates, risks were insured, and a fund of premiums collected, from which losses and expenses were paid, and at the end of a stated period it was possible, by keeping a separate account with bricks and frames, to determine whether the individual rates so assumed had been adequate or inadequate. In this way the individual rate created the fund, and the ratio of losses paid from this fund was the standard from which the individual rate was adjusted, on the basis of experi- ence. But experience developed numerous other differences in hazard, internal and external; and at the present time every prominent company keeps a debit and credit account with classes, and can tell its ratio of loss on each class with which it keeps an account. In every class, however, there remained other and more elusive distinctions, which in time caused the companies to resort to class basis schedules as a means of determining the relative hazard of the individual risks in each class. Whether the specific rates established through these basis schedules bear accurate relations to each other there is not, and probably never will be, any way of exactly determining. Meanwhile, the rela- tive rates thus established constitute the working hypothesis, from which we must reason to a reasonable certainty in other and more important problems of fire-rating. The basis schedule of each class, however, is in effect an analysis consisting of estimates of the specific factors, so far as analyzable, which create the individual rate; hence the individual rate itself 60 The Individual Rate 6i has ceased to be the ultimate unit in the rate-making compu- tation. It is the charges and credits in basis schedules which consti- tute the real units, and it is with these we must reckon, as the individual rate is simply a result which may be stated as the sum of its charges less the sum of its credits. These charges and credits for the appraised features of risks may permeate an entire group, or even several groups, of risks. They are, as a rule, individually insignificant in amount, and in many classes the indi- vidual rate may be created by the addition of scores of these units to the class basis rate, which we must regard as a residuum of hazard appraised as a whole, because it resists further analysis. Hence the real question is to determine the relative equity of each of these factors which cause the effect known as the indi- vidual rate. Charges and credits are necessarily provisional assumptions. The most we can claim for them is that they are based upon united judgment and experience, through which alone approxi- mate truth can be estimated. While even this claim will admit of debate (for they have always been the source of much contro- versy), there is no disputing the fact that these specific charges and credits have in them the element of abstract fairness. Apply- ing to features common, perhaps, to all the risks of a class, or to a large portion of the risks of many classes, they are free from the possibilities of personal favoritism. It is proper to assume that as many of these elementary factors will be too low as too high, and when a risk is unduly taxed in one charge it is reason- ably sure to be insufficiently taxed in another. If a charge is too high to be ratified by the average judgment, competition begins at once to seek risks having this feature, and the charge is forced down to a point where competition ceases to make special efforts for the class. Under these leveling influences, it is safe to assume that each charge is automatically regulated within limits not far from the true mean. Under the law of averages, the range of deviation from exact adequacy in each charge (which might possibly be determined by elaborate statistics) is so reduced that probably not one risk in a hundred is mulcted in an amount greater than its rate would 62 Fire-Rating as a Science be increased by the additional expense necessary to maintain such statistics. Finally, there are many factors in fire hazard which can be closely estimated by analogy, yet there is no way to tell whether these factors originate a fire, or what measure of influence they exert in increasing or decreasing the loss. For this reason their charges are not amenable to statistical investigation, and they must remain purely arbitrary hypotheses. We only know that under the law of probabilities plus quantities may be considered to offset minus quantities, thus producing an equipoise which tends toward a closer approximation to true relations in the indi- vidual rate they create as compared with other individual rates. It is the true relation of these individual rates, one to the other, with which we have to do, rather than with their adequacy or inadequacy. The cost ratio generated by the coexistent relations synthesized from basis tariffs into individual rates will eventu- ally prove the reasonable accuracy of these rates when we once begin to recognize the vital fact that they are coexistent relations which we destroy the instant we attempt to change them into sequential relations. Basis Tariffs It has been shown that the individual rate as it appears in regular tariffs is not the ultimate unit in the rating problem, but a compound result of charges and credits for specific features of hazard, arbitrarily analyzed and appraised, added to a basis rate which itself is a lump charge for the nucleus of hazard that resists analysis; hence the individual rate is the result of a num- ber of provisional assumptions, except when assumed bodily as a "flat rate," in which case, instead of appraising the parts we simply guess at the whole. Every class basis schedule is an inventory or series of arbitrary valuations of the factors of hazard found in individual risks of a given class, an inventory more or less minute and more or less logical, but as an inventory necessarily more accurate when thrown in the scales of the individual rate than any guess as to the entire rate in one sum. In fire-rating we thus obtain an indi- vidual rate — the sum of or the difference in a series of assump- tions known as charges, credits, and basis rate. In our state basis tariffs we have utilized the principle of classified standards by establishing grades of fire department protection and of hazards in personal property, as well as by assuming basis rates, charges, and credits for every important property class. Some of these charges and credits apply to many classes, though we have not made any attempt to correlate or co-ordinate these elementary factors in order to secure logical relations among them as they appear in different classes or states. Again, in adopting basis rates to represent the residuum of unanalyzable hazard in each class, we appear to have proceeded on the theory that this nucleus should be proportionate to the relative hazard of its class, and in some instances proportionate to the relative loss ratio of states, though we seem to have done this without attempting to correlate these relations. Neither do we appear to have made more than a crude attempt to observe con- 63 64 Fire-Rating as a Science sistent relations with regard to grades of fire department protec- tion. That these relations have been observed, however vaguely, indicates a correct, if indefinite, drift in our reasoning -processes. In the relations between the charges for preferred, non-pre- ferred, and hazardous stocks, as found in different tariffs, as well as between the rates for occupancy as compared with buildings, we find a similar vague conception of the fact that some sort of correlation is desirable. Summed up, our completed instrumentality for establishing rates shows a well-defined analysis and classification of parts, supplemented by a feeble attempt to establish true coexistent relations among these parts, with an unending and unavailing series of efforts to make these coexistent relations do violence to their nature by serving as sequential relations. The building up of each rate from a series of estimates of the integral parts of hazard is as logical as the reasoning of the builder who estimates the quantity of lumber, brick, stone, nails, paint, plaster, and labor he will need in a building, instead of guessing at the cost of the building as a whole. The division of towns according to their grade of fire protection, and of risks into classes, is in harmony with the fundamental law which makes the classifying function and the establishment of standards of comparison inher- ent in every reasoning process. The establishment of a ratio between the basis rate and the relative hazard of classes is also logical, for it is but a natural inference that the larger the total hazard of a class the larger will be the residuum that resists analysis. The establishment of relations among basis rates and charges in the several states is a necessity forced upon us by state sovereignty, as well as by the permanent differences found in climatic and social conditions. In fine, it may be stated that basis tariffs, with all their imper- fections, are as well adapted to their purpose of establishing coexistent relations, and in all respects as logical, as a hoe, hand- saw, jackknife, or any of the innumerable utensils evolved by human necessity. While it may be possible to improve the con- struction of any of these utensils, it would be difficult indeed to utilize a new mechanical principle in their construction which would qualify them to render better service. For similar reasons, Basis Tariffs 65 it is equally hopeless to expect improvement through any radical departure from the established principles embodied in our present class basis tariffs regarded as a system of coexistent relations, because, like the hoe and the jackknife, they are the results of a natural evolution from human necessity. The basic defect in fire-rating is found in our failure to recog- nize the fact that in the whole work of measuring fire destruction and establishing rates we are under the law of relativity of knowl- edge dealing with a series of relations ; that these relations are of two kinds, coexistent and sequential; that our charges, credits, basis rates, basis tariffs, and local tariffs as a system are an analysis of coexistent relations, and that we cannot mix these relations with the sequential relations found in the movement of annual waves of fire destruction without destroying all relations. It is not new principles we need in fire-rating so much as a clari- fied understanding of principles which are half recognized, and are constantly appealing to us for entire recognition. An interesting experiment in the wholesale destruction of fundamental principles and established relations is found in the so-called Universal Schedule. As strenuous efforts have been made during recent years to secure the adoption of this schedule as the sole rating basis of the country, it cannot well be ignored in our discussion of fire-rating as a science, inasmuch as we are led on to the conclusion that a national basis schedule is a necessary preliminary to scientific rating. In the explanation which accompanies the Universal Schedule, it is stated that "the committee early in its deliberations reached the conclusion that it should be formulated upon the following lines, and that it should recognize — " 1. A standard of environment — the city, (This wipes out the classification of fire departments, and precludes the reasoning faculties from establishing relations among standards of munici- pal fire protection.) 2. A standard of construction — the building, (This banishes the classification of buildings, and makes it impossible to establish relations among standards of construction.) 3. An addition for the ignitibility and combustible features of occupancy, (This dictum is carried out by substituting for existing classification of occupancies a list containing two or three thousand different mercantile or 66 Fire-Rating as a Science industrial occupancies, each tagged with a selling price. This prevents the exercise of the reasoning faculties in establishing relations among occu- pancies.) The schedule further states that it is obviously expedient that rates throughout the United States should be made upon one and the same basis. By thus abolishing the autonomy of states which authoritatively insist upon recognition, state basis tariffs are consigned to the waste-basket along with all possibility of exer- cising the reasoning faculties in establishing relations among states. The basis rate, which, as has been explained, is the residuum of unanalyzed hazard, is referred to in the following language: " The basis rate or starting-point for rating a standard building in a standard city has been fixed at twenty-five cents (25c.) after careful con- sideration of the experience tables of the companies. It surely was not a difficult task to fix this rate for the simplest form of risks under the best conditions as a starting-point." As a celebrated polemist once said, "Refrain from rendering your terms into ideas and you may reach any conclusion what- ever. " To define the residuum of unanalyzed hazard or basis rate as *'a starting-point" is to render a term into an idea which might answer as well for a horse-race as for the work of estab- lishing a preliminary assumption in the ambitious task of constructing a universal schedule; but be this as it may, the definition and assumption of twenty-five cents as a cosmic basis rate dis-establishes classification and relativity among basis rates. As has been reiterated, *'all knowing is classifying," and "all reasoning is the establishment of relations"; hence, in the light of the generalizations quoted, it may be truthfully said that the Universal Schedule makes a clean sweep of the twin functions of intelligence — classification and reasoning. When God sorted out chaos into an orderly creation, we are told that he divided the light from the darkness and called them day and night, and divided the water under the firmament from the water above the firmament and called them heaven and earth, and commanded the dry land to appear; and gathered together the waters and called them seas, and established lights in the heavens to divide day from night, and be signs for seasons, days, Basis Tariffs 67 and years ; and caused the waters and the earth and air to bring forth abundantly — fish, fowl, cattle, and creeping things — every living creature after its kind. This sublime example of classifi- cation and relationing set by the Maker of the universe seems to have been wasted upon the maker of the Universal Schedule. This tariff (constructed upon the assumption that it estab- lishes a science of fire-rating) leaves no room for the exercise of further judgment by substituting the judgment of its maker for every microscopic detail of the building; but after this fine-tooth- comb analysis of the building itself, no attempt whatever is made to analyze or classify or establish relations among the hazards of occupancy. A specific charge is named for two or three thou- sand different occupancies, in each of which the rate is estimated in a lump sum, amounting in many cases to several times the rate of the unoccupied building, after it has been laboriously con- structed from scores of charges and credits, in many cases as small as one or two cents. In place of a synthesis of classified and valued relations, the Universal Schedule offers us a volume of dicta which precludes the exercise of other than the purely mechanical functions of addition and subtraction. A basis tariff ought to be an instru- mentality for establishing intelligent coexistent relations, and probably no tariff will ever be constructed so complete as to eliminate the necessity for personal judgment in its application. That masterpiece of constructive statesmanship known as the United States Constitution provides for a supreme court to inter- pret its provisions, and even Divine Wisdom does not seem to have been able to bequeath to humanity a code of morals that does not need constant expounding. With any tariff, rating itself must remain an art; and it is as idle to expect that a tariff itself will rate every variety of hazard without the exercise of judgment as to expect that a hoe will raise a crop of corn without intelligent manipulation. The Universal Schedule is an ingenious analysis, but as has been well said, **No number of analytical surmises, or even truths, can make up that synthesis of thought which alone can be an interpretation of the synthesis of things." Classification in General Like the hero in Moliere's comedy who began the study of grammar late in life, and was astonished to learn that he had all his life been talking in prose, many fire underwriters would doubtless be surprised to learn that classification in fire insurance has evolved into an advanced stage of differentiation ; that from its earliest beginnings it has been constantly engaged in detecting differences and grouping like with like. It is, perhaps, a truism to say that in the beginning everything unexplainable was attrib- uted to either chance or supernatural influence. Out of this original mass of the unknown, intelligence has been sorting out and classifying or grouping the explainable; and as knowledge increases, the scrap-heap of chance decreases. The ability to distinguish differences, to group like with like, may be extremely loose, but the endless process of classification is to take cogni- zance of more and more minute differences, and thus keep up a continuous process of differentiation. To discard classification because it is not exact would be to return to the primitive con- ditions which underlie intelligence. Not infrequently the greatest utility is derived from absurdly loose groupings of phe- nomena. The alphabet is a classification of the elementary sounds of speech. Every written language has its own classifi- cation, more or less inexact, but in English this classification is notoriously loose. Selecting, for example, the first letter of the alphabet, we find it serves to represents seven different sounds, as will be seen in the following words : any^ able, air, at, arm, all, about. In the same way, nearly every letter which, theoretically, should stand for the symbol of a single elementary sound is made to do duty for several sounds, and each of these letters usurps the functions of other letters, so that we have not only one sym- bol for several sounds, but several symbols for one sound, with the result that most of us spend our lives in the impossible task 68 Classification in General 69 of trying to group these symbols accurately — in other words, in trying to learn how to spell; but the combined efforts of the spelling reformers have been able to make no material improve- ment in this preposterously loose classification of things capable of being grouped with scientific accuracy. Again, these letter atoms are grouped together in word mole- cules, which themselves are built up by welding classified prefixes and suffixes to verbal roots, just as we construct individual rates by uniting charges and credits to a nuclear basis rate. These word molecules, the tertiary results of classification, may in turn be used to represent a wide range of ideas, many of which are antagonistic to each other; or on the other hand, several words may be used to represent one and the same idea. Again, the significance of words is constantly shifting. We have an instance of this in the recent metamorphosis into an offensive sense of the word trust. Word-building itself is an endless process of classifi- cation, for we cannot proceed without a name for each class; and on the other hand, words cannot be made faster than things are classed. But we have in this grouping of the phenomena of language an illustration of the fact that classification, however crude, may be very useful in the absence of something better. Classification and reasoning, or the grouping of things and the relationing of things, are complementary to each other, and have accompanied intelligence from its lowliest beginnings, though classification is found in living organisms before intelli- gence begins, down in the dim life-regions where conduct is governed either by instinct or by the reflex action in which a nerve ganglion serves in the absence of a brain. The reason for this is fundamental, for *'it is a condition under which only it is possible for any creature to avoid danger and obtain food, that it shall be differently affected by different objects." In fire insurance, the classifying instinct began with the detection of a difference in hazard between frame and brick buildings, which were separated at the outset into two classes. Then a difference was discovered between buildings and con- tents; next, differences among the hazards of contents. It was found that some property resisted fire and was not easily 70 Fire-Rating as a Science damaged, or was easily removed from a burning building; other property was easily damaged or difficult to remove; other prop- erty was highly inflammable and of a nature to propagate fire. These classes were grouped separately as preferred, non-pre- ferred, and hazardous. Then the important distinction was discovered between inherent hazard and exposure. Then a dis- tinction was made between the hazard of property under constant human protection and that which was not, and dwellings were classed apart from other hazards. Then fire departments were grouped into standards according to efficiency. Then the rela- tions between the factors of known parts of hazard were analyzed and classified under arbitrarily fixed charges and credits, and the remainder called a basis rate. Then the law of relation between the basis rate and the total hazard of each class was inferred, and a separate basis rate established for each property class. It may be observed that all these results achieved by classifi- cation bear relations to each other of coexistence and not of sequence. The upward progress of knowledge is comparable to a stair- way, of which the runners supporting every step might be called classification; for classification begins with the lowest intelli- gence, and accompanies its growth up through every stage in the evolution of the reasoning faculties. The philosopher who makes it his business to study all sciences must classify as well as the oyster which furnishes him food for reflection as well as digestion. Every school of philosophy has tried its hand at classifying the different sciences, yet no two schools agree. The reason for this is that the faculty of detecting likeness and unlikeness is a function of perception, and not of reason. This accounts for the fact that differences of opinion result from every attempt to classify, and in this fact we find another proof of the relativity of all knowledge. Fire insurance has reached what might be called a "wide- open" agreement in its classification of coexisting relations as found in our tariff system, because necessity has compelled it as a preliminary to the establishment of any rating system what- ever; but we have not yet been brought to a realization of the fact that there is a difference between coexistent and sequential Classification in General 71 relations, or that sequential relations cannot be logically estab- lished by a periodical breaking up and rearranging of the coex- istent relations which have been forced upon it by necessity. We find an embryotic idea of classification, for the purpose of establishing sequential relations, in the classification lists main- tained by individual companies. These lists serve the several companies in a general way for their own information as a means of following sequential relations between income and outgo as shown by the fluctuation in annual waves of loss and premium, but this classification is separate and distinct from that found in our tariff system of classified coexistent relations. With all the bandying about of the word '^classification" during recent years among fire underwriters, without any really definite idea as to the true import of the word, it is a fact that its ceaseless influence has shaped and molded the very soul and body of fire insurance, which without classification would be that vague and formless thing known as chance. But when this word, which in its coexistent aspect has been the very life-breath of insurance, is mentioned, there is a shaking of heads and a questioning of the practical utility of classification in establishing sequential relations. What these head-shaking people probably mean, if they know what they mean, is that classification in fire insurance can go no further; that its capacities have been exhausted in establishing the coexistent relations found in tariffs, and that a function which accompanies all intelligence, from the oyster to the philosopher, becomes worthless in fire insurance the moment we attempt to utilize it in establishing sequential relations. If a child of ten years should cease to classify, it would con- tinue as long as it lived to be a ten-year-old child ; and something akin to this phenomenon is found to-day in the arrest of the classifying instinct in the rating function of fire insurance. The real controversy over the much abused word "classifi- cation" is not over the introduction of a new principle, but whether a principle woven into the very fiber of the industry, a principle which has imparted to it all it has and is that is not purely chance, shall be permitted to expand as a natural growth ; whether it shall be fostered as a thing useful or repressed as a ya Fire-Rating as a Science useless excrescence. There are many phases to the manifesta- tions of classification in the rating problem, but the one phase around which interest has centered lies in the proposition to use the classified lists kept by the several companies in establishing combined statistics which will show the actual results of the aggregate experience of all companies by classes year after year; in other words, show the classified experience of the industry as a whole in its sequential relations as a basis for the intelligent control of rate waves as determined by waves of fire destruction. The Individual Classification List It is probable that from the earliest days of fire insurance the companies have maintained tabulations of their experience with grouped hazards. These lists have slowly expanded in differing degrees, though some have reached a far more advanced stage of differentiation than others. In the primitive days when each company not only had the privilege of making its own rates, but from lack of association was compelled to do so, when compe- tition was so small that it could make rates which insured a wide margin of profit, these lists served as a crude scale — something like the farmer's fence-rail and stone — for the quantitative meas- urement of class hazards in their sequential relations as indicated by individual experience; but in these days of competition, when a company is compelled to keep in the swim by carrying all classes of property, of every grade of desirability, in deference to the wishes of more and more exacting agents, these individual classification lists have fallen into a sort of innocuous desuetude, surviving like the coccyx and vermiform appendix as the remains of organs that served their purpose during some earlier stage of evolution. Kept up at a great expenditure of time and money, and carefully guarded among the secret and sacred archives of each company, it would be difficult to determine what intelligent end these lists serve at the present time that would not be as well served by a Roman soothsayer's chicken-gizzard. Their utility as a practical guide in determining the relative profitableness of classes may be inferred from the following tabulation of the comparative experience shown by a number of these individual lists for the same five-year period. The figures in the column marked *'low" show the loss ratio of the company having the most favorable experience, and the figures in the column marked *'high" show the loss ratio of the company having the most unfavorable experience, with each of the classes designated by numbers. The column marked "combined" shows the combined 73 74 Fire-Rating as a Science loss ratio of all the companies on the same class for the same period : Class No. I. 2. 3- 4 I 7- 8. 9 lo. II- 12- 13 14- \k \l. 19. 20. 21. 22. 23 24. 26. 27. 28. 29. 30 31 32 33 Loss Ratios Shown by Loss Ratios Individual Experience Sho wn by /^„„ bined jrience Low High Exp ,00 I. II 53 .10 2.13 54 .00 I-3I 43 .06 1.88 66 .18 1.69 50 .03 .92 60 .05 .91 60 . .19 1.05 67 .10 i^37 ^S •34 1^73 5« .12 1.32 74 .16 1.79 63 .21 1-35 44 .18 '■^ 77 .02 25 .01 2.11 I 21 .08 2.46 53 •43 4.95 97 .19 I. II 72 .04 1.02 P •33 1.50 61 .29 1.05 57 .16 1.04 50 .29 1.76 62 .18 1.03 46 •13 .86 52 •30 2.64 64 .30 1.65 .67 .22 4.46 97 •17 .67 43 .03 2.CX) 2° .10 2.16 .81 .11 1.77 .47 These classes, selected from the lists at random, show that with each and every class one company had a very low loss ratio, while another company had a loss ratio that would bring swift ruin had it not had a more favorable experience with other classes. A mere glance down the two columns marked "low" and "high" will show the utter worthlessness of the separate experience of a single company as a criterion to the average loss ratio of each class, while on the contrary, a comparison of these The Individual Classification List 75 individual experiences with the column marked "combined" shows that there is an established mean which, if known, would constitute a reliable standard for determining adequate class rates. But further examination into these individual lists reveals an inaccuracy and wastefulness of method which would destroy their reliability, even were the experience of each company broad enough to constitute a reliable criterion. At a rough estimate, one hundred and fifty companies maintain these classification lists, at a heavy expense for clerical work. During a single year these companies receive, let us say, a total of five million daily reports of policies issued, each of which contains a verbatim copy of the written portion of a policy. The necessity for determining the proper class of each daily report received requires that it be carefully scanned and its class number noted upon it, in order that it may be properly entered upon the records. This work is necessarily done in a hurried manner by a clerk or examiner who cannot possibly give much time or thought to each daily report. In many cases it is impossible to tell from the written description how the risk should be classed. In thousands of cases, from fifty to one hundred companies receive daily reports covering the same property, which, in the hurry of current necessity, are entered haphazard in any one of a dozen different classes on the ledgers of the several companies, and the same work thus mani- folded from fifty to one hundred times creates a corresponding liability to error. A loss on a single risk wrongly classified destroys the value of the records of two classes.* Another important element of unreliability in these individual lists results from the constant fluctuation of rates. The lists contain the total premiums received and the losses paid on each class, a comparison of which is supposed to reveal the loss ratio of the class. This loss ratio, however, is only useful in deter- mining the adequacy of rates; and with rates constantly changing, the standard ceases to be a standard, and tabulated experience without a standard of comparison is worthless. *In the office of a prominent insurance company a five-thousand-dollar line was recently classified as a printing-office. When a loss occurred, it was accidentally discovered that the risk belonged to an entirely different class. This single error affected the company's loss ratio with the one class twenty-five per cent, and with the other nearly one hundred per cent. 76 Fire-Rating as a Science Let us take for illustration the rates on the dwelling class, which have declined throughout a large portion of the Northwest from twenty-five to thirty-five per cent during the period named, assuming the premiums and losses on the same amount at risk to have been as follows : Year Premiums Losses 1892 $100,000 $50,000 1893 90,000 40,000 1894 80,000 45,000 1895 75,000 60,000 1896 66,000 50,000 Total $411,000 $245,000 Total loss ratio, sixty per cent. Assuming the normal loss ratio of the class to be fifty-five per cent, the average loss of sixty per cent shown by the above figures would indicate that dwellings ought to be advanced about five per cent, but if we compare the last year's premiums with the losses of that year, we find the loss ratio to be about seventy-six per cent, and that dwellings should be advanced about twenty- one per cent from current rates, hence, any attempt to fix rates from the figures shown would be met with the question. From what point shall rates be modified — from the highest point or the lowest point, or from some intermediate point? In other words, the value of the figures for quantitative reasoning is destroyed by the vacillation of one of the quantities necessary to the com- parison. Another element of unreliability in the lists of individual companies lies in the non-concurrent grouping of classes. In this respect, probably no two agree; and in the constant evolu- tion of hazards (in the absence of any common source of infor- mation), lists are in constant course of change, as determined by the judgment of classification clerks under urgent necessity for immediate action. In view of the uncertainty of grouping, the uncertainty whether a risk, even when properly grouped, will get into the group to which it belongs, and the destruction of the standard of measurement caused by rate fluctuations, the individual classifi- cation list as a basis for quantitative measurement is by several The Individual Classification List 77 degrees more crude and primitive than the farmer's fence-rail and stone; but as the latter contained the germ which has evolved into the chemist's scales which will weigh an eyelash, these indi- vidual company classification lists constitute the embryo which must ultimately evolve into a logical, uniform, and combined system for the quantitative measurement of sequential relations. Uniform and Combined Classijfication Ordinary candor compels the admission that the classification of coexistent relations found in our present tariff system consti- tutes the only feature of fire insurance which gives it the slightest right to claim that it is not a world-wide game of guess. The same degree of candor will not permit us to deny that, as a prac- tical guide in accepting or rating risks, company classification lists in severalty are worse than useless, because in their limited way they are misleading. It should be borne in mind, however, that these lists show a distinctly different phase of classification from that found in our tariff system, for the reason that they constitute the embryo of a system for establishing sequential relations. A careful study of these lists shows that, with all their imper- fections, they contain no fault that is not easily and inexpensively remediable. To co-ordinate these lists into a uniform grouping of classes and combine the individual experience of each company into grand aggregates showing the annual experience of all com- panies with each class, would require neither violation of scien- tific procedure nor departure from methods suggested rather than established through these individual classification lists. There can be no verification of sequential relations (which are the combined effect of annual fire destruction and the coexistent relations established through basis tariffs) except through uniform and combined classification. This is the statistical basis upon which fire-rating as a science of sequential measurement must rest. It would seem to be a reflection upon the intelligence and honesty of the fire underwriting community that during the past quarter of a century every effort to bring about uniform and combined classification for the purpose of establishing intelligent sequential relations should have been thwarted by a silent oppo- sition which has seemingly disdained to argue the question. It 78 Uniform and Combined Classification 79 has been charged that this opposition emanates from a belief on the part of the management of some of the larger companies that under existing conditions these companies possess advantages which would be lost by the revelation of class averages. It is hard to believe, however, that the intelligence which has brought these companies to the front could be blind to the compensating advantages which would accrue from the placing of fire insurance among the recognized and legitimate branches of commercial activity. At most, combined classification would simply establish averages derived from the experience of all. It would not unseat common sense, nor dethrone the individual judgment, which itself has been well defined as a finer and more discriminating classification. The establishment of these averages would leave even greater advantages to underwriting ability, capital, and established reputation than under existing conditions, which enable unscrupulous and plunging methods not only to upset the possibility of legitimate underwriting, but not infrequently to win a greater financial success. Greater disparities are found in the comparative success of banks, merchants, and manufacturers, than among fire insurance companies, because legitimate enter- prise gives ample scope for the qualities necessary for success. Without doubt, selfishness, inertia, and ignorance are largely responsible for the failure of fire insurance to realize the benefits of combined classification, though it would be as illogical to censure the motives of the fire underwriting community generally as to censure the community at large for its inertia in many important matters of reform which do not admit of logical dis- cussion. *' Direct complicity with human affairs is not infre- quently a hindrance to the scientific investigation of phenomena. Even the axioms of geometry would be disputed or ignored if men's passions or interests were concerned with them." The English-speaking peoples adhere to an orthography that is the despair and wonder of the world. We boast of our decimal currency, but refuse to adopt a decimal system of weights and measures, while the complacent Briton refuses to adopt the decimal system for either his currency, weights, or measures. During the slow evolution of single-entry and then of double- entry book-keeping, the English government stubbornly adhered 8o Fire- Rating as a Science to a primitive system of keeping accounts by cutting notches in sticks. It would probably be using this system yet had not a conflagration in 1884 burned up all its exchequer tallies. Inertia hath its uses, however. "The man who will not look at the new moon, out of respect to that ancient institution, the old moon," was not created in vain. Perhaps it is fortunate that combined classification was not started too soon, for a false start might have brought the system into disrepute, and it is always easier to start anew than to undo and patch up a system full of errors. To-day, however, fire insurance is in the position of the British government when its exchequer tallies were burned. Many states have destroyed our rating system, such as it is, by anti- compact laws; many others are threatening to do so, and a new start is inevitable. If we start along lines that cannot be justi- fied by scientific reasoning at every point, so much the worse for us, for we will ultimately be compelled to tear down our system and rebuild from the foundation. Class Differentiation The classification lists of some companies contain not over twenty-five classes; others as high as two hundred and fifty- classes. In the construction of a uniform list to be used by all companies, it is an important question how far differentiation ought to be carried to achieve the best results. From the most reliable data at present obtainable, it may be inferred that, excluding farm property, the two great property groups, known as mercantile and dwelling, produce about two- thirds of the fire insurance premiums received by the companies, and it would be possible to select fifteen, or at most twenty, property classes which produce ninety per cent of the total premiums of the country. It is obvious that uniform classification of these few groups would embody so nearly all property as to be a practical working basis. On the other hand, among unusual risks, we find in some cases perhaps less than a dozen establishments in the entire country. In these unimportant classes it is impossible to establish an average. They can be intelligently rated only through their resemblance in hazard to established features in established classes, and this necessitates their grouping as a miscellaneous class. Should the companies adopt uniform classification, the first step dictated by intelligence would be to classify each risk when it is rated^ and print its class number in the local tariff. This would not only save an immense amount of clerical work in company offices, but ensure the entry of each risk in its proper class on the records of every company interested. As the classifying of each risk when rated would obviate the necessity of classifying each daily report in every office, it would matter little whether the uniform classification list was long or short, complicated or sim- ple, as the necessity for consulting it in company offices would cease. 8i 82 Fire-Rating as a Science Again, certain classes, while seemingly unimportant in com- parison with the aggregate business of the country, are important in certain sections, as cotton risks in the South, grain-elevators and flour-mills in the North, and textile-mills in the East. These classes, while of minor importance in the aggregate, are entitled to careful classification as being important sectional industries. There is an intelligent mean between the two extremes of differ- entiation which can be reached through conference, though the objections to a highly differentiated list vanish in view of the fact that when one list is used by all companies it will become possible to classify each risk when rated and print its class number in the local tariff. '*The continuous equilibration of every organism with its environments is an ever-present necessity, ' ' however, and it may be expected that the necessities of the industry will exact an ever-increasing nicety of distinction. It is as impossible to formulate a classification list which will last forever and a day as it has been found to formulate a consti- tutional government through a written instrument which will not need to be changed to meet changing conditions. It is safe to assume, however, that the more complete the differentiation at the outset, the fewer the patches that will be needed in future. Rate Standard With all companies maintaining uniform classification, the loss ratio derived from a tabulation of their experience would not be the true loss ratio if rates had fluctuated during the period tabulated. With the equalization of class rates liable to result from combined classification, the ascertainment of accurate ratios becomes more important in proportion as class rates gravitate toward a uniform margin of profit, which means a small margin. A comparison of premiums and losses with the aggregate amount at risk would show the average rate and average loss to risk for each class, but under present conditions neither of these ratios would be of any service in determining the important question, How much shall rates on a given class be raised or lowered to maintain a reasonably uniform margin of profit year after year, and equilibrate the profits of each class with the profits of other classes? All science recognizes the fact that quantitative meas- urement of relations must be made by the aid of some recognized standard of comparison, and fire-rating as a science would not be exempt from this law. The preceding question can be answered in but one way. Our tariffs of coexistent relations must be allowed to remain coexistent as a fixed and permanent standard of comparison. No matter how often or how widely our rates, may be changed with reference to this standard, the standard itself must be inviolable. This does not signify that the standard should not be modified to embrace the innovations in hazard which will never cease, for these innovations are the results of a slow evolution which will never appreciably affect the accuracy of statistical aggregates. To stand still in fire insurance is to become obsolete. A standard tariff should be instinct with life-growth and adapta- bility. The whole idea of a rating science based upon the law of rhythm means mobility. There can be no finality in standard tariffs, for they must be adaptable to future exigencies. On the 83 84 Fire-Rating as a Science other hand, local tariffs constructed from these standards must not be changed to suit whims or exactions of individuals or com- munities; they must reflect existing conditions, and be changed only as actual alterations occur in the physical hazard of each risk. In this scientific necessity for fixed standards, without which quantitative measurement is impossible, lies deliverance from most of the difficulties arising from our persistent attempts to ignore this necessity. Theoretically, we make permanent rates based upon a claimed average class experience. Practically, rates are not and never can be permanent, and as a matter of fact we know little more of our combined class experience than the people who buy our policies. Manufacturers universally recognize the necessity for prompt and systematic changes in their selling prices by percent- age changes which will not disturb or disorganize their published price-lists. In our local tariffs we have by far the most expen- sive and extensive price-lists of any industry in the world, and yet we have steadily refused to recognize any system for changing our selling price which did not make it necessary to destroy and re-create our price-lists. While in theory we have steadily ignored the possibility of any system of percentage rate-changes, com- petition is constantly forcing us into percentage changes in all parts of the country, until they have become the rule rather than the exception. It is admitted that physical changes in risks will never cease, and that constant revision of local tariffs will always be necessary to meet these changes ; but aside from this revision of local tariffs, made necessary by actual changes in physical hazard, there is an equally constant necessity, arising from the exigencies of competition, which makes sweeping rate changes in the selling prices of indemnity necessary in classes, and occa- sionally in all classes, in towns, cities, or states. When we do make a percentage advance, people who by persistent jewing or bullying have secured competitive rates are advanced less than people who have paid tariff rates, without question; but aside from this injustice resulting from our percentage changes, our tariffs are disorganized by such changes, relations are destroyed, and every few years a complete rerating of a city or state becomes necessary, to get out of the chaos created by disintegrating fac- Rate Standard 85 tors which again begin their swift work as soon as new rates are made. All these illogical results of an illogical system which refuses to recognize the necessity for systematic rate modifications might be avoided through local tariffs containing estimated relations of hazard to be used as a basis for systematic rate modifications by percentages ; for percentage changes from standards would affect all policy holders equitably, instead of rewarding the rate cheap- ener at the expense of other people. In this simple expedient lies the panacea for our diseased rates, but its success depends upon two things: First, uniform classification by all partici- pating companies; second, the appearance of the class number of each risk in local tariff as a means of concerted rate modifi- cations. The second, however, is in a manner independent of the first. Whether we adopt uniform and combined classification or not^ there seems to be no reason why the companies should not adopt a classification for rating purposes^ and publish all future local tariffs with the class number opposite each risk. This would at least give .them flexible rates, which could be changed by percentage announcements without destroying tariffs of coexistent relations established at so great an expenditure of time and money. It has been argued that the public has no more right to know the cost of our goods than we have to know the cost price of other people's goods; but we are quasi-public servants; our cost as a whole is published to the world at the end of each year. The public learns from many sources that on some classes we make large profits, and on others large and constant losses, and each man suspects that he is in the class that is helping to pay for other people's insurance. Suspicions of this sort are the natural result of a system in which injustice is not only inherent but unavoidable. Under any system admitting of prompt rate changes, profits on all classes would have a tendency toward uniformity; and nothing could do more to allay the suspicions which create bargain-hunting for fire indemnity than to let the world know just what our profits are on each class. We have far less to fear from an honest publicity than from the suspicions generated in the public mind by an ignorance of the facts. This brings us to the consideration of the question as to what basis should be adopted as the rate standard. What Shall the Standard Be? In the light of experience, every fire underwriter must realize, whether he admit it or not, that fire rates must always be in con- stant process of adjustment. Our past treatment of the rating problem has been like that of a physicist who should attempt to deal with a fluid by the law of solids. The object of scientific rating might be stated as the main- tenance of logical coexistent relations as a permanent basis or standard for the measurement of the sequential relations found in the form of wave motion known as the annual-cost wave, and the modification of this annual-cost wave through an ancillary rate wave into dimensions that will be endurable to purchasers of indemnity. The mariner who is tossed skyward on the crest of an approaching wave, to be plunged into the gulf as the wave recedes, knows that there is a sea-level which is the average of all the waves, and the sextant with which he takes his reckonings is constructed to maintain a parallel with the sea-level. Stand- ard estimates of hazard based upon, say, a ten-year experience in fire insurance would be to the annual-cost wave what tLe sea-level is to its storm-tossed surface — a certain base from which to take our bearings ; but the question is. What is the natural base from which we must reckon? As the sailor takes his bearings from the sextant while it is borne alternately above and below the sea- surface, so we can take our bearings from any given level above or below cost, or at cost itself. It is only necessary to assume a level and maintain it as a permanent standard of reckoning, be it above, below, or at the actual sea-level of the average cost com- posed of losses and expenses. For practical purposes, as a standard of comparison, exact- ness is not essential ; for as before stated, all standards are arbi- trary. Even if in the attempt to establish cost the basis of one class were slightly above and another slightly below cost, the 86 What Shall the Standard Be? 87 basis in either case would answer equally well, either permanently or temporarily, as a standard of comparison, bearing in mind that the object of this standard is simply to determine relations, to learn at stated periods what percentage we ought to raise or lower rates as compared with this standard in order to maintain sequential relations between class rates and their annual-cost wave. While the result would be the same whether we select an arbi- trary standard or cost itself, there are strong reasons why the standard selected should as nearly as possible be cost itself, if we keep in view the fact that we are simply seeking an average line as a standard of comparison. With the present trend of legislation, the publication of tariff rates will probably be interdicted in every western and southern state in the early future, and the companies have before them the alternative of giving up all further attempts to establish rates, or of devising some plan through which they can maintain statistical landmarks which will not be in violation of statutory law. The publication of local tariffs of estimated cost relations based upon the aggregate experience of all or of any considerable number of companies could not be construed as a violation of the letter or spirit of existing statutory law in any state. There could be no agreement as to securing these estimates as rates^ because being simply estimates of coexistent relations they would not in any sense be rates. Any agreement among the companies would necessarily have to be an agreement regarding established ratios of profit on these estimates of cost relations; and with informa- tion based upon actual statistics, it is questionable whether agreements would be necessary. It happens that in most of the states affected by anti-compact laws the aggregate business is made up of a small number of classes. On a rough estimate, leaving out farm risks, over nine-tenths of all the insurable property in Iowa, Kansas, Nebraska, North and South Dakota, and Illinois (outside of Chicago) consists of dwellings, mercantile risks, and grain. In Michigan, Wisconsin, and Minnesota, the same proportion would be found to consist in dwellings, mercan- tile risks, and lumber. In Texas, Arkansas, and many other southern states, dwellings, mercantile risks, cotton, and lumber. 8 8 Fire-Rating as a Science In Kentucky and Tennessee, dwellings, mercantile risks, tobacco, and whisky. In fact, in the entire western country, Ohio and Indiana, as manufacturing states, are probably the only ones which contain more than ten to fifteen per cent of insurable prop- erty outside of the classes named, and it might be said that throughout the Western and Southern states practically all insur- able property would be embraced in about twenty classes. The publication of local tariff estimates of coexistent relations, embracing these classes alone, would establish for the first time a reliable basis of statistical information, and the announcement by a single prominent company to its agents of its minimum profit on a few important classes would practically establish a minimum rate for nine-tenths of the business in the Mississippi Valley, without other definite agreement. It is true, however, that in considering fire-rating as a science it is necessary to take into consideration every class that pro- duces a sufficient volume of premiums to establish an average, and it is proper to inquire whether we can construct estimates of cost relations with an approximation sufficiently close to the truth to entitle them to be so called. The Establishment of Cost Estimates Theoretically, there is but one average cost for each class in the United States. Practically, fire insurance is not transacting business in the United States, but in forty-five states, each of which insists upon being treated as an independent sovereignty. Even if state lines could be wiped out, the loss ratio of different sections, or even different parts of the same state, would differ on account of climatic and social conditions; but it is, perhaps, a good thing from the standpoint of system that state boundaries do exist, as these boundaries divide the country into geographical areas with similar characteristics, thus enabling us through state basis schedules to establish coexistent relations in hazard with reference to space areas having comparatively homogeneous con- ditions. Basis tariffs are in one sense classified analyses of fire hazard. These analyses as to form and method should be uniform for the entire country. In other words, there is an obvious necessity for a national basis tariff as a central standard of comparison in bringing about uniformity of analysis and arrangement, and pre- serving consistent relations among state tariffs to each other. In this way only can consistency be maintained in basis rates, charges, credits, standards of construction, protection, etc., in each state tariff with relation to other state tariffs. Unfortu- nately, the Universal Schedule, for reasons stated, is not available for this purpose. The real work of constructing a national schedule of coexistent relations remains to be done; and in con- structing this as the basis of a scientific system of rating, it will be necessary to bear in mind that it is too late to change the structural nature of what has been a natural and inevitable growth in an activity seeking to adapt itself to its environments. Science does not destroy, but conserves and utilizes all available material. In the construction of this national tariff, an exact estimate in 89 90 Fire-Rating as a Science dollars and cents of either basis rate, charge, or credit is not a sine qua non^ for the establishment of logical coexistent relations is the real end sought. These relations being once established in a fundamental tariff, it follows that similar relations will ensue in the state tariffs constructed by percentage modifications of it. The construction of state tariffs from this central tariff would consist in such percentage change of each charge, credit, and basis rate as would give coexistent relations reasonably close to average state cost of each class. State tariffs built in this way would in turn become the stand- ard of relations for each state, and in like manner it would be immaterial whether they were too high or too low, because the function of these tariffs would be to establish reasonably true rate relations among individual risks in local tariffs. Finally, local tariffs constructed from these state tariffs, being an effect, would necessarily show similar relations, and they would in turn become the standard from which class rates could be changed by percent- age announcements from the companies as determined by past experience with each class for any given period. It will be noted that this does not give us established rates; on the contrary, as a system it permits the abolishment of the overworked and unpopular word *'rates" from our vocabulary. What we have really established is a series of standards of coexistent relations to be used as a basis for quantitative reason- ing with reference to the relations of sequence found in class loss waves; in other words, without violent organic change in existing methods, which are the results of a slow process of evolution, we make the same step forward that resulted from the farmer's experiment with the fence-rail as a measure of weight, and thus lift fire-rating to the plane of quantitative measurement, which is the aim of all science. Relations Between National and State Tariffs of Cost Estimates The preceding chapters may leave the reader in the dark as to the real functions of and relations between the national and state tariffs suggested. He will naturally say, You construct a general tariff as a standard from which to establish relations among state tariffs, which in turn become the standards for establishing relations among cost estimates in local tariffs. These things are simply a series of stratified assumptions resting upon indefinite data in the first instance. Why not guess at the rates at once, and save all this trip around Robin Hood's barn? In answer, it is proper to reiterate that all reasoning is a com- parison of relations, and that in the absence of established fact the reasoning process must start from some fundamental assump- tion as a working hypothesis. The national tariff, as this assump- tion, would be a series of estimates of the analyzed parts of hazard found in each class; these estimates establish coexistent relations among the parts known as charges, credits, and basis rate, as well as of class to class. This central tariff would constitute a standard for establishing state tariffs bearing consistent relations with each other through percentage modifications of the central tariff. These state tariffs in turn would thus become standards for establishing similar relations among classes and individual risks in the limited geographical areas known as states. We thus obtain a series of orderly coexistent relations among charges, credits, and basis rates, with reference to risks, classes, and states, as an instrumentality for the construction of local tariffs of estimated cost relations, which in turn are simply a sequence of correlated effects known as individual cost estimates, produced by a system of correlated causes known as state tariffs. Up to this point the only end sought has been to preserve logical 91 92 Fire-Rating as a Science relations of coexistence through estimate and comparison of a series of standards. With these standards established, each company's records at the end of the year would show : * 1. The total footings of the average cost column. (Standard for the year.) 2. The total footings of premiums actually received at rates charged. (Income.) 3. Total losses and expenses; i. e., actual cost of carrying the year's business. (Outgo.) We thus obtain from the footings of cost column a standard for the year with which to compare income and outgo ^ a self -creating annual standard, derived from permanent local cost estimates, which strictly conforms to the scientific definition of a standard. (See chapter on "Standards.") This standard enables us at the end of each year to compare and establish true relations which will qualify us to determine intelligently what changes should be made in our selling prices. In other words, we would for the first time possess reliable data from which to take our annual reckonings and modify our selling prices intelligently to meet existing conditions. Following out this chain of reasoning, it is obvious that we establish a series of sequential relations through a system of per- manent coexistent relations assumed as a standard of comparison. This establishment of correct relations is the real end of the rating function, as it is the end of all reasoning, quantitative or qualitative, inductive or deductive. It does not follow that rates need to be changed every year, in every state, or for every class. It is not necessary that each class should show exactly the same margin of profit each year as every other class. The end sought is to secure the ability to regulate the relationship between cost and selling price intelligently. With this relationship constantly ascertainable through standards of comparison, we would have a latitude of discretion in modifying rates that we do not enjoy with present rating system, under which every change in rates destroys the reliability of our ratios, and creates appearances *This presupposes that daily reports will show the cost of each risk as given in local tariff, as well as the actual premium paid, and that these two amounts will be entered in separate columns in the companies' registers. National and State Tariffs of Cost Estimates 93 illusive alike to the public and ourselves. Reasonable uniform- ity is all that can in reason be expected ; nor does it follow that changes should be made on the experience of single years. There is an underlying logic with relation to sequence as well as coex- istence. Classes composed of few risks of large value naturally have large waves in loss ratio. Cost estimates of such classes should be founded on an experience of not less than ten to fifteen years, and rate changes made from the experience of a term cor- responding with the relation between the amount of single fire hazard and the total premiums. In other words, wide loss waves would tend to create long rate waves. It is in the important competitive classes, such as dwellings and mercantile risks, where rate modifications would become necessary most frequently. When we have obtained the ability to intelligently control rate waves, we will be free to exercise intelligence in their control. The Comity of Fire Insurance No analytical consideration of the rating problem can over- look the relations of loss and rate waves to time and space, as well as to individuals and property groups. While theoretically classification recognizes each separate property class as a distinct entity, and every company keeps a ledger account of debits and credits with each class, precisely as a merchant keeps a ledger account with each customer, in practice this complete segregation cannot be rigidly enforced without hardship. Fire insurance is based upon the divine injunction, "Bear ye one another's burdens," and this implies a vast network of comity permeating time, space, property classes, individuals, and commu- nities. This comity compels a modification of the inexorable results of classified experience precisely as equity is necessary to temper the rigors of the law. In bearing each other's burdens all owe a common obligation to each, and each to all. Whether we consider the artificial division of space into state areas, of time into years, or of property into classes, the obligation to bear each other's burdens is as strong and as undeniable as the obligation of individual to individual, for this obligation is the warp and woof of all insurance. The measurement of comity from this broad point of view is beyond exact human prevision. It lies in the domain of ethics, and is recognized by society and the world in every great calamity which causes a destruction of property too great to be borne by limited communities. Under existing condi- tions it has been impossible to establish any canons for the reason- able control of these vast ethical obligations in fire insurance, but in the light of the theory that fire-rating has for its end the intel- ligent control of a rate wave ancillary to the wave of cost, the possibility of an equitable control of these broad interrelations, in which individual rights are subordinate to the rights of com- munities, becomes at once apparent. In considering this possi- bility, we must take things as they exist in their relations to each 94 The Comity of Fire Insurance 95 other, for in this, as in everything else in the problem of fire- rating, we are dealing with relations. At Decatur, Illinois, there are two industrial establishments, one manufacturing rings for hogs' noses to prevent their root- ing, and the other a patented device to insure the planting of corn at regular intervals, known as the '* check-rower. " At Niagara Falls there is an establishment for the manufacture of carborundum. Each of these "plants" is probably the only one of its kind in the United States, probably in the world. The first is a cold-metal worker with japanning, the second a cold-metal worker with dipping, and each similar in the main features of hazard to well-established groups of metal workers. The third is similar to the hazard of, say, a tile fac- tory. A comparison of the main features of hazard in each of these risks with other more common industries makes the task of consistent rating by analogy an easy one ; but each of these risks stands alone — to place it in a class by itself would be to deprive it of the benefits of insurance. There are thousands of similar unclassed risks throughout the country which, from the standpoint of comity, would be outlawed were they not grouped into a forced alliance as a miscellaneous class, and made to share each other's fortunes, with relation to the hazard of fire. One may be rated at three per cent, another at fifty cents, as analogy or the analysis of hazard may determine, but this relation in inherent hazard being established, it is clear that a community of interest is better than for each to stand alone, which would be tantamount to dispensing with insurance altogether. Again, when we come to risks numerous enough to group into classes, we find many groups composed of so few risks as to be little nearer the law of average than the unique establishments above named. An examination of the statistics made up from the combined experience of two score companies shows that nearly one-half of the classes important enough to be grouped do not yield in their aggregate premiums one per cent of the total premiums received from all classes. It would be far better for all these groups, however divergent their hazard and rates, to be thrown into one miscellaneous class in which they could share each other's losses, than for each group 96 Fire-Rating as a Science to be compelled to pay its own losses, always provided that their rates were apportioned to show reasonably true relations to each other according to relative hazard. A further analysis of the relative importance of classes, as shown by the premiums they yield, reveals the fact that some classes yielding large premiums are composed of a small number of risks where large values are concentrated. This applies to breweries, distilleries, terminal elevators, packing-houses, flour- ing-mills, wholesale lumber-yards, opera-houses, oatmeal-mills, cotton-compresses, and many other classes. The slightest con- sideration of the question would convince any intelligent mind that the aggregate premiums of any one of these classes in any one state would be too small to establish reliable averages, or, considered from another standpoint, the loss wave would be sub- ject to fluctuations so violent that it could not be reduced to endurable proportions. State the question to a property owner in any of these classes, whether he would rather share in the loss ratio of his state or in the loss ratio of similar property through- out the country, and it would not take him long to decide that it would be to his advantage to share in the national loss ratio of his class. On the other hand, the numerical majority of classes consists of numerous risks of comparatively small value, as dwellings, stables, mercantile risks, hotels, boarding-houses, churches, schools, public buildings, retail lumber-yards, saloons, restau- rants, printing-offices, blacksmith and carpenter shops, bakeries, etc. Leaving out the liability of these classes to sweeping con- flagrations, the average value exposed to one fire as compared to total premiums of each class is so small that these classes may run along for years with a cost wave that does not exceed endur- able proportions. It is true that the average value of churches, schools, and public buildings is relatively much larger than that of the other classes named, but in view of the fact that they are, as a rule, isolated, and not so liable to the hazard of municipal conflagrations, the relative amount exposed to one fire would not differ greatly from that of other classes. Bearing in mind the facts stated, it will be readily appreciated why separate basis tariffs are maintained for each state in rating some classes while The Comity of Fire Insurance 97 in rating other classes state lines are ignored, and the same tariff used in many states. This is particularly the case with industrials connected with the staple products of geographical sections. There is ostensibly but one tariff in the Northwest for fiouring- mills, elevators, packing-houses, and wholesale lumber-yards, and in the South for cotton, sugar, tobacco, and whisky risks. In this fact we have unconsciously recognized the law of the relation between the average amount at risk and total premiums, and in this way have established interstate comity, under which risks of these classes are made to share in the national loss ratio of their class instead of their state loss ratio. But when we care- fully consider the classes ostensibly rated on state averages, we find that on account of their mutual exposure, they are about as liable as the other classes to destructive state loss waves, result- ing from municipal conflagrations in the minor cities, which would make an intolerable addition to the rates of any given class or of all classes, if each state's rate wave were made to follow its loss wave without modification. No year passes in which a municipal con- flagration does not more than double the loss ratio of some state. These facts clearly establish the inference that public welfare demands an interacting system of comity which will distribute the crests of dangerous annual-cost waves so widely over space, time, and property values that these waves will be reduced to endurable proportions. This would require the establishment of formulas determining what are tolerable additions to rate waves, and this once established, the excess of class or state loss ratio could be methodically spread as a small but uniform addition to the rates of all property. Taking the classes where value exposed to single conflagration is large compared with the aggregate pre- miums, the total premiums on packing-houses, for instance, for a five-year period, may be a million dollars. One total loss on a packing establishment would double the average rate for the entire period. This would be an intolerable expense for the industry; and if the companies should attempt to collect the increase through a rate advance, it would result in the business being lost to com- petitors who do not pay any regard to averages or experience. Let us suppose that a twenty-five per cent increase in packing- house rates be tolerable for one year, or to put it in another way, 98 Fire-Ratlng as a Science that if this increase were maintained longer than a year it would generate an undue competition for the class. This would leave seven hundred and fifty thousand dollars to distribute in the next year's average basis rate on all classes throughout the country, which would amount to about one-half of one per cent; in other words, a seventy-five per cent increase in packing-house rates would be changed into a one-half of one per cent increase in the aggregate premiums of the country. Applying this principle to state ratios as developed by sweep- ing municipal conflagrations in the minor cities, we find that if the destruction of a city, say in North Dakota, should give an aggregate loss of three million dollars (equivalent to possibly three years' premiums of the entire state) this would require an advance of three hundred per cent in rates for the ensuing year, or one hundred per cent for three years. Either of these increases in the state rate wave would be intolerable, and would simply give rate-cutting competitors a chance to pick up all the desir- able business of the state, which they would do, on the theory that lightning does not strike twice in the same place. Let us suppose the maximum endurable rate increase for one year in any one state to be twenty-five per cent. By shifting the remainder of this loss on the broad shoulders of all insurable property of the country, it would require two million two hundred and fifty thousand dollars to be added to the national average rate, or say an advance of less than one and one-half per cent in the next year's rates in all states. In this way a system of interstate and interclass comity would be established which would appeal to the common sense and self-interest of every citizen, because the logic of shifting an unbearable burden from classes or states on the community is as apparent as the necessity for shifting a similar burden from the individual to his property-class or state. This principle of comity, while not recognized by any logical system in fire insurance, is forced upon it by necessity. We have made seemingly no attempt to analyze or keep track of it through any system of interclass or interstate accounting. When a state or class has experienced a tidal wave of conflagration, or series of such waves, we have either made an unendurable rate advance and lost business to the rate-cutters, or dumped the The Comity of Fire Insurance 99 excess into our national average, and kept no further track of it. In a year or two it is forgotten, and tlie state or class that under any system of suspended accounts would be the largest debtor to our national indemnity fund becomes the most persistent in nagging fire insurance through inimical laws, and the most per- sistent in demanding lower rates. Under scientific rating, it would be possible to deal with phe- nomena of this kind intelligently and justly through state and class accounts. Old balances would be kept track of and col- lected as fast as it became possible without creating intolerable rate waves, or generating rate-cutting competition in states or classes. In this way, true comity could be maintained in lieu of the no-system of the past, which has at times compelled fire insurance to rob Peter to pay Paul, and at other times forced it to submit to be robbed by both. From its concrete aspect, fire-rating establishes coexistent relations through estimate; from its abstract aspect, its function should be to maintain sequential relations among classes and states through uniform and combined classification^ and finally in its broadest socialistic aspect, it is its duty -to temper unbearable waves of conflagration to people's ability to pay, through national statistics which keep track of these wave excesses, and in the end exact compensation as far as the beneficiaries are able, restoring deferred payments to the fund from which they came in order that the community at large may in the end be reimbursed through rate reductions. This of course can be done only through national statistics, and the maintenance of accounts with states and classes. Probably fire insurance has not evolved sufficiently to even contemplate this, its ultimate and noblest function — a function which would command the respect and admiration of the world, and place it in the forefront among recognized modern activities. Meanwhile, no harm will come from pointing out this broadly humanitarian task, which awaits his industry, to the man whose soul is engaged with nickel charges for ash-cans and sawdust spittoons, things which could be more promptly regulated by an interview between the inspector and owner than through a tariff catechism which usurps the duties of the janitor and chambermaid. The Law of Relation Between Net Under- writing Profit and Class Cost Waves. In an earlier chapter it was stated that the service rendered by capital in the transaction of fire insurance consisted in its assumption of risk^ and that this risk increased in proportion to the width of vibration found in the cost wave of each class. This leads to the inference that capital does not render the same amount of service to each and every property class, and that it is entitled to a larger net underwriting profit in assuming the wave- risk found in some classes than in others. With our present inflexible tariff system, it would be impossible to change rates with sufficient promptness or precision to control the net under- writing profit on property classes, but the fact remains that igno- rance of or at least indifference to this logical law of class profits has contributed liberally to the destruction of morale in the industry of fire insurance. It should be borne in mind that this law has nothing to do with agents' commissions, for a class with a small loss wave may require more labor on the part of agents than a class with a large wave. The character of the service rendered by capital in assum- ing risk is entirely distinct from the service rendered by agents. Through a general indifference to the inexorable logic of this law, preferred classes have been generated, and a traffic created in these classes, as disastrous in its moral effect upon the industry as the liquor traffic has been in its influence upon public morals. As the liquor traffic creates the "saloon influence" in politics, so the traffic in preferred classes has created a malefic influence in fire insurance that has enriched numerous corporations which, under the pretense of transacting fire insurance, have confined themselves to the classes with small loss waves and large profits. To seek the minimum of risk for the maximum of profit is not in itself culpable, but to accomplish their ends these pseudo-insurance Net Underwriting Profit and Class Cost Waves loi companies have systematically appealed to the selfish instincts of agents, and sought to create prejudice in the public mind by con- stant misrepresentation of the companies really engaged in fire insurance. These pseudo-companies owe their existence to pre- ferred classes, which are invariably classes with small loss waves. If we select the dwelling class as the most important of the pre- ferred classes, we find it to consist of small detached risks, with a loss wave which, in width of vibration year after year, is incon- sequential. Under the law stated, the services of capital in assuming the risk of this class have been, and always will be, cor- respondingly small, and the wage of capital should have been constantly kept so low as not to attract special competition to the class. Had the law of maintaining class profits to corre- spond with width of vibration in loss waves been systematically observed, there would be no preferred-class companies in exist- ence to-day, and the business these companies have been able to secure by fouling the nest of fire insurance would never have left the books of real insurance companies. It does not follow that rates on preferred classes might not have been maintained high enough to justify a commission to agents adequate to the greater service they render in securing these classes, but by maintaining the rates that made these classes preferred, and not paying agents for preferred services, the preferred-class traffic was generated, with its long train of evils. The inconsistency of capital demand- ing a maximum wage for minimum service, on its own part, while denying the same principle as applicable to the services of agents, is the result of ignoring a logical formula as simple as a syllogism. While this inconsistency was stubbornly maintained year after year in the treatment of classes with small waves, on the other hand classes noted for their tremendous waves were carried year after year at cost or less. Where insurance capital assumed the largest risk, and was entitled to the largest wage, it has contented itself with rendering its service for nothing, and in many classes has actually paid a bonus for the privilege of rendering this ser- vice to large corporations and trusts, who have repaid the mis- taken generosity of fire insurance capital by systematically fomenting adverse legislation. In many of these classes the wave of destruction is so wide I02 Fire- Rating as a Science that fire insurance capital, as a whole, assumes the risk of a wave that approximates the full value of all property in the class. Under the law stated, these classes should pay fire insurance capital in proportion to the wave dimensions assumed, and for many of these classes a net underwriting profit of fifty or even one hundred per cent would not be inadequate, yet fire insurance capital has rendered its service to these classes as a free gift. The enormous aggregation of value in many individual risks of these classes is such that they cannot be insured without ex- hausting the market of indemnity, yet we are regaled with the spectacle of companies climbing over each other for a line on these colossal aggregations of values as if there were not enough to go around, while some broker representing a few obscure companies, by simply bidding for the risk, is able to cause an epidemic of unreason on the part of local agents willing to sacrifice their companies to save their badly crippled commissions. Fire insurance has suffered untold evils from its ignorance of the law that the service rendered by capital is commensurate with width of vibration in class waves. It has nourished preferred class companies, sown the seeds of demoralization among its agents, catered to powerful trusts and corporations, who have repaid it by using their legislative lobbies to concoct laws against fire insurance, all of which goes to prove that it is not well to systematically ignore a natural law. The Relations of Fire Insurance to Chance and Probabilities. " We deal in probabilities, not certainties, and the laws of chance form the basis of our business." Mimoires of an Insurance Man, In its popular sense, chance is defined as "a supposed agent or mode of activity not governed by law or purpose, also the operation or effect of such agent." To this definition is added the explanation that there is no such thing as chance. In the light of this definition, the preceding dictum can only be construed as an assertion that the laws of a supposed something which has neither laws nor existence, form the basis of fire insurance. Waiving this double-barreled Hiber- nicism, if we again turn our attention to the dictionary, we shall find chance further defined as "an event not calculated upon." In view of the immense amount of statistical calculation in fire insurance, and that in theory at least its income is adjusted to outgo upon this calculation, we must again infer from the asser- tion of **an Insurance man," that fire insurance exists by cal- culating upon "events not calculated upon." In its scientific sense, chance is further defined as synonomous with probability and will be considered in this sense in connection with that word. Taken as a whole, the dictum of two lines above quoted, is a fair sample of the loose use of words entering into the unsupported assertions which form so large a portion of fire insurance pol- emics. It is probable that in any assemblage of fire underwriters there would be as much difficulty experienced in defining the relations of fire insurance to chance as in defining its relations to science. A true understanding of both relations is of equal importance to the future of the industry, for nothing has done 103 I04 Fire-Rating as a Science more to place fire insurance in an odious light before the com- munity than the prevalent opinion — by no means confined to the outside public — that it is a form of gambling. If fire insurance is chance, it cannot be consistently classified in the public mind or dealt with by the popular will, except along with lotteries and other gambling devices. With this conception of its nature, it is idle to expect that it will ever stand in a more favorable light with the masses who make our laws. As human needs or desires constitute the store of latent energy from which every form of industrial activity emanates, it is perti- nent to consider the respective motives which generate gambling and insurance. These motives might be said to lie at the oppo- site poles of necessity. A fundamental need of every healthy mind is relief from monotony, for, like the body, the mind becomes cramped from remaining too long in one position. Excitement of some kind is as necessary to our mental Men ^tre as exercise to bodily health. Some minds are so constituted as to find relaxation in the pursuit of a hobby, but the masses find relief from the monotony of existence in divers ways, which, when analyzed, resolve themselves into objective and subjective, objective, when diversion is sought by witnessing the dramatic play of fortune with others, as in novels, plays, and the spectacle of athletic contests; subjective, when life is intensified by taking personal chances as in war, the chase, gambling, specu- lation, or participation in games of chance, skill or strength in which there is more or less hazard of life, limb, or property. All these things are vents for the gambling spirit within us, which seeks diversion by pitting victory against defeat — they create what might be called a form of emotional wave motion. On the other hand, there is neither excitement nor pleasure to be obtained from the possibility of death or impoverishment by fire. There are no alternations comparable to wave motion in a settled dread of calamity, for the constant apprehension of misfortune constitutes in itself an unendurable form of monot- ony — an absence of healthful mental wave motion, and in this monotony of apprehension, we find the motive which generates the necessity for insurance. From this point of view, it is obvious that insurance and gambling as activities, are generated by human Fire Insurance to Chance and Probabilities 105 needs, diametrically different, and while there may be a resem- blance in method between a gambling device and the transaction of insurance, the resemblance is purely superficial. The lottery company itself takes no chance, but thrives from the sale of chance to others. The insurance company sells exemption from chance, which it can do with safety under the law of average. The difference between the lottery ticket-holder and the insurance policy-holder is, that the former buys chance while the latter purchases immunity from chance. With this explanation it is proper to investigate the relations of fire insurance to the uncertainty called chance, viewing fire destruction as a form of wave motion. On page 40, the law of the wave of fire destruction was stated in the following language: " Waves of fire destruction tend toward reduced width of vibration in proportion as hazard is segregated into smaller unexposed values." In this chapter it was shown that the range of the wave of destruction lies between nothing and entire destruction, or (meas- ured by percentage), between nothing and one hundred per cent of value. It was also stated that the possibility of waves approach- ing the maximum was the cause that created the need for fire in- surance on the part of owners. It was further shown that the companies under the law stated were able through the device of maximum lines to disperse and reduce hazard with relation to their own capital, while relieving the owner of all chance. With the expansion in volume at risk and dispersion of hazard with relation to this volume, the wave of aggregate fire destruction in the United States has tended toward reduced width of vibration, until (as will be shown by diagrams in succeeding chapters) the wave fluctu- ation has settled down within a range of ten to fifteen points above and below the mean line or national average rate of one dollar per hundred. This is certainly a long step in eliminating chance, when we reflect that for long periods of time, insurance capital as a whole has modified a destructive tidal wave of ten thousand points as regards the owner into a duck-pond ripple of twenty-five points as regards itself. In doing this, it may be said that fire insurance has obliterated chance so far as the io6 Fire-Rating as a Science owner is concerned, and, so far as itself is concerned, has re- duced it to a point where it ceases to be chance. In other words, taking a situation where uncertainty was a portentous and con- stant whole, fire insurance has with a residuum of about one- fortieth of one per cent, transmuted this uncertainty into cer- tainty for all concerned. The chance, if any, found in fire insurance, must be sought in its methods of measuring fire hazard, for in other respects it is as free from chance as other callings. It has been shown that this measurement of hazard consists in the establishment and maintenance of true relations of two kinds, and it is proper to consider these separately in order to determine the degree of chance, if any, in each. Coexistent relations are found in the factors which compose our tariff system and in the specific rates created by the application of tariffs. Granting that the charges, credits, and basis rates, which make up the rate of every rated risk, must to a large extent be established by estimates based upon experience ; granting that we can never have a more definite basis of judgment than combined experience, the fact remains that if we leave out the disturbing effects of personal influences as found in competition and legislation, the element of chance does not appear to a greater degree in the process of measuring fire hazard than it appears in every other calling. It might be added that in respect to coexistent tariff relations, the factors of causation are more logically correlated than in other forms of industrial activity, because in the process of establishing these relations, analysis is carried further, and closer attention paid to consistency. Hazard is minutely dissected into its ele- ments and in appraising these elements which are combined in individual rates, we reach, under an established law of logic, the nearest possible approach to truth. This law, known as the law of error, is stated by Gauss in the following language : "Partly from experience and partly from a priori considerations, we may readily express the comparative probability of errors of various magni- tude, and lay down certain conditions to which the law will certainly conform. " It may be fairly assumed as a first principle to guide us that large errors will be far less frequent and probable than small ones. We know Fire Insurance to Chance and Probabilities 107 that very large errors are almost impossible, so that the probability must rapidly decrease as the amount of the error increases. The second prin- ciple is that positive and negative, errors will be equally Probable, which may certainly be assumed because we are supposed to be devoid of any knowledge as to the causes of residual errors."* Under this law, it is obvious that errors of judgment in estab- lishing the factors of the individual rate tend to offset each other and produce a mean which lies closer to the truth than any mere de novo guess in each individual rate as a whole. It is claimed that the merchant knows exactly what each specific article of merchandise costs him, while fire insurance does not, — that it can only know what an aggregate of a thousand or more risks cost, and that it is pure chance as to which of these risks it will have to pay for. As this really constitutes the mythical chance in which fire insurance is supposed to differ from com- merce and manufactures, and this difference has done much to create the supposition, it seems proper for once to inquire whether there is more or less of chance in this, than is found in othei activities. Depreciation, as is well known, plays an important part in every branch of commerce, and it is especially in evidence among retailers. Every adjuster knows how important depreci- ation is among small dealers, and bargain counter sales and "bar- gain days" in large establishments show how important it is with them. Let us suppose a clothing merchant buys a thousand coats. He knows that under the laws of average there is a reasonable certainty that one or more of these coats will be ruined by mouse, moth, or other cause ; in other words, that there is a certain life-expectancy even among ready-made coats. Some will be damaged by the wear and tear of handling; others will be left in stock by changing fashions; in fine, among these thousand coats there is a hazard of depreciation less in degree, perhaps, but similar in nature to the hazard of fire destruction which confronts the company insuring one thousand risks. Scientifically speak- ing, it might be said that depreciation is largely composed of the form of slow combustion known as oxydization. The company does not know which of its risks will be destroyed or damaged by fire; neither does the merchant know which of his coats will ♦Principles of Science, Jevons. io8 Fire-Rating as a Science be consumed by the slow combustion of depreciation before he can sell them, and it is as inconsequential to the insurance com- pany as to the retail clothier to know, for under the law of aver- age the insurance company covers its loss in its average rate, while the merchant covers his depreciation in the average allow- ance he makes in marking the selling-price on his coats. Both act on an assumption, warranted by experience, that there is uni- formity in average, and under this law of uniformity they can afford to be equally indifferent to the fate of the individual things which constitute the aggregate in which the average is inherent. From the standpoint of chance the two cases are strictly analo- gous, yet the merchant is prone to look upon the insurance company's transaction as chance, while his transaction is business. But there are other things besides depreciation in which the merchant's relations to chance are analogous to those of the insurance company. It is true that he is able to determine from his bills of purchase what each item of merchandise costs him in some distant city, perhaps in Europe, — but this is only a fraction of his selling-price. He must add to each separate article for freight, marine and fire insurance, rent, clerk hire, taxes, adver- tising, depreciation, profits, etc., an amount often exceeding original cost. In making this addition it is impossible for him to enter into a mathematical calculation to find just what ratio of invoice cost he should add to each specific item in establishing its selling-price. He meets the difficulty by adding a uniform percentage, established by the faculty of estimating, precisely as the insurance company does in its no-wise-different problem, with this difference, however, that his process is the reverse of logical according to the law of error as above stated, for unlike fire insurance, the merchant does not resort to a systematic analysis or synthesis in which one error tends to offset another, but to a reverse process which precludes all probability of approximate accuracy in detail. He solves his problem precisely as fire insurance would if it should charge one dollar per hundred for every risk in the United States regardless of specific hazard because the average rate shown by experience had been one dollar. Comparison shows that in its coexistent relations the element of chance enters into fire insurance to a smaller extent than it Fire Insurance to Chance and Probabilities 109 enters into the affairs of every merchant in the land. The fire insurance company fixes its prices by an organized system of coexistent relations far from perfect, it is true, but still far more perfect than the system of merchants, manufacturers, or railways. Average has nothing to do with individuals or specific events. The greengrocer buys a box of eggs, or a crate of cabbage, in which breakage and decay are inherent, and it is as inconsequen- tial to the insurance company which of the risks it insures will go to the ash heap as it is to the greengrocer to know which identical eggs and cabbage-heads will go to the garbage heap. It must be admitted that a company insuring a thousand risks may have an experience very different from another company insuring another thousand of the same hazard-group, even though both companies write at the same tariff rates. In periods as short as a year, this difference may be due to the latitude found in all averages, which increases the nearer we approach the individual instance, but in any period long enough for the law of average to take effect, no practical underwriter would question that the difference in the experience of the two companies was occasioned by the exercise of discrimination in the selection of risks. The characteristics of desirability and undesirability in individual risks are as unmistakable to the skillful underwriter as similar characteristics to the buyer of live stock, and the skill in selec- tion which makes one company prosper while another meets dis- aster is no more chance than is the quality of discernment which enables the successful doctor or lawyer to correctly diagnose a case, or the successful merchant to select goods which will meet or create public demand. The ability to wisely discriminate in the selection of individual risks, is not chance. It is judgment, without which failure is inevitable in any walk of life. The worthy gentleman whose memoirs assert that his business is based upon the laws of chance, would have been nearer the truth had he stated that it has accomplished more, perhaps, than any other human instrumentality in eliminating chance from human affairs. He was no nearer the truth when he stated that fire insurance deals in probabilities. The subject of probabilities is a large one. Quoting from a prominent modern writer: no Fire-Rating as a Science *' It has perhaps given rise to more profound investigation, to a greater variety of opinion, and in consequence to a more extensive history and literature than any other single problem within the range of mathematics." Fortunately, fire insurance has nothing to do with probabili- ties. The relations between the two are stated by the same writer in the following language : " The practice of insurance does not, I think, give rise to many ques- tions of theoretic interest and need not therefore detain us longer As an illustration of this we need merely refer to the works of De Morgan, a professional actuary as well as a writer on the theory of probability, who has found little or no opportunity to aid his speculative treatment of proba- bility by examples drawn from that class of considerations." * If we now turn our attention to the sequential relations found in the changing of rates to conform to experience, we find that all sequential relations have to do with time, and as to future time, we have the alternative of embarking upon the shoreless sea of probability or hugging the shore line of the past. Fire insur- ance judgment has shown its wisdom by adopting the latter alter- native. Except in the beginning of each class when its hazard, for lack of experience, must be established by pure surmise, it may be said that no class- rate was ever advanced or reduced in the history of fire insurance, except as a result of experience, or as dictated by expediency in meeting competition. The leading underwriters' associations of the country during the past year, appointed committees to investigate unprofitable classes and determine what should be done with them. These committees submitted long lists of unprofitable classes with the recommendation that each should be advanced in proportion as it had been unprofitable in the past. In doing this, they simply followed precedent. Facts like these show, whether we are ready to admit it or not, that in actual usage fire insurance is not con- cerned with probabilities. Our sequential relations, which we have never recognized as distinct and separate from coexistent relations, are invariably established by taking the past as our yard-stick to estimate the future, though we are frequently in doubt as to whether it is a yard-stick or a "two-foot rule." ♦Logic of Chance, J. Venn. Fire Insurance to Chance and Probabilities in In the evolution of fire insurance there is a growing recog- nition of the fact that rating must be a science, not of prevision, but of revision, a science of adjustment of logical and permanent coexistent relations, to be used as an unvarying standard in adjusting the sequential relations of the past to the future, a science of the correct exchange of balances between stockholders and policy- holders, having in view the relations of time and space. The one thing necessary to accomplish this promptly and scien- tifically, after coexistent relations have been so established that we will know whether we are measuring with a yard-stick or a two-foot rule, is the flexibility in system which will enable us to control these sequential relations promptly and logically. The element of chance found in fire insurance comes not from the law of the wave of fire destruction, but from deviation from the principle enunciated in this law. The legitimate purpose of every company is, while adhering to this principle, to acquire and maintain a sufficient volume of premiums to secure the stability found in the law of average, and keep its expense ratio below the safety line, a problem full of difficulties, but neverthe- less not a problem which lies in the domain of chance or proba- bilities. Metropolitan Conflagrations Great city conflagrations, like tidal waves, cannot be foreseen or modified into bearable proportions. The only safety of the fire insurance company lies in confining its lines in "congested areas" to dimensions which will not engulf it when the catas- trophe occurs. It is true that the increment to average cost from this source is measurable within reasonable limits. The total of past conflagrations in theory might be distributed through a long period of years until made good. Assuming that the Chicago and Boston fire losses equaled the entire premiums of the country for two years, if the average underwriting profits on the business were five per cent per annum, this would be equal to about forty years' profit, or an addition of five per cent for forty years, or ten per cent for twenty years, or twenty per cent for ten years. If we do not take into consideration the interest on the vast sums disbursed for these tidal waves of fire, and these sums could be spread out in a permanent increase of average rate, possibly one or two per cent might be adequate to cover our naked disburse- ments for loss in these conflagrations, but even this small addition would be more than the margin of average profit of all companies, and any attempt to maintain this as a permanent increment to normal rates, through periods free from these conflagrations, would generate a competition and demoralize the business beyond repair. In this fact alone is found unanswerable evidence against the possibility of maintaining unfluctuating rates for long periods. With the ability to promptly change rates with the swing of the cost wave, the forays of irregular competition during every period of unusual profits would cease, because the ability to so change rates by classes or sections would prevent sufficiently prolonged periods of profit to invite these forays. It is true, at the worst, that the great city conflagration is no more destructive to fire insurance capital than financial panics are to other capital. These panics come in cycles, and every ten or twelve years a 112 Metropolitan Conflagrations 113 considerable portion of the commercial capital of the country is wiped out of existence by a rapid decline in values. These panics are even more frequent and regular than the great metropolitan conflagrations which swamp fire insurance capital, but the fire insurance company is compelled to encounter both these catas- trophes, for financial panics are hardly less ruinous to fire insur- ance than to other capital. All told, however, the great metro- politan conflagration may be classed among the cataclysms which set at naught all human prevision, and fire insurance capital must bear the brunt of these calamities until that indefinite time when the lion and lamb shall lie down together. With flexible rates, however, it would be possible after a great city conflagration to make intelligent and instantaneous rate-advances throughout the land, without resorting to the wild slogan "Double the rates," as was done after the Chicago fire. The companies that really transact fire insurance might also find in the rate equalization which would inevitably result from flexible rates, an opportunity to maintain a continuous, if small, increment to rates as an offset to the infrequent but inevitable metropolitan conflagration, because this flexibility would prevent the inroads of rate-cutting competition which has always been ready to take advantage of the rate-advances which follow these conflagrations. The Personal Equation The personal influences which constitute so large a portion of fire cost are an inseparable part of the basis rate, because from their nature they elude analysis. Without the ability to estimate these influences quantitatively, we only know that they are exerted from without and within, and that the most important exterior influence emanates from state legislation, while the chief internal influence is found in compe- tition. Without attempting the task of further classifying or meas- uring these disturbing factors, they cannot well be overlooked in any attempt to discuss fire-rating as a science, for science depends upon natural laws, and no science is possible where lawless influences interfere. We are met, for instance, at the very threshold of any consideration of these influences by the fact that a reasonably uniform proportion of insurance to value is necessary in establishing true rate relations. When a state decrees that we shall not have the power to enforce these relations, and selfish interference at every turn tends to upset all logical relations between insurance and value, scientific prevision is blindfolded at the outset. In the matter of legislation, the increase in annual cost occa- sioned by inimical laws would be met by standard tariffs of cost relations, for these tariffs would become the instrumentality for promptly assessing the results of bad laws upon the property owners who, for selfish ends, have been most active in securing the enactment of these laws — a thing we are always threatening to do but never do, under our present unwieldy rating system. On the other hand, personal influences within our ranks con- stantly tend to disturb established relations. We can estimate the average cost, upon which the whole fabric of rating must rest, only by estimating some percentage of average expense, because cost is largely composed of expense, but the larger share 114 The Personal Equation 115 of this expense is caused by commissions, and without the ability to limit this part of expense it is impossible to start a reasoning process on the problem of scientific rating, because our funda- mental assumption is certain to be upset by the competition which thrives by a systematic system of upsetting system. These are embarrassing factors which disturb the possibility of accurate reasoning, but they are temporary factors which have sprung from existing conditions created by the very defects in method which it is the object of this inquiry to reform. Anti-coinsurance laws are a real wrong to the small insurers of the country, in the fact that they actually discriminate in favor of the great corporations and trusts at the expense of small prop- erty-owners, and there can hardly be room to doubt that anti- coinsurance legislation will be expunged from the statute books when we make a united effort to educate legislators into a reali- zation of the fact that anti-coinsurance laws are anti-populistic laws. With the facts properly understood, the instincts of the great American demagogue may be trusted to enthusiastically espouse a cause so prolific of effective populistic argument. But even admitting the impossibility of securing the repeal of these laws, flexible rates would give us the ability to include the increased loss ratio in the rates of the states on whose statute books they appear. Again, the causes that have generated high commissions have always existed in the antecedent, inflexible rates and its conse- quent, preferred classes, coupled with the fact that we have loaded our rates for expenses to justify high commissions. In a large portion of the country it has never been possible to secure any agreement limiting commissions, and in no part of the United States has it ever been possible to induce more than a respect- able majority of the companies to agree as to a maximum com- mission to agents. Company associations have tried every expe- dient to limit the constantly increasing expense ratio of the country (occasioned almost wholly by the remorseless growth of commissions and brokerage), except the simple expedient of load- ing loss ratio with a reasonable addition for expense and estab- lishing cost estimates on this basis, leaving to the discretion of the individual companies how they shall dispose of this allowance 1 16 Fire-Rating as a Science for expense. If our loss ratio is loaded but thirty-five per cent for expense, no company can long exceed this expense with- out trenching upon its capital, and no pledge or commission agreement or mandatory rule would be necessary to hold it to this maximum expense, with the equalized rates which would result from flexible rates. When we are able in a day to change our rates in a town, city, or state, on a given class, or all classes, by a simple rate announce- ment; in other words, when we can control our selling prices as promptly as other industries, high commissions will die an early and natural death. Again, flexible rates mean rates always well in hand. The absurd necessity of suspending rates which has invariably resulted in the companies giving away their policies for long terms, and ruining their own agents, would cease under flexible rates, because they would enable the companies using them to instantly make such reasonable rate modifications as would remove the temptation to cut rates. Under this prompt and effective expedient the prevalent tendency to rate-cutting would die out just as piracy has ceased on the high seas. In the past, systematic rate-modifications have been impos- sible, and we have been compelled to resort to the brutal expe- dient of suspended rates, which not only crushed our agents but ruined our established tariffs, for after a rate war it has never been possible to restore the old tariff in its entirety. Under a flexible rating system no amount of percentage rate concessions would have any effect upon the established coexistent relations appearing in tariffs. However wide or frequent the rate fluctuations might be, they would not disturb these as the permanent landmark showing what the rate ought to be. It is a well-known fact that the tariff rates of thousands of important risks have been so frequently juggled that all accurate notion of their true hazard relations has been destroyed in the minds of underwriters. Under permanent tariffs of cost relations the esti- mates of such risks would stand through periods of demoraliza- tion as a constant reminder of their true hazard relations to other risks. If a given number of companies should furnish their statis- tical experience for the purpose of establishing data of this kind, The Personal Equation 117 this data would be their own property with a tangible and increas- ing value; property that other companies would have no moral right to confiscate or share in by the farce of coming into the same agencies, and appropriating in whole or in part the services of the same agents. The companies furnishing the data would have the unquestionable right to refuse access to their statistical property to outsiders, hence the separation of associated and non-associated companies, or more properly, perhaps, statistical and non-statistical companies would follow as a logical necessity, a necessity that would appeal to the self-interest of agents, for every intelligent agent would give the preference to companies doing business through flexible rates based upon permanent tariffs of coexistent relations, because these things would be advantageous to his own interests. With this separation of companies, it would be immaterial what commissions other companies might pay their agents, as the statistics of the contributing companies would not be affected. Reference has been made to the fact that the statistical infor- mation furnished by the associated companies would have tan- gible and increasing value. This increasing value may be judged by the fact that as the system became established it would be suicidal for any company to attempt to transact business without the advantages of this information. Access to these statistics would eventually become as valuable, and membership as essen- tial, as in our city stock boards and exchanges. Membership in these bodies has a cash market value equal to a moderate fortune, because men cannot transact business outside of them, because they represent the true principle of healthful co-operation which in the end inevitably crushes out wasteful non-co-operation. National Loss Waves in the Light of the Diagram If science is to be regarded in the light of its usual definition, as a body of organized knowledge, and all knowledge is relative, then fire-rating as a science is concerned with relations, and relations only. It has been shown that our tariff system establishes coexistent relations, and that fire-rating has been floundering about in a quagmire of confusion from its attempt to mold them into sequen- tial relations. " The beginning of every science may be said to be the date when it begins to assume a definite quantitative character." It has been shown that by adopting cost estimates as perma- nent relations of coexistence in lieu of our present tariff rates it becomes possible to establish permanent standards of comparison by which we can measure the sequential relations of class and state cost waves, and thus intelligently determine from past expe-" rience the future price of fire indemnity. It was further shown that all exchange of intelligence between mind and mind must be made through symbols of some kind. The natural symbol of sequential relations is the diagram. Waves of fire destruction and rate waves are forms of motion, and as all motion is sequential, these relations are best shown through dia- grammatic symbols. It is therefore proper to turn our attention to the diagram as an index of both sequential and quantitative relations, and as affording the comprehensive view of the data necessary for deductive reasoning, for these are the ends sought in every department of scientific thought, and the practical utility of every science increases in proportion as we are able to achieve these ends. Let us suppose the cost, i. e. losses and expenses, of a given class to have been for each $ioo, at risk, as follows: ii8 Loss Waves in the Light of the Diagram 119 1890-- — - -$0.90 1891 ___ 0.96 1892 — 1.05 1893 1.00 1894 0.85 1895 „ 0.87 1896 - 1. 10 1897 __ 0.92 1898 0.98 1899 - -- 0-89 Average -$0.95 Without considering the question of profit, it is plain that the companies could insure this class for an average rate of ninety- five cents and come out even at the end of the ten years ; or on the other hand, with exact information, the rate each year could be based upon the experience of the preceding year, and at the end of the eleventh year the company would come out even. This would give us the following diagram, the black line indicating the wave of annual cost and the dotted line the ensuing rate wave. DIAGRAM No. i ,„ no ^ ; j \ / 1 . / \ / \ / , 100 / ^ < ' J « / \ / \ 1 \ / N/ *^N \ 1 \ / k \ j \ lOi / \ N^ y \ / L 1 \ \ / y j \ / f \ > 1 , \ \/ \ ' V / \ \ 1 / \ / » Q( / \ » j / \ A \ / / / \ \ 1 \ / \ / / \ \ * \ / \ / \ \ / \ \ f 1 / \ ,' \ / \ 1 \ \ \ Qri / f \ \ 1 \ \ \ \ \ ! \ « j \ \ < \ ^ ,' 85 ^ \ " . 18t k) IB 91 IB 02 181 bd i8t 34 IBI »5 18 96 IB B7 »e 98 18 99 I9< 3b The preceding diagram shows the wave of annual cost and rate wave to be identical; the latter following the first at an interval of a year. If rates were made as indicated by the dia- gram, insurance would simply act as a clearing house for the I20 Fire-Rating as a Science transfer of annual balances year after year between stock-holders and policy-holders. The same result would be accomplished by collecting an average rate of ninety-five cents throughout the entire period, in which event the transfer of balances would be determined by the fluctuation of the wave of cost above and below the average line, and in this event the transfer might be deferred for many years. If the cost wave were uniformly confined within narrow limits it would entail no particular hardship on the public to have its rates established each year to follow the exact wave of cost, but class cost waves are subject to violent fluctuations. On the other hand, if companies during the entire period should adhere to the average of ninety-five cents, periods of large profit and large loss would intervene as a source of misunderstanding between the companies and policy-holders who know nothing of the record of their class. To apply a concrete illustration, let us suppose in the city of New Orleans a large grain elevator for the storage and trans- shipment of grain to Europe. Louisiana is not a grain-producing state, and it is not unreasonable to assume that there is not another grain-elevator in the state. Let us again suppose this elevator to have a capacity of one million bushels, and to be filled soon after its completion with wheat, when a fire occurs destroying property worth a million dollars on which a premium of ten thousand dollars had been collected. The elevator class for the year in Louisiana would show premiums of ten thousand dollars and losses of one million dollars; in other words, the loss would be one hundred times the premiums for the year. This would leave the elevator class in Louisiana indebted to insurance nine hundred and ninety thousand dollars, which, by the first plan of having the rate wave exactly follow the loss wave would require an advance of one hundred fold in rates ; in other words, the next year, the elevator people would be compelled to pay to the companies one million dollars in premiums, which practically would amount to the same as the return of the property to the insurance companies. • On the other hand, if insurance did not raise the rates one hundred fold, it would have to charge the assumed average rate of one per cent for one hundred years, and thus wait a century to get even on the elevator class in Louisiana, Loss Waves in the Light of the Diagram 121 provided no more elevators were built. But let us suppose their experience to have taught the owners the impolicy of rebuilding the elevator, there would be no further premiums on elevators in Louisiana, and in this event fire insurance would be compelled to pocket the loss perrtianently, whether it collected its premiums under the first plan or the second — in either event, it is placed in the position of a gambler who bets one million dollars against ten thousand dollars on the mere happening of an event isolated from any possible connection with the law of averages. There are thousands of large industrial establishments, scat- tered through the several states, one, two, or a dozen, perhaps, to a state, which bear the same relation to averages as the hypo- thetical New Orleans elevator, but elevators and grain storage risks belong to a class quite common in grain-producing states ; a class which produces possibly ten million dollars in annual premiums, and the loss on elevators, if shared by all the other risks of its class, would affect the aggregate cost of the class, perhaps, ten per cent, which at most would require a moderate advance in rates, though in view of the class being ordinarily profitable to the companies, would probably require no advance at all. On the contrary, light losses elsewhere might justify a reduction in elevator rates, so that if the New Orleans elevator were rebuilt, its rate might be reduced the next year ten per cent instead of being advanced one hundred fold, and the knowledge of this fact might be the cause of the reinstatement of the prop- erty and maintenance of an industry valuable to the city and state. This suppositive case proves the impracticability of observing state ratios in all classes where large values are concentrated in one risk, and few risks in a state ; or to put it in another way, it clearly demonstrates that the state not only has no concern in the ratio of these classes, but that from the standpoint of public welfare, the best interests of the community are conserved by allowing people the benefit of the interstate comity which common sense shows to be advantageous not only to both parties to the insurance contract, but to the local community as well. Granting the advisability, even necessity to all parties concerned, of main- taining interstate comity with classes of this kind, it is proper to consider the elevator class as a whole for all states. Assuming 122 Fire-Rating as a Science that after deducting expenses the annual premiums of grain stor- age risks in the United States aggregate ten million dollars per annum, the companies could, out of their premium fund, stand an annual outlay of ten million dollars for losses on the elevator class and come out even, or they could stand a loss of twenty half-million-dollar fires, or one hundred hundred-thousand-dollar fires, but fires do not come in this way. The universal law of rhythm is nowhere more constantly in evidence than in fire destruction, and periodicity of maxima and minima is the rule with the elevator class as with every other property class. Judg- ing from experience, it is not unreasonable to expect that elevator fires will come in waves in which a depression lasting four or five years will be followed by an epidemic of fires, which will send the wave up above mean cost, where it will remain for a year or two, consuming the profits of 'the minima years. This would produce a wave diagram about as follows: DIAGRAM No. 2 ' ™ IOC ■ / V, \ / "^ V / )J5 N / l/C 105 IOC / V 95 / \ / N, y V / N, / \ / -^^— — \- ^ 9C / \ ^ ■ / -T' / / #<^ ■- / 86 1 • Id idi bo- ■ -IBJ b 18 91 18 32 I8( 94 i8 96 IB »6 IB 97 IB BB IB 99 I9< Loss Waves in the Light of the Diagram 123 During the minima years, owners become dissatisfied, claiming that rates are too high. Competition sets in and demoralizes rates, and when at last a period of maxima years sets in, compe • tition drops out and the tariff companies, in the absence of statis- tics, forgetting the period of minima years, establish a large advance in rates about the time another period of minima years is due. This produces another period of inordinate profits and of renewed dissatisfaction. Competition again forces down rates about the beginning of another maximum period. This whip- sawing process is the history of nearly every class important enough to receive specific attention, but meanwhile the loss and rate waves have been clashing against each other, and the surface of the rate wave, erratic as it is, is churned into chop waves by personal and local influences. The owner of one elevator or line of elevators, taking advantage of competition, succeeds in beating down his rate. In certain sections competition develops a similar influence affecting all elevator rates of a city or state, under which tariff-rate relations are battered into fragments and a just treat- ment of individual patrons and localities is rendered impossible. In addition to these perturbing influences in the cost waves of specific classes, we find similar and even more widespread influences in climatic, social, and economic conditions which affect not only property classes but entire state areas, producing a permanently higher average in cost in some states than in others. Climatic influences for instance produce a higher cost on creameries in Kansas and Missouri than in Illinois, Iowa, and Wisconsin. Glass works are not undesirable risks in Indiana, while very undesirable in Ohio on account of the absence of natural gas fuel. It may be stated as a generalization that every species of industrial life, like animal and vegetable life, has its natural habitat. Again, existing conditions are such that the average level of the cost wave as a whole is permanently higher for all classes in some states or sections than in others — in the Western states, it is higher than in the Eastern, and higher in the Southern than in either. In the past there has been no way of intelligently observing experience by classes, and a "diagrammatic record of class-cost waves by states affords the means of recording our condensed 124 Fire-Rating as a Science experience in a way to enable us to maintain intelligent relations based upon actual statistics, instead of compelling the profitable sections and classes to make good the deficit of the unprofitable. Comparative diagrams afford a means of portraying the con- densed history of not only classes but states, showing at a glance their rate relations, and enabling us to preserve a permanent record of each, which will serve as a constant reminder to the public, as well as the companies, of past experience. Our reckless rate advances after a year of heavy losses and equally reckless reductions after a year of light losses, are the results of a lack of definite knowledge of class and state experience, for we have no combined class information and the fire his- tory of the states is buried in a mass of tabulated statistics which no one reads and which no one could understand if he did. Diagrams would enable us to take a bird's-eye view of the past and would give at a glance the suggestions on which we could, with intelligence, mold our plastic rates into a modified form of the cost wave from data so unmistakable as to silence criticism and repress the competition caused by ignorance. Taking the national record as a whole, we find the tabulated results of all the states for ten years, ending January i, 1900, to be as follows: UNITED STATES. Loss Aver- Loss Year. Risks Written. Premiums. Losses. to Prems. age Rate. to Risk. 1890 $11,231,273,644 $114,581,079 $58,998,511 .52 1.02 .0053 189I 11,938,730,952 119.052,005 71,490,508 .60 1. 00 .0060 1892 12,266,950,492 131,509,416 75.775.526 .58 1.07 .0062 I«93 10,877,725,112 133.040,054 85,007,362 .64 1.22 .0078 1894 11,192,399,954 130.189,350 74,724,377 .57 1. 16 .0067 1895 11,539,948,920 131,735,460 68,860,402 •52 1. 14 .0060 1896 11,807,226,248 130,577,280 65,905,495 •51 I. II .0056 1897 12,706,051,099 134,872,998 63,026,914 48 1.06 .0050 1898 13,384,966,045 134,571.960 73.406,773 •55 I.OI .0055 1899 13,731,813.698 139.759.919 87,093,286 .62 1.02 .0063 $120,677,086,164 $1,299,889,521 $724,289,154 .56 1.08 .0060 The preceding tabulation to the busy underwriter is simply a mass of unsuggestive figures to be glanced at and consigned to the waste-basket, but for once let us subject it to the analytical light of the diagram and see what it reveals. Loss Waves in the Light of the Diagram 125 DIAGRAM No. 3 Showing wave of loss to premiums for all states for the ten- year period ending January i, 1900. " ( ^ ' / / f-^t\ / ,' \ , / / f 1 f^'S 1 1 t •■^ / \ ~., 1 5c 'x "v .... 1890^ 1891 .1692 1893 1894 1896 1896 1897 1898 1899 1900 DIAGRAM No. 4 Showing wave of loss to amount at risk for all states for the ten-year period ending January, 1900. 80 ^. l\ 75 / \ / \ / \ / \ / \ 70 / \ / \ / \ / \ / V / \. ii-j / \ \ \ / ^ \ / ^ > / 60 7 \ / / \ / / \ / / \ / / \ / / \ / / \ / \ / \, / cr N / )8( K) 18 \\ 18 92 18 93 181 94 18 9b 18 96 18 97 18 98 18 99 19 DO 126 Fire-Rating as a Science DIAGRAM No. 5 Showing wave of premiums to amount at risk (average rate) for all states for the ten-year period ending January i, 1900. i V nn 1 \ 1 v 1 \ 1)5 *««v. 1 ''s. ^. / V / > V '. \ \ / 105 / K. \ / •V, ^ ^.« ""^ IOC ^ f 18( )0 18 31 18 92 I8( )a i8< H 18t 35 1896 1897 1898 1899 1900 As every wave must fluctuate above and below its mean line, it follows that if we superimpose the three waves shown by the preceding diagrams upon the same average or mean line, we shall be able to determine the sequential relations of each wave, not only with its own mean but with each of the other waves, and with a background ruled to scale measurement, it becomes possible to estimate these relations quantitatively. By thus placing the three ratio waves upon the same mean line, as shown by diagram 6 (page 127), we are able, for the first time, to obtain a bird's-eye view of their sequential relations to each other for a period of ten years. The first noticeable fact is that the three waves exhibit a tendency to vibrate in sympathy and that they present a general similarity of contour. In view of what has been said of the inharmony between rate waves and loss waves, this statement does not seem to be justified by diagram No. 6, for the rate wave moves up and down with the wave of loss to risk with a harmony which could not have been anticipated. It should be remem- bered, however, that this diagram embraces a continent and a Loss Waves in the Light of the Diagram DIAGRAM No. 6 127 Showing waves of loss to premiums, loss to amount at risk, and premiums to amount at risk (average rate). Loss to premiums — Dotted line. Loss to amount at risk ^^--Light line. Premiums to amount at risk (average rate)- Dash and dot line (heavy). ao 1 / / \ 15 / \ 1 / \ / i V\ / • \\ ! // \\ / ' \\ 10 // \ / ' \ // ' ^t ' *^, /' ' V '"•^ e //' \ \ >- J // \ ^ ' '-., /■/ \ \ , " »j 1 > V / / .' 1 ^ / / ^ 1 V \ \ ,' / r \ 1 ' / / ^^ \ "N; / / / N \, ^ 1 i / 1 N \ ' 1 \ \ / 5 J f ^. ' V T^^ \. / A » .• ^ •"^ 1 \n / /^ ' \ / i 1 \ / (8 90 18 91 18 92 18 93 18 94 18 95 18 96 18 97 18 98 18 99 19 00 , decade. When we turn our attention to the state diagrams in the next chapter an utter lack of harmony will be noted between the rate and loss waves. On the contrary, diagram No. 6 affords a suggestive illustration of the rhythmic manifestation in space and time of the all-embracing law of averages. Out of the seeming chaos of physical and personal influences which have tangled our ratios into an inexplicable maze within the limited fields of states and classes, we find emerging a synchronous movement of these ratio waves when we are able to look down upon their movements over a broad field of time and space. If it were possible to look down upon the earth from the distance of the moon it would doubtless appear to be a smooth, silent, and motionless sphere, J)ut to us mortals who are down in the "thick of things" it appears 128 Fire- Rating as a Science anything but smooth, silent, and motionless, and it is our life function to deal with its rugosities and incessant changes — we cannot ignore them. So in fire insurance we are concerned with the details of states, localities, and classes, and these things can- not be ignored, for it is our duty to bring about synchronous vibration between rate and loss waves in their details rather than in their aggregates — our policy holders are interested in these details even if our stock-holders are not. The fact that the aggregated ratio waves of a continent oscillate with a movement which at least approaches harmony, indicates that, if it were possible to construct a similar wave embracing the civilized world, they would vibrate in complete harmony. In any event, diagram No. 6 is not without interest in its testimony that the world-wave of fire destruction in its rhythmic swing moves on through the puny influences of blind matter and purblind motive as resistless and undisturbed as the sweep of planetary matter through space. It will be observed from diagram No. 6 that loss to risk shot upward from 1890 to 1893 inclusive, when it began an equally sharp descent which continued to 1897. In 1891 the rate waves started up after the loss wave so rapidly that it caused the wave of loss to premiums to drop far below the wave of loss to risk. The maximum of the rate wave was reached contemporaneously with the maximum of the wave of loss to risk and it began to descend at the same time, continuing its descent until 1898; but from 1895 to 1897 inclusive, notwithstanding its rapid descent, it remained from six to eight points above the wave of loss to risk, while still further above loss to premiums for a period of five years. The relative positions of the three lines in 1899 was almost identical with their position in 1891, which year was followed by a sharp advance in both loss lines. The low position of the rate line in 1899 made another sharp advance in 'loss to premium, a mathematical certainty, and this certainty was realized by the experience of 1900 (not yet tabulated). There is this difference, however, between present conditions and those of 189 1 — we could then readjust our rates without vio- lating the statutory law — now we cannot. The diagram shows that Loss Waves in the Light of the Diagram 129 we did readjust our rates in .1892 and 1893, with a vengeance, and that we were more successful in raising a similar spirit of vengeance on the part of the public than we were in maintain- ing the rates so established. Altogether there seems to be a great deal of really suggestive information in diagram No. 6, in which, for the first time, we are able to intelligibly observe sequential relations among our ratios, but this information becomes more clear in the light of State experience shown by similar diagrams in the next chapter. State Loss Waves in the Light of the Diagram The following ratio-diagrams include twenty-two of the most prominent states, embracing a period of thirteen years ending January i, 1900. In the cross ruling, the vertical lines indicate years, as denoted by the figures at the bottom of each line. The transverse lines measure the number of points in the percentage rise and fall of each wave as denoted by the vertical column of figures at the left of the page. As every wave must fluctuate above and below its mean or average line, by superimposing the three ratios on the same mean line, the relations of the three waves are shown for each year during the entire period. Each diagram has been carefully calculated from the tabulated figures which appear on the oppo- site page. The same ratio is indicated by the same line in every dia- gram, /. e. Loss to amount at risk Light line. Loss to premiums Light dotted line. Premiums to amount at risk (average rate) Heavy dash and dot line. 131 132 Fire-Rating as a Science CALIFORNIA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1888 1889 1890 189I 1892 1893 1894 1895 1896 1897 1898 1899 $327,910,952 352,321,776 352,179,723 368,699,916 380,059,144 392,294,125 388,522,503 377,813,892 358,671,159 336.335,228 324,254,113 453,198,140 382,277,165 $5,590,354 6,087,041 6,158,215 6,304,814 6,712,456 7,030,488 6,780,454 6,336,734 4,703,897 3.816,537 4,766,989 6,660,069 5,640,766 $2,101,483 3,049,030 2,580,002 2,755,289 2,433,942 2,689,033 2,667,160 2,815,670 2,850,642 2,651,487 2,637,678 3,578,142 2,935,619 .38 .50 .42 .44 .36 .39 .39 .44 .61 .70 .55 •54 .52 1.70 1.70 1.75 I.71 1.77 1.79 \il 1.31 1. 14 1.47 1.47 1.48 .0064 .0087 .0073 .0075 .0064 .0069 .0069 .0075 .0080 .0079 .0081 .0079 .0077 $4,794,537,836 $76,588,814 $35,745,177 .48 1.59 .0075 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk . . ,«^, . indicates Average Rate State Loss Waves in the Light of the Diagram 133 DIAGRAM No. 7 CALIFORNIA 20 / « V^ / ' \ V / \ / \i / « J5 \ >, v / « d X ' / v f \ f' \ , t 10 \ V 1 \ 1 \ 1 1 \ ! \ j \ 1 / 1 \ •.^, s 1 \ / . ^ ^ '•^^ 1 \ • ' / ^~»..^ ^ '^ ^-. 1 \ // V ' 1 \ \/ V, 1 i \ \ \ \ /', \ \ ^^ / \ 1 1 \ \ ^^ \ / ;* ! \ / ! \ 11 \ / . 5 \ \ \ / / 1 // X *' \\ c \\ / / 1 f \\ / 1 f \\ / . / 10 1 \\ / --' 1 1 V / y 1 I 1 ' t i5 •. 1 \ 1 1 \ 1 20 1 \ - i" » 1 25 1 f 1 • f ' 3o . ■ 1 ■ \ / \ 35 \ / \ 1 \ ; A-o \ ■ 1 \ 1 ■ \ f • A^ ' i m J7 I8J 38 181 39 18 90 I8( »l 18 »2 181 »3 18 94 18 B6 18 96 18 97 18 98 16 to "" 134 Fire- Rating as a Science COLORADO Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1897 1898 1899 $ 48,570,113 62,024,844 76,017,600 91.753.216 94.429.757 101,654,117 95.21 1.931 85,894.340 92,299,396 95,711246 98,425,131 100,456,128 123,085,228 $ 904.196 1,120,189 1,324.261 I.551.059 1,569,749 1.723.563 1.555.363 1,422,026 1,485.570 1.557.627 1.524.733 1,541.613 1.705.295 $ 380,246 398,979 571.425 519.549 572,263 827,062 928,500 793.805 519,548 I.155.580 374.855 547.936 1.072,669 .42 •36 .43 .48 .60 .56 •35 .74 .21 •36 .63 1.86 I.81 1.74 1.69 1.66 1.70 1.63 1.66 1.61 1.63 1-55 1.53 1-39 .0078 .0064 .0075 .0057 .0061 .0081 .0098 .0092 .0056 .0121 .0038 .0055 .0087 $1,165,533,047 $18,985,244 $8,662,417 46 1.63 .0074 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk . . . . . indicates Average Rate State Loss Waves in the Light of the Diagram 135 DIAGRAM No. 8 COLORADO . , 1 . ,.. 1 1 1 1 1 ' 1 \ t s / \ i, \ \ \ / \ ,' \ / \ ■ \, / \ 1 k / \ / \ / /i \ / / 1 \ / . ^ ' 1 ' \ / / ^x 1 1 1 \ / / \ I ' V / / \ 1 1 J \ / / > / ,' / s / ; • ■ ) / \ / '1 \ > t \\ y , X '1 ff A \l ■ ■ ■ \ f 1 / \ . W 1 /• •s. >\ ' /; \ ■ y *il J If > Y^ 1 j>' 1^ -r-' V ; 1 11 \ N - " ' I ii \ T \ 1 / t I 1 7 ■ // J \ \ r/ \ \ ^ \ ' i \\ // \\ 1 \ 1/ jj \\ ' '\ 1 / ff // "■ ■ 1^. "■ \\ / \v ' s ^'^ 1 1 \\ j \ I ♦J 1 / \ / 1 \ I / \ [ 1 / \ \ / / \ \ / / \ ■ / y / ' / / / / / / / / / \ 1/ f 18 dt 18 88 18 69 18 eo 18 91 16 92 18 93 18 84 1896 18 96 1897 18 8a 18 to 136 Fire-Rating as a Science CONNECTICUT Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1895 1896 1899 $167,182,877 174,445.556 184,002,882 201,264,338 195,234,620 226,683,733 230,354.580 221,828,297 242,682,930 265,956.569 274,180,716 280,455.909 284,821,203 $1,742,677 1,771.757 1,792,085 1,849,569 1.839. 174 2,055,054 2,141,835 2,171.851 2,314,763 2,426,387 2.443.855 2,432,546 2,513.795 $ 858,496 837.566 754.495 812,560 705,628 1,140,298 1,014,102 927.191 1.043.331 1,180,625 920,096 1,070,699 1,178,464 .60 •47 .42 .44 •'I .56 .47 .43 •45 •49 •38 •43 .47 1.04 1. 01 .97 •92 .94 .91 ■^ •95 .91 .89 .87 .88 .0051 .0048 .0041 .0040 .0036 .0050 .0044 .0042 .0043 .0044 •0034 .0042 .0041 $2,949,094,210 $27,495,348 $12,443,551 •45 •93 .0043 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _._..i_.^.._ ._ indicates Average Rate State Loss Waves in the Light of the Diagram 137 DIAGRAM No. 9 CONNECTICUT 15 > > X iO ^-1 \ v 1 \ \ V I \ ^ \ > Ni '^ \ 5 N > 1 1 \ \ ^ \ 1 1 \ \ • V \ if \ t S, ' \ \\ / "s. .' » \ 1 1 \ ^'^^ / \ \ ^ -'J. ■ \ \ ■■\ ... ^ ^-^ :^--^' '*=H \ » i' '7'n ^- \ \ \ / 7^--^ ^>cC^ \ Ai / v^^ v«-- / 5 >:. ^•/ Xx \ \ -'7*^ X \\ ''/ \ / \ / 10 18 87 18 88 18 89 18 90 18 81 18 92 18 93 18 94 18 96 18 96 18 97 18 88 18 to 138 Fire-Rating as a Science GEORGIA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to . Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1896 1897 1898 1899 $115,292,842 117,711,285 124,688,557 137,845.257 155.557,458 156,289,615 155,425,140 138,769.873 142,789,146 146,150,040 150,157,897 157,983.654 177,137,318 $1,456,318 1,444,492 1,544,162 1,760,647 1,960,730 2,035,894 2,044,381 1,905,826 2,000,476 2,033,956 2,125,228 2,136,639 2,349.841 $ 726,271 693.137 1,056,457 949.519 1,156,905 1,319,812 946,850 987.775 1,281,165 1,297,416 1,037.301 1,436,387 1,278,294 •5? ■& •54 fs .46 % .64 .49 .67 .54 1.26 1.23 1.24 1.28 1.26 1.30 1.32 1.37 1.40 1-39 1.42 1.35 1-33 .0063 .0060 .0085 .0069 .0074 .0084 .0061 .0071 .0090 .0089 .0069 .0091 .0072 $1,875,798,082 $24,798,590 $14,167,289 .57 1.32 .0076 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _._..._.^_.._._ indicates Average Rate State Loss Waves in the Light of the Diagram 139 DIAGRAM No. 10 GEORGIA ■ """'" I I" -r — 151 1 i i^ / \ !\ / \ io \ ! ' \ _' • \ y ^ / ■ \ < \ \y \ /■' \ \ 1 , \ \ 1 ""'^••-j \ \ 1 / \ \ n \ r 1 \ \ : \ \ 5 \ \ '7 ^' 1 1 \\ / / \\ // \ / \ \ \\ 1 / \ ^. • \, / / \ \ f , \ \\ \ \ ' K \ /,' ^.A \ \ \', . 1 \ iw. (^ 1 / / 1 \» / ( 1 1 \ ii \ ). / f U^ 1; V \ Y 1 1 / 1 h '. \ Y \ '. / / / l: \ \ y \ - L / I • : \\ /i 1 5 1 1 )r ^•/ / \\ b ji 1 1 ^»^ / -^ /■ >^ • j / \ y ^ \ • » --X : 1 • \ 1 / \ <\ \ ', to 7 1 \ 1 / / / \ ' / / \ \ '■ S / • 1 <7 \ \ 1 1 1 1887 1888 1889 1890 1891 1892 1893 1894 1896 1898 1897 1898 1899 140 Fire-Rating as a Science ILLINOIS Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1899 $ 806,454,052 813,114,963 859.338.805 1,005,062,959 913,652,560 1.017,559,758 1,000,857,380 946,661,803 973.295.739 973,164,456 1,047,053.087 1,046,822,043 1,141,060,852 $ 8,694,951 9,090,435 9,529,452 10,840,621 10,383,901 11,893,952 11,916,597 11,805,170 12,046,275 11,987,846 12,270,817 11,927,507 12,709,739 $4,913,741 3,791,156 4,461,360 5,116,232 4,038,214 6,571,080 6,907.974 6,003,583 6,141,814 5,909.299 8,026,369 8,316,189 •57 .42 .46 .41 .49 •34 •55 .59 •50 ii .65 1.08 1. 12 I. II 1.08 1. 14 1. 17 I.I9 1.25 1.24 1.23 I.17 1. 14 I. II .0061 .0047 .0050 .0044 .0056 .0040 .0066 .0073 .0062 .0063 .0056 .0077 .0073 $12,544,098,457 $145,097,263 $74,534,571 .51 I.16 .0059 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk __,«^, ._. ._ indicates Average Rate State Loss Waves in the Light of the Diagram 141 DIAGRAM No. 11 ILLINOIS , V / N, 15 /, ^■^\ /,' "^ / ^ /; / \ // / \ /i / \ /< / \ \i / i It f / / \ \ ^ /' r y \ \ v /i •, \ \ \ j; \ / \ ^ \ jt N. \ "^ r ^t > ^ i \ \ ^ \\ ^ A. ^>^ \ \ A -v\ ^. \\ / \ "s, \ \. '•t \ 5 \ ''^ \ V' y *' 1 \", ' A\ 'v^ // 1 \i ^ \\ x'' ^ N f/ \\ ' \' •'' 1 1 \\ /-\ \ > "v \ w \ ^ \" 1 ^ / s. J ■ " \ 1 il \, j \\ ,1 IS \ \\ \i \' \ 18 «7 l€ 188 IC 80 IC \9o IC 81 18 92 l( 193 .« M4 It 198 If 90 i{ 97. I{ we ti 180 142 Fire-Rating as a Science IOWA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 z z 1899 $190,954,696 191,581,258 202,364,570 216,476,095 220,870,002 242,137,418 241,834,384 232,011,959 213,502,862 214,064,986 228,247,254 242,591,231 280,071,272 $2,841,596 2.936,703 3,111,801 3,475,911 3,404,762 3,703,513 3,818,708 3,867,475 3,576,803 3,456.855 3.461,576 3,584.937 4,180,790 $1,408,441 943,827 1,478,040 1,570,675 1,634,563 1,575,681 2,118,857 2.235.598 1,621,962 1,591,184 1,340,157 1,484,080 1,965,221 .50 .32 .47 •45 .48 •43 •I •45 .46 .39 .41 .47 1.49 1-53 1.54 1.58 1161 1.52 1.48 1.49 •0073 .0049 .0073 .0073 .0074 .0065 .0088 .0096 .0076 .0074 .0059 .0061 .0070 $2,916,707,987 $45,421,430 $20,968,286 .46 1.56 .0072 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk __, . . . , indicates Average Rate State Loss Waves in the Light of the Diagram 143 DIAGRAM No. 12 IOWA zo J / / •9n / JLu / / / 1 *$ .'' J V— / i / \ 1 1 i ' / \ \ 1 1 \ \ \ 1* / \ 1; t • V \ •v / \ f \ ^v. \ » -V^ J / \ ^ '•y v^ / ~ \ ^ \\ Jt / \ i\'> / V / '^''ij "tA / / 1 1 ! 1 \ \ ^v « ,•*% J \ ' } 1 V _/,*"^ \ 1 • I ''1 ir^ 1 \ \ ' 1 1 ^ I I ^ \ 1 1 '^ 1 f 1 j j *"* ^ 1 ' ' ii dZ IMS 18 30 iB 90 a 81- 16 «2 18 83 18 94 18 86 18 96 If 97 le 08 If 99 ' ' ^ 144 Fire- Rating as a Science KANSAS Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 ;i^ 1897 1898 1899 $131,148,505 129,945.032 134.585.640 135.503.370 131,054,976 142,146,123 138,041,771 140,109,802 128,902,971 128,026,786 142,217,570 147,481,944 183,444.721 $1,926,252 1,826,310 1,848,429 1,803,799 1,771,788 2,028,185 1,929,936 1,961,450 1,744,693 1,712,336 1,745.981 1,771,862 1.945.797 $1,209,091 1,030,930 I.053.187 1,007,775 793.669 1,011,487 943.576 1,070,572 1,171,672 958,629 636,330 762,197 1,170,751 •1 t .45 •50 .49 .36 .60 1.47 I.41 1.37 1-33 1-35 1.43 1.40 1.40 1-35 1-34 1.23 1.20 1.06 0092 0079 0078 0074 0061 0071 0068 0076 0091 0075 0045 0052 0064 $1,812,609,211 $24,016,818 $12,819,866 •53 1-33 0071 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _...... ._.._._ indicates Average Rate State Loss Waves in the Light of the Diagram 145 DIAGRAM No. 13 KANSAS 20 , ' \ \ \ \ t s \ \ \ \ // ', \ \ \ / / \ \ JO / ; \ \ Vl / V \ \ \ \ . N » \ 't--. / N // • \ \ / > \ »• s s. '^l \\ i> \ / /N \ \ ' < f ( s.. v.*^ / , "^"'-^ f -^ X ■ r-: ' 1 'v— ^ V / N_ \ 1 \\ / \ ^ / \> ,< • lit 5 \\ I.' \i\ \> /' \'i'« 1 / \'\ \ ,7 \' • J 7 l\ \ / »0 / \ / 1 \ ', s/ / \ '. /N / 1 1 / 15 \ 1 / / 1 1 v \ ^ X \ A - \ 10 \ / \ / \ \ / \ / / zd / \ \ 18 87 18 88 18 ^9 18 00 18 81- 18 02 48 03 18 04 18 06 It) 96 18 187 18 to Id M ' 146 Fire-Rating as a Science KENTUCKY Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- Ra^e. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 z 1897 1898 1899 $161,271,533 164,039,504 176,854,086 200,918,013 201,890,152 229,726,283 206,910,552 187,397.787 182,870,044 183,728,026 194,964,327 184,305.328 201,319,734 $1,972,319 2,034,097 2,240,779 2,489,122 2,455»307 3.001,735 2,764,246 2.605,337 2,651,147 2.573.834 2i6o8]o85 2,762,480 $1,613,306 981,070 1,820,966 1,875,906 1,806,510 I.804.721 2,340,787 1.434.727 1.531,757 1.898,295 1,166,298 1,712,571 1. 793.9 19 .82 .49 .81 .75 .74 .60 •85 •55 .58 •74 :^ .65 1.22 1.24 1.27 1.23 I.2I I-3I 1.34 1-39 145 1.40 1.37 1.41 1-37 .0100 .0060 .0103 .0093 .0091 .0079 .0113 .0077 .0084 .0103 .0060 .0089 $2,476,195,369 $32,834,141 $21,780,833 .66 1.33 .0088 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk «^. . . . . indicates Average Rate State Loss Waves in the Light of the Diagram 147 DIAGRAM No. 14 KENTUCKY ■ 1 — ■ .... 5*5 i 1 1 n 1 / / / ( / ,' i ^ / ' - ■ »\ \ ; « 1 \» jl • ' \ \ J \ \ |/-» -■ \^ /l ••1 •j J • ; \ ' / f ; \ /' \ /\ \ / ii f ^^. ■y 6 .' \ f ; y . *. r ^, \^ / 1 \ / ^ \ ^^\^ » / 1 1 N. 1 > / All / .' , \ Y "% / ^ -x / ' / \ r\ \ \ ; / / '.1 1 1 \ I r-^ ', j 1 \ 1 r '^ / ,' 11 ,' \ '>> If / < \ ^ ; 1 /. K 1 1 , \j\ ' '1 / / /,' X \ / / 1 /' 4 ^^ Vw /\ ^ / ,' 1 /i 1 1 / 1' /T i /,'' 1 f i/\ L*^ ' . j \ ', i \\ j 1 1 1 j 1 T \ 1 .' 'i ^ 1 ', i 1/ 1 1 ./ 1 'a ij I il // 1C 1 1 • ,'/ \ ' // I I / \ / 1 / Z5 1 / 1 1 ; 1887 1888 1880 1890 1881 1892 1893 1894 1896 1896 1887 1898 1898 hs Fire-Rating as a Science MAINE Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 z 1899 $ 83,241416 80,701,943 89,140,620 95,447,324 92,841,159 101,063,423 103,875,200 94,894,475 98,758,548 106,617,256 109,006,873 115,196,313 125,673.733 $1,143,901 1,130,704 1,198,570 1,297,300 1.248,815 1,381,601 I.473.319 1,477,289 1,516,165 I.531.259 1,554,500 1,588,062 1,731.087 $654,054 539.092 55941 1 688,357 785.822 917,002 932.637 1,023,162 825,815 800,961 576,203 878,679 1,048,150 ii 47 n 1 .69 .55 .52 .37 i\ 1.37 1.40 1.34 1.36 1.35 1.37 1.42 1.56 1.54 1.44 143 1.38 1.38 .0079 .0067 .0063 .0072 .0085 .0091 .0090 .0108 .0084 .0075 •0053 .0076 .0083 $1,296458,283 $18,272,572 $10,229,345 .56 141 .0079 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk ._._._._._..i~. indicates Average Rate State Loss Waves in the Light of the Diagram 149 DIAGRAM No. 15 MAINE 25 ^ 1 520 15 /- — t 1 \ 10 nV -^ -/ \ \ :^ / / » // '/ / / 4 \ \ • c # \ \ /j / t S '. // \ \ ^ // / --^ \ ^**'«»_ — -y / / ' \ V // ^ / / / ^-\~ "TJ \\ \ ^ ' V\ y k^ / ^v \ • V f-i — 'A —\ /___ •} r^\ ■ ' 7^ ^^ ^ . - \ ''» \ '> y '""^ ^ ' ■ .' \ <>' u 1 j \ \ / \\ ''~^->~, / / \" .1 1 10 \ / -\« , 1 \ / \ , ' 1 / 1 / \ / / / s. / 16 \ / \ 4 / / \ f 1 / \ > / / \ '; 1 7n \ j \ 1 \ 1 \ 1 \ j *> •? \ 18 37 18 38 10 oa 18 80 18 01 18 82 18 93 18 84 18 96 18 96 18 97 18 98 18 ^9 ISO Fire- Rating as a Science MARYLAND Year. Amount at Risk. Premiums. Losses. Loss to Prems. '\^^X Loss to 1887 $226,786,346 $1,427,165 $1,173,622 .82 •63 0052 1888 218,223,721 1,535-143 1,440,481 .93 .70 0066 1889 235,465,129 I.665.551 818.561 •43 .71 003 s 1890 225,865,121 ''703,538 1,098.628 .64 •75 0049 189I 211,591,612 1,568,268 873,099 956,298 .56 .74 0041 1892 222,927,705 1,690,010 •5S .76 0043 189^ 217,470,280 1.750,443 1,546,829 .88 .80 0071 1894 214,414,675 1,859,261 954,875 •51 .87 0044 189s 206,288,859 1,841,560 722,576 •39 .89 00^5 1896 201,213,720 1,763,268 793,271 .45 .88 0039 1897 221,107,128 1.976,754 777,929 ■35 .89 003s 1898 218,436,489 1,888,716 1,042,267 •55 .86 0048 1899 226,004,649 1.985,522 707,750 •36 .88 0031 $2,845,795,434 $22,655,199 $12,906,186 •57 .80 0045 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk . , . . . indicates Average Rate State Loss Waves in the Light of the Diagram 1 5 1 DIAGRAM No. 16 MARYLAND •ac 1 ' , TH ' ' / 1 •7 \ ; '. 20 \ ' « / , 16 87 Id U 16 M la «0 Ifi «l 18 82 18 as 18 94 18 «6 18 96 18 •7 18 88 Id M 152 Fire-Rating as a Science MASSACHUSETTS Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 '^95 1896 1899 $573,023,604 627,167,983 618,513,881 653.153.647 648,573.843 720,240,195 731,321.894 687,413,281 748,641,946 793,066,762 876,144,166 869,245,243 912,129,097 $6,205,626 6,394.645 6,261,100 6,610,684 6,375^850 7.340,152 7,713,797 7,648,298 7.997.708 8,260,419 8,841,923 8,349.737 8,547,413 $2,657,562 3,781,151 8,527,354 3. 1 1 1.373 3.774.535 3,779,004 6,943,023 4.645.784 3.347.803 3.676,543 3,004,845 5,044,966 4.643,153 .43 •^? 1.36 •47 .59 .52 .90 .61 .42 •45 •54 1.08 1.02 I.OI 1. 01 .98 1.02 1.05 I. II 1.07 1.04 I.OI .96 •94 .0046 .0060 .0138 .0048 .0058 •0053 .0095 .0068 .0045 .0046 .0034 .0058 .0051 $9,458,635,542 $96,547,352 $56,937,096 .60 1.02 .0062 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk . . , . , indicates Average Rate State Loss Waves in the Light of the Diagram 1 53 DIAGRAM No. 17 MASSACHUSETTS 1 r TS fv 65 An 1 5 \ I 55 3 1 i J \ f 60 k ! { t 40 1 05 30 . \ '^ ■25 ^ i\ f f '\ I f t f '\ 20 f M 1 ;) i 1 / \5 1 \ J I ', \ 1 \ 10 1 1 \ 1 'y \ % 5 x \ ] / < S,, \ 1 N. 3 .'^ ' \ V ¥^ \ \ ff \ ^ ';! ' 1 \ s~7 -"! I I •■^' V 11 ^, f n > ff^V •[ \ », s 1 a 'J i V ^ 1 H .7 ' \ V\ -, 1 rt // s;^ u "S 1 .'/ \ > / \^ 1 ,'/' \ , / V tf\ 1 •/ \\ \ 1 .7 ^ 1 •I ",\ / f «\ / 'A I < // i ,/ --*-' f' Vv ■/ \\ ;/ 2c \< \l ,',' y. .'/ \> •/ y .7 ' \ ' ■ 18 &J iBbS IS idd i6d0 iS 4i is t8i 18 M 18 04 18 w n »6 18 07 18 08 la so 154 Fire-Rating as a Science MICHIGAN Year. Amount at Risk, Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1895 1896 1897 1898 1899 $241,717,833 250,349,014 275,290,724 285,900,676 279,473,169 298,767,231 301,887,793 283.738,338 288,477.918 287,902,997 303,754,605 330,603,384 370,791,030 S3.395.832 3.538,045 3.756,392 3.981,756 3.999,826 4,275.173 4,470,490 4,302,988 4,345.713 4,254,856 4.358,068 4,498,445 4,498,772 $1,929,752 1.677,544 1,722,590 2,445.754 2,478,920 2.231,883 2,571,734 2,422,483 2,089,652 2,789,439 2,115.385 2,467,546 2.299.558 •1 .46 .61 .62 •1 .56 .48 .66 .49 .55 •51 1.40 I.4I 1.36 1.39 1.43 1.43 1.48 I.51 1.50 1.48 I.2I .0080 .0067 .0063 .0086 .0089 .0075 .0085 .0085 .0072 .0097 .0070 .0075 .0062 $3,798,654,712 $53,676,356 $29,242,240 •54 I.4I .0077 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk , , . . . indicates Average Rate State Loss Waves in the Light of the Diagram 155 DIAGRAM No 18 MICHIGAN 1 JLO \ \ 15 \ I \ j \ \ y \ 10 /" j , y / 1 \ y > \ ^--' , \ t ^ , ', \ \ \ jf \ ^' 1 S \ \ \ ^ \ 1 } \i \\ \ M' / j ' \ 1 1 y , \ j I H V T, / 1 / \ \ >\ \ / JA*"^ // \ \ I • 'j ■\ \\ l^V, / ' X \ \ » \\ \ 11 y \ \ \ '\> Vv \ \ '1 J, / X \ 5 \\ \ f^\ \ 1 P / /\ \ \\ \ / \ \ \ I j / \ \ \ \\ 10 ' \ "\\ \^ \ \ \, > \ \ \5 * \ \ V 20 18 87 18 88 18 88 18 90 18 91 18 92 18 83 18 84 18 96 18 96 18 97 18 98 18 89 156 Fire-Rating as a Science MINNESOTA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 $223,062,679 $3,160,700 $2,269,072 .72 1.42 .0101 1888 222,906,027 3,244,326 1,776.256 .55 1.46 .0080 1889 240,933,687 3,349,129 1.697,747 •51 1-39 .0070 1890 262,975,835 3,084,018 1.517,771 .49 1.17 .0058 189I 239.341,353 3481,054 2,276,646 .65 1.45 .0095 i8q2 294,899,556 4,154,328 2,290,891 •55 1.41 .0078 1893 263,846,977 3,862,249 3,179.494 .82 1.46 .0121 1894 233.942,097 232,782,685 3,680,966 2,457.259 .67 1.57 .0105 189s 3.640,519 1,864,019 .51 1.56 .0080 180 243,829,165 3.717,370 1,733.368 .47 1.52 .0071 1897 251,771.259 3,499,131 1,584,703 .45 1.39 .0063 1898 277.831,536 3,590,517 1,655,650 .46 1.29 .0060 1899 309,860,117 3,908,696 2,163,642 .55 1.26 .0070 $3,297,982,973 $46,373,003 $26,466,518 .57 1.41 .0081 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums _^_^^________,^^___ indicates Loss to Amount at Risk «__,_«.«^. .«..««■. indicates Average Rate State Loss Waves in the Light of the Diagram 157 DIAGRAM No. 19 MINNESOTA Ar\ *xO 1 . \ \ \ .... \ \ \ \ \ \ \ \ \ \ 1^ \ ' 1 ', 1 ,' / « \ \ ; \ \ ; 1 «5 \ A S ! / \\' 1 • f\ ^. 1 \ \ 1 \ \ \i 1 \ \ 1 \ \ \ \ ', \ r \ 1 \ It \ \ 1 ^ c \\ > t \ \ 'v V '< / \ \ , 'V* V 1 ■ v\\ > \ V ^ i\ / y "\ \, »\ ■1 ' ^ y \ \ \ / f \ II ' ^ \ .'// \l « ^ L \\^ ■ ' \ / 5 \ ^, 1 t \ / \ ■'^ \ ' / • \ • \ 'V- ' /» •^ \ / \ \ "-^ "»» \ \ > \ ^^\ 10 \ \ / • \ \ \ '. / • \ ^^"^ — -\ / \ \ // \ s / \ \ \ ^/ 16 \\ \ /^ \\ \ / \\ \ / \\ \ / ^ V / \ N / ) X 1 ; 16 dt Id dd Id 66 18 96 Id M 18 02 18 03 18 04 18 06 18 oe 18 07 18 08 18 Ao 158 Fire-Rating as a Science MISSOURI Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1897 1898 1899 $345,519,997 357,645,224 365,027,822 376,902.754 376,398,844 418,077,261 398,858.869 348,602,501 364,577,698 382,982,600 381,870,790 405,978,355 455,156,845 $4,158,826 4,265,044 4,455,171 4,501,382 4.394.697 5,062,634 5.017,147 4,903,494 4,924,312 4.769.386 4,605,889 4,732,281 4,768,402 $3,104,470 2,437.489 2.895,381 2,632,084 3,251,195 3.857.776 4,470,416 3,464,458 2,441,923 2,366,995 2.639,951 2,967.755 2.771.528 .75 .57 Ve .89 •71 .50 .50 1 1.20 1. 19 1.22 1. 19 1. 17 I.2I 1.26 I.4I 1.35 1.25 I.2I I.I7 1.05 .0090 .0068 .0079 .0070 .0086 .0092 .0112 .0099 .0067 .0062 .0069 .0073 .0061 $4,977,599,560 $60,558,665 $39,301,421 .65 1.22 .0079 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _.^.......— .— .i... indicates Average Rate State Loss Waves in the Light of the Diagram 159 DIAGRAM No. 20 MISSOURI 1 y 30 \ \ \ \ \ \ /-o \ \ \ \ ZO / / \ ' \ » i . / / \ / 1 V 16 / 1 / 1 I / 1 s / /» / i\ \ iO A' / > \ \ r-r / ' I \ / \ \ / / \ ( \ 1 \ .K ,' f \ \ 1 1 1 y 1 \ \ ', \ «v 1 / 1 \ V \ \ \ I V / s. '■"— '^L^ y fj \*^ \ ■ \ \\ N\ / \ '\ K \i 1 1 ll *N f \ \ ,'\ w 1 j \\ \ \ .'■ y / / j \ \ \ i / JO \ 1 \ \ J / \ > t / \ < V ■ \ \, 1 / 1*^ \ ,' / >. / \ / Id 69 i6 dd \t 69 Id d6 id 61 18 92 18 93 18 94 18 96 16 96 18 97 \i 68 Id 66 ' i6o Fire-Rating as a Science NEBRASKA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 $ 89,103,912 $1,489,132 $ 636,335 43 1.67 .0071 1888 104,705,436 1,735,492 482,592 .28 1.66 .0046 1889 111,603,629 1,856,507 852,166 .46 1.66 .0076 1890 128,059,204 1,973.830 1,060,460 •54 1.54 .0083 189I 124,623,830 1.809,995 874,731 .48 1.45 .0070 1892 137,564,820 2,109,878 842,986 .40 1-53 .0061 I«93 132,591,141 1,998,147 1,288,448 .65 I.51 .0097 1894 107,641,249 1,816,538 1,126,152 .62 1.69 .0105 94,469,027 89,740,440 1,524,576 947,386 .62 I.61 .0100 1896 1,377,686 611,712 .44 1.54 .0068 1897 98,103,685 1,378,589 438,905 .32 I.4I .0045 1898 106,583,277 1,407,416 616,351 .44 1.32 .0058 1899 121,390,473 1,490,067 734,487 .49 1.23 .0061 $1,446,180,123 $21,967,853 $10,512,711 .48 1.52 .0073 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk __,__, , . . indicates Average Rate State Loss Waves in the Light of the Diagram i6i DIAGRAM No. 21 NEBRASKA — _- y \ 30 / \, / \ / \ / \ / 15 / f 1 I j \ 20 / \ / 1 1 \ / \ / J k \ \5 1 1 \ \ ''^^•— « / / 'U \ / 1 r \ \ \i • \ \ /.' 1 \ 1 \ \ li »u • / J /i i \ v/ \ /; t ^\ V \ ( A \ 1 1 V \ 5 y \ ^^ \ j \ \ . y \ \_\ I 'V ' A ^ / 1 \ \ Y 1 "iP / ^ \* i( 1 t\ y \\ / V ' ij ' ■^ i \ / / / \ \ \ ' // ^ ^ / i / ^y 1/ V \ , / \ 5 \ V N // '. \ \ // \ A > i| \\ jl \ ^\ \ '/ \ \ 1 ',\ 1 >. ^ / i\ ^ A / \ 1 10 1 / \ \ \ \ \ \, \ ' * 1 ^ il N \' « y \\ ,1 ■ \ \ \ y /5 \> ij \ \ t\ y • 1 \ \ J 1 j \ \/ \ < ' / \ V \ \ 1 j 1 \ /, 2C \ /> \ I \ / \ 1 \ / \ j \ / ' \ / \ 1.5 j \ / \ / \ \ / . 18 87 18 88 le 89 l£ 90 18 91 18 92 18 93 18 94 IE 195 l£ (96 18 97 18 98 18 90 162 Fire-Rating as a Science NEW JERSEY Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1895 1896 '^97 1898 1899 $316,313,369 385,930,288 . 352,146,777 384,731,941 392,431,147 422,688,761 435,614,110 433,453,659 467,273,355 479,964,742 520,577.823 554,472,830 565,003.431 $2,536,478 2.810,113 2,754484 2.896,856 2,944,715 3449.835 3,690,461 3,735,983 4,030,764 4,129,033 4,365,253 4,332,731 4,219,370 $1,149,991 1,037,164 1,395.505 1,552,731 1,785.629 2.452,766 1,796,498 1.774,818 2.079,568 1.765,321 1,953.978 1,902.484 2,177,167 .46 •37 •51 •54 .71 49 .48 .52 43 45 44 .52 .80 •73 .78 .75 il .86 .86 .84 .78 •75 .0036 .0027 .0040 .0040 .0046 .0058 .0041 .0041 .0045 .0037 .0038 .0034 .0039 $5,710,602,233 $45,896,076 $22,823,620 .50 .80 .0040 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk ._..._. . ._ indicates Average Rate State Loss Waves in the Light of the Diagram 1 63 DIAGRAM No. 22 NEW JERSEY •. .■"" 20 , / / ' / JS ' / / / / / / / • / /o ,' / i / \ t / • / -/ — j ■ ■■-- 5 ^'"T^ / ■">.. ..-^ / • \ / V / ^ \ / . ,"' / i / / ; \ \ J f .•' \ / k / 1 .' \ \ \ \ // **•«... .• \ / / \ V ^„,--'*" ^ V// \ s, • \, ,yl s '\, \ S, «'/ s A \ '» .,•' .\ ■f * \ / y \ -'' \ 10 '\ \ ] 18 W.I8 88.18 »» Id 90 t8 91.18 9a 18 93 18 94 18 95 18 96 18 97 18 08 Id te 164 Fire-Rating as a Science NEW YORK Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 \^ z 1899 $3,195,208,683 3,322,381,343 3,217,904,667 3,547.736,160 3,798,177,149 3.549.943,155 3,232,021,194 3.078,604,705 3,139,439,171 3,306,139,822 3,641,688,074 3,804,973,604 3,409,483,536 $18,646,059 19,828,143 18,974,441 19,689,457 19,969,024 21,411,016 21,994,619 22,339,420 22,942,274 23,444,686 23,766,292 19,963,316 19,197,447 $14,062,621 13,611,608 12,355,411 11,846,607 15,204,536 12,975,186 14,201,935 12,835,405 11,160,953 10,928,322 9,900,062 9,934,447 17,482,810 .61 .65 .58 .49 •47 .42 .50 .91 t .68 .73 •73 .0044 .0041 .0038 .0033 .0040 .0037 .0044 .0042 .0036 .0033 .0027 .0026 .0051 $44,243,701,263 $272,166,194 $166,499,903 .62 .62 .0038 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk __.«_. .^, . . indicates Average Rate State Loss Waves in the Light of the Diagram 165 DIAGRAM No. 23 NEW YORK ■■■-■T- ■ *7n ■ c .■ ■ — u T n , 1 /5 1 ' ; > 1 \ \ in I / V. ' / •« 1 'i ^ \ < \ / <, 1 / \ \ \ ; / •^ \ / \ 1 / 5 \, "v ( J ^ , 1 / \, ■>, / / N "' 7 N « / ^ \ , / \^ > /' ', S, • / V / } V \ /•' \ ,' / ' / s \ /r \ s, y ; / \ \ 7 \ \ 1 / >. > / \ > \ ' / ^ \ / > > \ \ 1 / ^ N. / / \ N '/ 5 X^ , \ • / ^ » \ (7 S, \ N, \ 7 " ^ N * \ \ ('/ y \ / \, \ '/ • 10 S, y \ f — ~-._^_ '\ } ■v. > 1 T "-». > »^ ,' ,' » \ / 18 87 18 88 18 89 18 80 18 81 18 92 18 83 18 84 18 88 18 86 18 87 18 88"«8 89 - i66 Fire-Rating as a Science OHIO Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 $447,054,235 $5,174,161 $2,729,971 •53 I.16 .0061 1888 460,342,682 5,261,188 3,182,116 .60 1. 14 .0069 1889 535,225.962 5,875,000 3,150,068 •54 1. 10 .0059 1890 581,942,938 6.177.959 3,329,238 •54 1.06 •0057 189I 504,639,964 6,392,011 4,373,743 .68 1.07 .0074 1892 595,372,645 6,784,237 4,903.114 .72 1. 14 .0082 I«93 598,904,129 7,004,871 4,146,939 .59 1. 17 .0069 1894 564,925,910 6,749,335 4,063,636 .60 1. 19 .0072 i«9.S 605,718,102 7,312,646 4.835.983 .65 I.2I .0080 1896 584,625,285 6,849,597 3,071,691 •45 1. 17 •0053 1897 647.526,369 7,138,509 3.665,554 •51 1. 10 •0057 1898 675,430.664 7,036,634 4,240,146 .60 1.04 .0063 1899 718,428,503 7,174,898 5,766,413 .80 1. 00 .0080 $7,610,137,388 $84,931,046 $51,458,612 .61 1. 12 .0068 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _. . . . . indicates Average Rate State Loss Waves in the Light of the Diagram 167 DIAGRAM No. 24 OHIO 20 • ■' • IS < / / , / / y / \ y IQ f '* \ / \ \ / ^' -z^'' ^T- I'v / / f «\ I ' K / \\ >" / \ \ f- - 1^ • / s // ^\ y ' / "v r^ M y \ \ \ .' / '^ V y / \, / y / X / / / '. \ V / / /. n // A \ • I \ / /' k il \ ' ' j h ■^ \ » 1 \ \ 1 5 // —^i..,. // \\ il,^^" ' \ \ / f/ Y^ -f i \ J /A \ j / / \. 10 ^ , \^ "^ •\ ,' / \ ,\ 'V \ ',\ ^ / f <; ■ <'' la B7 18 88 18 80 18 00 18 01 18 02 18 03 18 M 18 06 18 08 18 07 18 08 Id 80 i68 Fire-Rating as a Science PENNSYLVANIA Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1895 1896 1897 1898 1899 $ 729,037.662 766,087,877 811,767,696 883.457,672 881,296,334 934,832,895 938,403,423 886,271,730 937,276,624 961,133,999 1,017,684,501 1,033,516,858 1,097,119,021 $ 7.755.078 8,008,492 8.333,666 8,614,399 9.926,961 10,029,557 10,125,807 9,808,572 10,265,067 10,535.570 11,204,154 11,360,040 11,519,276 $4,157,588 5.095,289 4,477,232 4,716,361 5.746,927 6,110,434 6.057,111 4.874,744 5.094.715 l'¥'556 6,561,060 7,074,432 7,766,127 .64 •54 .55 ;6o .50 .50 •51 .62 .67 1.06 1.05 1.03 4 ;:S I. II 1. 10 1. 10 1. 10 1,10 1.05 .0057 .0067 .0055 .0053 .0065 .0065 .0065 .0055 .0054 .0056 !oo68 .0071 $11,877,886,292 $127,486,639 $73,077,576 .57 1.07 .0061 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss ta Amount at Risk 1 . . . ..-.•..- indicates Average Rate State Loss Waves in the Light of the Diagram 169 DIAGRAM No. 25 PENNSYLVANIA yf ^' / /' s A / V\ — . V-. U^ JJL ^ =V \—^ — -^^^ r i \\ j ^-^-\ H "TT ,^1* s^ \\ y j — ^^^ // — A —j- — 5 T" V f \ \ li ^ [I ^-'' ^"^ \ 1 3 V ^' 18 87 18 88 18 88 18 90 18 91 18 92 18 «a 18 94 IC m 18 «6 i8 97 18 98 18 89 170 Fire-Rating as a Science TENNESSEE Year. Amount at Risk. Premiums. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 $ 91,177,649 $1,264,480 $1,300,497 1-03 1-39 .0142 1888 106,966,686 1,490,866 846,727 •57 1-39 .0079 1889 109,647,406 1,543,273 691,466 •45 I.41 .0063 1890 121,502,336 1.780.539 853,620 .48 1.46 .0070 189I 125,910,310 1,855,847 1,360,249 •73 1.47 .0108 1892 129,366,106 1,970,017 1,943,659 .99 1.52 .0150 i«93 122,186,972 1,879,793 1,245.035 .66 1.54 .0102 1894 115,880,325 1,784,281 1,124,404 .63 1.54 .0097 1H95 118,133,723 1,947,130 941,932 .46 1.65 .0080 1896 124,113,750 1,964,975 985,013 .50 1.58 .0079 'H 135,541,324 2,036,228 1,926,250 .95 1.50 .0142 1898 132,068,762 2,024,408 1,703,921 .84 1-53 .0121 1899 156,448,397 2,346,475 2,001,652 •85 1.50 .0128 $1,588,943,746 $23,888,312 $16,924,425 .71 1.50 .0107 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk —........_. ._..-i. indicates Average Rate State Loss Waves in the Light of the Diagram 171 DIAGRAM No. 26 TENNESSEE r ■ , / j] ll 1 \ «( 1 \ ll j \ IJ jj , ( / / t t I t • ' ', • \ ; \ \ 1 • " J 1 1 ' '* \ / 1 ', 1' \ \ / ; / t / , 1 ■ \\ / Q *i k V r ' II ■1 1 \ N \>. \ jl / 1 ^\ 1' /' ■ • / \ ; r I ; )( ! / > \ . 1 1 k ; t \ 1 ' \ , • t \ 1 ' \* ', ^'A ^ y V / *^ 1 - -4 , 1 ,' / 1 -"m 1 4 1/ ' }l ^- } / •I V.> >V^ / > 1 N, ^ ; / \ \ ■4^ ; 1 ' / f \\ 1 \\ : ,' V » / i ' \\ ; • , • J 1 / — vH • ' \> \ V / V ,' ', ^' ■ 1 y \ \ / \ 1 \ \ \ \ / \ / \ / \ / \ /' >^ / > 1887 1888 IG 89 IE 80 l£ 9i 18 92 IG 93 IG 94 l£ (96 1898 1897 IG 98 Ifi dd 172 Fire-Rating as a Science TEXAS Year. Amount at Risk. Premmras. Losses. Loss to Prems. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 1891 1892 1893 1894 z z 1899 $123,136,846 136,007,009 146,313,830 167.634,576 198,268,974 210,487,358 206,596,810 179,937,487 198,613,042 215,976,009 223,883,452 263,245,896 277,853.544 $2,209,491 2.342,908 2.497,474 3.039.255 3.352.397 3.477.506 3.658.308 3.217.273 3.589.867 3.575.845 3,606,896 3,990,856 4,289,804 ;55i,445.30i 985,242 875.756 1,359.884 2,580,959 2.513,245 2,465,783 2,332,294 1,892,879 2,631,947 2,092,317 2,485,617 2,547,431 .65 .42 .35 .45 •77 •72 .67 •73 •53 .74 .62 .59 1.79 1.72 I.71 I.81 1.69 1.65 1.77 1.79 I.81 1.66 I.61 1.52 1.54 .0117 .0072 .0060 .0081 .0130 .0119 .0119 .0130 .0095 .0122 .0093 .0094 .0092 $2,547,954,833 $42,847,880 $26,208,655 .61 1.68 .0103 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk . . .._..-. .—. indicates Average Rate State Loss Waves in the Light of the Diagram 173 DIAGRAM No. 27 TEXAS „,.f . , L 1 V J \ , 1 \ ' 1 \ 1 \ 1 \ 1 \ / \ / \ / \ \ \ \ \ \ > 1 \ • / \ ^x / ^'1 ^ / ' ', \ ^ L / \ ,^ »'"7 ; ,\ \ / \ U \ ^V \ I \ / •' \\ \ / \ i 1 I » / ' i\ \ / \V \f / \/' ^J ' w fs 1 I ^ \ \ V / \ ■^^ •• «^ \^ \> 1 j * 1 \ 1! \ 'i. s \ \ \l \ \ 11 I /■ \\ /' ^ I \ / "« \ • >1 i\ 5 \ \ . \ \ ^ r I 1 T ; ^\ 1 1 ^ 1 - 1 ,'1 \ \ " \ - tr > \ \ ^'^ I ' < > 1 1 \ / \ / / i \ s / 1 1 1 1 1 \ j \ 1 \ 1 \ f \ j \ 1 ■ \ 1 -» \ 1 \ j \ 1 ^ w 16 M i^ BO 18 OD 18 01 18 92 18 93 18 94 18 96 18 0618 07 18 98 18 90- 174 Fire- Rating as a Science WISCONSIN Year. Amount at Risk. Premiums. Losses. Loss to Prams. Aver- age Rate. Loss to Risk. 1887 1888 1889 1890 189I 1892 1893 1894 1895 1896 1897 1898 1899 $192,081,477 204,974,184 211,619,211 235.491.558 250,499,473 279,587,965 285,731.373 255,243,795 276,592,519 271,402,055 .288,145,411 311,624,325 338,230,869 $2,903,821 3,234,481 3,169,675 3,372.724 3,514,517 4,140,420 4,429,768 4,237,866 4,438,985 4,255,283 4,151,300 4.235.702 4,506,039 $1,836,123 1,784,585 1,652,574 1,422,343 1,517,358 3,333,970 3,124,279 2,750,077 2,995,474 1,833.119 1,540,914 1,825,009 2,300,906 .63 .55 .52 .42 ■P .80 •70 ii •43 .37 .43 •51 :i8 1.50 1.43 1.40 1.48 \:U 1.60 1.57 1.44 1.36 1-33 .0096 .0087 .0078 .0060 .0061 .0119 .0109 .0108 .0108 .0068 .0053 $3,401,224,215 $50,590,581 $27,916,731 .55 1.49 .0082 Note. — The waves created by the ratios in the above tabulation are shown in the ratio-diagram on the opposite page, in which indicates Loss to Premiums indicates Loss to Amount at Risk _...^. .... . indicates Average Rate State Loss Waves in the Light of the Diagram 175 DIAGRAM No. 28 WISCONSIN 5 I s 3 1 1 r ' 1 1 ->s — \ w 1 M — h V — 1 -f— -7A > £ 1 * -J f "H — \ ^ — -V- ==^ ^ ' ^r* ^^ -A- V V~^ ^ 4— ^ ' *- — -V- -r— ) y L i — \ ' 5 -\ — A- / tr* N t=^ ^!i: =\= bt= ^ / — 5 =^ h^ ^ ^ 1 1887 1888 1880 1800 1801 1802 1803 1804 1806 1806 1807 1808 1800 176 Fire-Rating as a Science The preceding diagrams have been constructed for the pur- pose of showing the contour of the waves with which fire insur- ance has to deal, rather than for the purpose of making an exhaustive study of the waves and their mutual relations, though it is proper to briefly point out the utility of such diagrams as a means of deductive reasoning. It is obvious at first glance that each diagram has a distinct character of its own as easily recognized and remembered as the lineaments of an individual human countenance. It is equally obvious that each diagram reveals, in a comprehensive whole, the sequential phenomena of the three ratios with which fire insurance has to deal, showing relations among these ratios which are hidden in the nebulous official tabulations from which we have been accustomed to seek in vain for practical information in a con- crete form. It should be borne in mind that the wave of loss to premiums may be considered identical with the wave of cost {i. e., losses plus expenses) as long as the expense ratio remains unchanged, for the addition of any given percentage simply elevates the wave without changing the relations of its fluctuations to its own mean line. In every diagram the rate wave fluctuates without apparent relation to the two loss waves; on the contrary, the two loss waves not only have the same general contour, but in some states accompany each other so closely as to be almost identical. In other states, while the contours of the two waves are similar, they spread widely apart some years, while accompanying each other closely during other years. Before inquiring into the reasons for this it is well to first consider the wave of average rate. This wave represents the fluctuations in the percentage obtained by dividing the total amount at risk each year into total premiums, hence it is a direct percentage. For the same reason, the wave of loss to amount at risk represents another direct per- centage, obtained by dividing the total amount at risk into the total losses of each year. On the other hand, the ratio of loss to premiums is obtained by dividing total premiums into total losses; and as premiums themselves are a percentage, the loss to premium line represents a secondary percentage — the ratio State Loss Waves in the Light of the Diagram 177 of a ratio; hence, the wave representing a direct percentage of amount at risk, and the wave of loss to premiums representing the percentage of a percentage of the same quantity, necessarily run in the same general direction, spreading apart in proportion as the relations between amount at risk and premiums vary.* When amount at risk rises with relation to premiums, loss to risk descends with relation to loss to premiums and vice versa. This is the law of variation found in the relations between the two loss lines, but as the rate line also represents the varying relations between amount at risk and premiums, showing the annual rise and fall of each with relation to the other, it would seem that in the absence of influences disturbing their normal percentage relations, the rise and fall of the rate line above and below its mean line would show proportionately the rise and fall of the dotted line above and below the line of loss to risk in each dia- gram. That the range of variation between the two loss lines con- tains much of the unwritten history of state rate disturbances goes without saying. Indeed, it might be said that the stage upon which the rate drama has been enacted lies between the footlights of the dotted line and the background of the line of loss to risk. It would take a Sherlock Holmes to unravel the tangled plot of melodrama shown by these two lines without explanatory notes in the shape of a diary of the rating history of each state. With such information it would be possible to analyze and apply quantitative measurement to the effects produced by these disturbances, through ratio-diagrams, quantitative diagrams, and differential diagrams, and such information under a continu- ance of present conditions would doubtless enable us to forecast the probable results of specific disturbances with a certainty unknown in the past. The limits of this inquiry will not permit such investigation, though it is proper to make the suggestion plainer by an examination of one or two states under diagram- matic analysis. Utilizing the tabulations from which the previous ratio-dia- grams were constructed, we are able to construct quantitative ♦It will assist in remembering the three wave lines to bear in mind that the ratio of loss to premiums being a ratio of a ratio is indicated by a dotted or shadow line in every diagram. 178 Fire-Rating as a Science diagrams of each state for the same thirteen-year period, showing the rise and fall in amount at risk and premiums above and below their respective mean lines. By imposing these upon the same mean line, we are able to see their relations to each other each year, as shown by the following quantitative diagrams of Massa- chusetts and California. DIAGRAM No. 29 MASSACHUSETTS Quantitative Diagram, showing relative annual increase in amount at risk and premiums, compared with their average for thirteen years. Heavy Line Amount at Risk= Light Line - - Premiums. '■■ ' |1%C > / / / I2( / j / V \ 1 \ 1 \, IJ5 / \, n \ y^ // s, y // / ' 1 110 / 1 /\ f y ) / / / / y / / / / / f / ^ / ^ 1 loo /l'^ V. I i^ \ / yr \ / \ / \ / CkK \ / > / ©0 ^ / // s. // \ // X 85 ^ '^^-^ r/ ^ / ^\ / / / / 80 / 18 87 18 88 18 89 18 90 18 91 18 92 18 83 18 84 18 96 18 86 18 97 18 98 18 89 State Loss Waves in the Light of the Diagram 179 DIAGRAM No. 30 CALIFORNIA Quantitative Diagram, showing relative annual increase and decrease in amount at risk and premiums compared with their average for thirteen years. Heavy Line --- - - Amount at Risk. Light Line Premiums. 1880 1891 1892 1883 188* 1886 1886 1807 i8o Fire-Rating as a Science In the two preceding diagrams the rise and fall of the premium line above and below the line of amount at risk can be shown more clearly by making the latter a straight line as a standard of comparison, as shown by the following diagram of Massachusetts. If we now compare the resulting wave of premiums with the rate- line in the ratio-diagram of Massachusetts (No. 17) the two will be found to be identical with the exception of the variation indi- cated by the dotted line in the following diagram which shows the divergence of average rate-line. This line was constructed by dividing the amount at risk each year into the premiums of the same year, while the quantitative line was constructed by dividing the mean or average amount of annual premiums into the premiums of each year, and the mean of amount at risk into annual amount at risk. In view of the widely different processes by which these lines were constructed, involving an entirely different series of calculations, the similarity of the two lines is notable. DIAGRAM No. 31 MASSACHUSETTS Diagram showing line of rise and fall of annual premiums above and below annual amount at risk, compared with rise and fall of average rate-line for same period. Heavy Line Annual Premiums. Dotted Line Average Rate Line. 1887 1888 1889 1890 1891 1892 1893 1894 1896 1896 1897 1898 1899 By superimposing upon the preceding diagram the line showir>g the rise and fall of loss to premiums above and below the line of State Loss Waves in the Light of the Diagram 1 8 1 loss to risk, as shown in ratio-diagram of Massachusetts (page 153), we have the following differential diagram showing the an- nual relations of rate-line; line of variation between premiums and amount at risk, and line of variation between loss to premi- ums and loss to risk. It will be observed that the last named follows the same general direction as the others, varying only one point for seven successive years (1887 to 1893 inclusive). DIAGRAM No. 32 MASSACHUSETTS Differential diagram containing the same lines as the preceding diagram, with additional line showing rise and fall of loss to premiums above and below line of loss to risk. Heavy Line Annual Premiums. Dotted Line Average Rate. Light Line --- .- Loss to Premiums. »o J V / / K / y \ > V. /< >. s. V ^ \ \ \^ y \, N V _^ \ N ^ s. ^-^r^:* y* ^-\ ■^i;^"^ ~1^ ^s« ^ ^v 6 ^~^^_^ •n. ^v^' x. 10 \ 1887 1888 1889 1890 1891 i89S^ 1893 1894 1896 1896 1897 1898 1899 The preceding diagrams, while they do not indicate that Massachusetts may have been more or less profitable than other states, do show a remarkable absence of disturbed relations for thirteen years during which the state experienced tremendous fluctuations in its loss ratio caused by the Boston and Lynn con- flagrations of 1889 and 1893. In marked contrast to the preceding diagram of Massachusetts is the following diagram of California, constructed for the same period, and in the same way: I82 Fire-Rating as a Science DIAGRAM No. 33 CALIFORNIA Differential diagram containing the same lines shown by the preceding diagram of Massachusetts. Heavy Line Annual Premiums. Dotted Line Average Rate. Light Line Loss to Premiums. 1 - 2C ^•^ ■ ^^^ ; 15 / x / y '"x. J '' \ ' / N _^ V \ r-^^ \, ^v iO y ^ ^. " / V ^ X / " — l._l 1 I / >r \ X ' ^-r \ >^ r ^ ^ \ \ 5 / \, [\ " / \ ;\ / \^ _^,^^.^^ / N ^^ 1 1 Xj ^ \l r% i\l lA " 1 \ u / • \\ / ■ 5 1 \ \ / '■ \ \ / 1 \ \ / I I ' / 1 \ ^ / j ^^ ^ )0 \ / / \ ,^^ 1 \ \ ■■/■f " 1 I \ / / ', \ \ / / 1 1 \ / ^ le 1 1 \ 1 \ ', \ > \ \ / ( \ \ / ' ^C \ / 1 ■ ■ \ / / \ / , \ / 1 25 \ ' ' \ 3C 1 1 35 > ' . ', ' ' 40 , 1 AC • 45 18 87 18 88 18 80 18 00 18 91 18 02 18 03 18 04 18 06 18 96 18 07 18 98 18 99 Note: It should be borne in mind that as premiums ascend in relation to amount at risk, the wave of premiums in the quantitative diagram descends, consequently, in order to show the relations with rate wave, the premium wave is inverted in the two preceding diagrams. State Loss Waves in the Light of the Diagram 1 83 The ratio-diagram of California (No. 7) shows that from 1887 to 1894 (with the exception of one year) the rate-line ranged from twenty to thirty points above the line of loss to premiums. The business was so profitable that no agreement could be maintained, and the cutting of rates and division of commissions became the rule rather than the exception. Finally, at the beginning of 1895, the situation culminated in an explosion and the line representing loss to premiums soared heavenward, while the average rate line plunged otherward. It will be observed, however, that the dotted line ascends far above the line of loss to risk because of the abnormal descent in the rate line. The California rate-war lasted about two years, when rates were restored at about thirty points above the lowest fluctuation of the rate-line. In the New York diagram (No. 23), it will be seen that the rate-line, while descending rapidly, remained from fifteen to twenty-five points above the line of loss to premiums from 1894 to 1898. The inordinate profits created by this brought about a reign of demoralization, which, as in California, culminated in a bomb-like explosion that sent the dotted line skyward where the diagram leaves it suspended like Mahomet's coffin, and the more recent record of the state for the past year gives no indication of its return to earth. The two ratio-diagrams of California and New York teach in a forcible manner the lesson, that it is a bad omen in fire insurance when the rate-line is allowed to soar too long and too far above the loss lines. In dealing with large statistical aggregates running into nin« or ten figures, there is a tendency in the popular mind to attach undue importance to disturbing influences, seemingly important in themselves, but really trivial when compared with grand totals. It is true that rates are constantly subject to these influences, but as a rule they either offset each other or are so insignificant, when compared with statistical aggregates, as to lose themselves in the immensity of figures. While all our ratios are more or less subject to minor perturbations from local and temporary causes, the average rate in the Western states has for years exhibited a notable downward tendency, caused by the gradual substitution of brick for frame. This tendency, however, has been a con- stantly diminishing quantity, and east of the Missouri River has 184 Fire-Rating as a Science become imperceptible. In the newer Western and Southern states it is still a measurable influence. When a state, during a given year, shows a large increase in amount at risk, about half the losses on annual risks accrue dur- ing the next year. If, during the next year, the volume of busi- ness is largely diminished, it follows that the losses on the larger amount must be charged to a year of small business, and the ratios of loss to risk and loss to premiums will both be materially increased. At times this increase in volume may be on either a high or low rate wave, which, in either case, disturbs the ratio between amount at risk and premium. This phenomenon is most noticeable in the agricultural states, where a year of large or small crops may cause a considerable change in volume of busi- ness. It is also proper to take into consideration the fact that the annual increase in national wealth, which is estimated at about four per cent, has a tendency to create in many states an apparent profit, year after year, which must eventually disappear when the amount of insurable property ceases to increase. TABLE COMPARING AMOUNT AT RISK AND PREMIUMS OF 1887 WITH THOSE OF 1899 States. Arkansas Georgia Colorado North Dakota — 1890-- South Dakota — 1890 .- Illinois Iowa Kansas Kentucky Massachusetts Michigan Minnesota Missouri New Jersey Nebraska Ohio Pennsylvania Tennessee Texas Wisconsin Oklahoma — 1891 Indian Territory — 1891 Amount at Risk, Amount at Risk, Per Cent 1887. 1899. of Gain. $ 26,509,590 $ 58,252,947 120 115,292,842 177,137.318 54 48,570.113 123,085,228 153 17,109,760 35,846,362 no 18,515.305 27,217,678 47 806,454,052 1,141,060,852 42 190,954,696 280,071,272 47 131,148,505 183,444,721 40 161,271,533 201,319,734 25 573,023,604 912,129,097 59 241,717,833 370,791,030 53 223,062,679 309,860,117 39 345,519.997 455,156,845 32 316,313,369 565,003,431 79 89,103,912 121,390,473 36 447,054,235 718,428,503 61 729,037,662 1,097,119,021 50 91,177,649 156,448,397 72 123,136,846 277,853,544 126 192,081,477 338,230,869 76 715,768 14,568,981 1937 2,044,876 13,520,035 561 State Loss Waves in the Light of the Diagram 185 In order to show approximately the effects of this increase in creating an apparent profit in each state, it would be necessary to construct a companion series of diagrams showing the quantita- tive relations each year between the amount at risk and premi- ums, embracing the same period shown by the state ratio-dia- grams. The effects of a steady increase in amount at risk and premi- ums may be inferred from the preceding tabulation, showing a comparison between the years 1887 and 1899 in amounts and percentage of increase. The following table indicates, approximately, the per cent of fictitious annual underwriting profits appearing in our statistics, occasioned by annual growth in amount at risk for the years 1897, 1898, and 1899: PERCENTAGES OF FICTITIOUS PROFITS Colorado Illinois Iowa Kansas Michigan Minnesota Missouri Nebraska Ohio Wisconsin Indian Territory _— Oklahoma Territory North Dakota South Dakota 1897. 1898. 2 I 4 3 3 5 2 3 4 2 5 3 4 4 5 2 3 4 14 13 19 19 10 3 9 2 9 4 '/ 10 6 I 6 3 4 15 19 13 9 The profits of many states would be materially reduced if we should eliminate this illusive percentage of apparent profit which has accrued from what is known in sporting parlance as ''playing on velvet." Without doubt this percentage of apparent profit in some of the newer states and territories has far more than offset any reduction in average rate from the substitution of brick for frame business. While these two counter-balancing influences (resulting from improved construction on the one hand and rapid increase in volume of business on the other) have tended to neutralize 1 86 Fire-Rating as a Science each other, there can be no doubt that the rate-line in the dia- grams is substantially correct in showing the real trend of rates in the Western states. The fluctuation of this line, as shown by the ratio-diagrams, is full of information of exceptional interest at the present time. It is a well-known fact that immediately following the panic years of 1892 and 1893 there was a general advance in rates throughout the West of about tv/enty-five per cent. The disastrous results of this arbitrary advance, in adverse legislation, and the phenomenal growth of irresponsible compe- tition, is a matter of history. The rates so summarily hoisted without regard to ultimate consequences, as will be seen by the diagrams of all the Western states, began to come down at once, and have been sinking ever since, but the extent of the decline in each state is shown for the first time in the preceding state diagrams. The decline in the rate-line since 1893 may be summed up as follows: TABLE SHOWING DESCENT IN RATE LINES FROM 1893 TO 1899, INCLUSIVE In Arkansas (average rate 216) 61 points or 28 per cent. In Colorado (average rate 166) 27 points or 16 per cent. In Illinois (average rate 125) 14 points or 11^ per cent. In Iowa (average rate 167) 19 points or 11 percent. In Kansas (average rate 140) 37 points or 26 per cent. In Michigan (average rate 151) 29 points or 18 per cent. In Minnesota (average rate 157) 30 points or 19 per cent. In Missouri (average rate 141) 36 points or 26 per cent. In Nebraska (average rate 169) 46 points or 27 per cent. In Ohio (average rate 119) 21 points or 18 per cent. In Texas (average rate 179) 30 points or 17 per cent. In Wisconsin (average rate 166) 33 points or 20 per cent. In view of the fact that present rates ensure an underwriting loss, it will be instructive to refer again to the state diagrams and note the positions of the line of loss to premiums and rate line with relation to their mean line and to each other at the beginning of the year 1900. This is shown by the following tabulation ; State Loss Waves in the Light of the Diagram 1 87 TABLE SHOWING POSITION AT THE BEGINNING OF THE YEAR 1900 OF LINE OF LOSS TO PREMIUMS AND LINE OF AVERAGE RATE, WITH RELATION TO THEIR MEAN LINE AND TO EACH OTHER Loss to Premiums. Average Rate. Loss to Premiums Above Average Rate. Ohio Illinois --- Michigan _ Wisconsin Minnesota Iowa Missouri -- Kansas - - - Nebraska - Colorado - Arkansas - Texas +19 +14 — 3 — 4 — 2 + I — 7 -- 7 -- I 7 I — 2 — 12 — 5 —20 —16 -15 — 7 —17 —22 —29 —24 —29 —14 31 points 19 points 17 points 12 points 13 points 8 points 10 points 29 points 30 points 41 points 30 points 12 points Note: The plus mark indicates above the mean line, and the minus mark below the mean line. " The progress of human knowledge has all along been equally charac- terized by analysis and synthesis; by the differentiation implied in the recognition of relations that are more and more special, as well as by the integration implied in the grouping of relations in classes that are more and more general." * A necessary corollary of the above is that the greater the number and diversity of the relations we are able to establish between any given phenomenon and other phenomena, the nearer we approach to a true understanding of its nature. An effort has been made in this chapter to utilize our data in establishing, through the symbolic notation of the diagram, a few of the most suggestive relations among the phenomena of fire insurance waves. These relations may be summed up as follows : The sequential relation of each ratio with its own mean or average for a given period of years. The contemporaneous relation of each ratio with other ratios. The quantitative relations, in annual sequence, of amount at risk and premiums to each other and to their respective mean lines. ♦Cosmic Philosophy, John Fiske. 1 88 Fire-Rating as a Science The deviation between the two loss ratios and the relation of this deviation to the fluctuations of the average rate-line, as well as to the quantitative relations between amount at risk and premiums. The law of fictitious profits or losses, arising from quantita- tive variations in amount at risk. The total descent in rate-line from maximum for each state, stated in points and percentage. The present position of each ratio with relation to its mean line and to other ratios. If the object of all reasoning is the establishment of relations, we have here an array of relations which ought to enable us to avail ourselves of the process known as dead reckoning in order to determine our position with relation to the sun of known cost, in which the mean lines of income and outgo converge. But there is an unknown quantity, without which we can determine our position only with relation to each state, as a whole. The exigencies of rating demand that we should know these relations with regard to classes and the unknown quantity which would enable us to determine these relations, if it exists, is at present carefully guarded in the strong boxes of the companies. Dead Reckoning In some states, if we add the expense ratio to the loss ratio for the thirteen-year period, embraced in the diagrams in the preceding chapter, the total makes a cost ratio of exactly one hundred per cent, which signifies that exactly one dollar was expended for each dollar received in these states; hence, the rates of these states, taken as a whole, would be cost estimates if our experience with all classes had been uniform, but experi- ence by classes has not been uniform. In these states, where the business as a whole has been written for thirteen years at exact cost, we have made a profit on some classes and a loss on others. If we had the combined experience of the companies on each class in these states year by year, it would be possible to construct diagrams of ratios and quantities, and thus establish relations for each class similar to the relations established among state ratios in the preceding chapter; but this data is unobtainable, and the estimating faculty we call into play in establishing basis tariffs must be utilized in establishing the estimates of relative cost necessary as a working hypothesis in scientific rating. It may be said that every science in existence has started with hypotheses or provisional assumptions which have one by one been proven or discarded, and fire-rating is no exception to this rule. It must utilize provisional assumptions. It does not follow that in the establishment of any given series of assumptions to be used as standards for ratiocinative proof, we are necessarily barred from utilizing such data as we have, or from following the reasoning methods upon which all science is based, but it does follow that the establishment of such assumptions in fire-rating is a work for trained thinkers untrammeled by considerations of expediency, personal interference, or the political influences which beset fire insurance from within and without. The work must be founded upon correct reasoning freed from extraneous influences, for the end sought is a logical system of coexistent relations to be used 189 190 Fire-Rating as a Science as a standard of comparison. The thing to be built is not a price list to be enforced by the companies, but a national basis schedule of estimated cost-relations based as nearly as possible upon com- bined experience. The companies must furnish the information, but the work of analyzing it and establishing the relations sought in our complex standard is not a work for caucus or cabal. When these relations have once been established, and state schedules of estimated cost relations constructed to show rational percentage relations to this national schedule, and the country has been rated upon this basis, it will then be for the companies to say collectively or individually what relation their rates or selling prices shall bear to this standard of estimated cost relations. It follows that what we really need is not exact cost on each class in each state, but a system of permanent coexistent rela- tions to be used as standards in adjusting our selling prices. These standards we are justified in calling estimated cost relations because they are inte?ided to show the cost of our goods instead of the selling price. The essential point is to have standards by which to measure wave motion, and that these standards be permanently established in order that they may serve their purposes as stand- ards. For practical purposes, it matters not whether they be too high or too low, for in either event they will serve their purpose as standards, provided they remain stationary and are not changed to suit individual caprice. Nor is it even essential in a national schedule that the basis schedules of individual classes should bear true relations to each other^ for each is intended to serve for the standard of its class only. Minor considerations, however, make it desirable that a national schedule of this kind, as nearly as possible, be based upon the average experience of all states. In other words, what we call cost should be as near cost as we are able to make it. It is an interesting question how best to approximate this average cost in a standard national schedule, and while the whole subject of tariff construction, depending as it does solely upon appraisal of analyzed hazard, lies outside of the discussion of fire-rating as a science, it seems worth while to submit the following suggestions: The average rate of any given state is determined largely by the character of its dominant hazards. A state with a high loss Dead Reckoning 191 ratio may have many classes rated lower than another state show- ing a low average rate, and vice versa. When we turn to the ratio of loss to premiums we find that this ratio, which is a percentage of a percentage, may be high in a state with a low average rate, or the contrary. If, however, we deduct from the average rate the per cent of underwriting profit, we have the rate of average cost, and in states where the deduction shows the cost so obtained to be the same as the national cost, it follows, if the state has been rated by tariff, that we obtain in this tariff a set of estab- lished cost relations more or less true, but at least established relations which would serve as a clue in building a national tariff of estimated cost relations. A comparison of this sort shows that the cost ratio of three states (Massachusetts, Pennsylvania, and Illinois), is substantially identical with the national cost ratio. We find by further compari- son that in these three states the ratio of loss to amount at risk is also practically identical with the same ratio in the national experience for ten years, as shown in the table on page 124. It is true that if we select any given class in any one of these states, we shall probably find its rates materially different from its rates in the other states, and the adjustment of these differences must be a matter of judgment. The point is, that in these three states, we find established relations covering a wide variety of important classes, which, as a whole, give exact national cost, hence, these relations constitute a logical basis of reckoning in the effort to establish a national tariff of cost estimates, for use as a standard, which will be reasonably close to what it purports to be. It may be assumed that the states having the largest amount of a given class of business will best understand this business, and naturally have the most complete basis schedule for this class. Massachusetts is the natural center of textile industries, leather-workers, paper-mills, and many other impor- tant industrial classes. Pennsylvania is the center of industries connected with mining, and is doubtless provided with complete schedules for coal and iron risks, glass factories, etc., while in Illinois we find the dominant hazards to be packing establish- ments, elevators, breweries, distilleries, lumber, wood-workers, and other hazards connected with the output of the Northwest. ig2 Fire-Rating as a Science In these three states we have, ready to hand, approximate cost relations established for nearly all the leading classes of the country. These relations would constitute a guide in the con- struction of a national schedule, and this schedule when con- structed would, with present data, constitute the nearest possible approximation to the average cost relations of the aggregate busi- ness of the country, which is the end sought. This tariff once constructed, the average cost of other states, as indicated by percentage of underwriting profit, would furnish a reliable clue to the percentage increase or decrease necessary in the compara- tively simple task of constructing state tariffs of cost relations as standards for the construction of local tariffs. When the mariner, in time of stress, seeks to determine the position of his vessel on the sunless waters, he is forced to resort to the log and compass in the process known as "dead reckon- ing," and in this process he is compelled to make proper allow- ance for drift and leeway. In the "dead reckoning" to which in our time of emergency we must resort, in order to determine the position of the sun of fire cost, it is proper to make due allow- ance for the drift and leeway of our business, by the exercise of common sense, but it is not necessary to quibble over niceties until our ship goes ashore among the breakers. To quote the advice of an eminent scientist: " Minor perturbing influences must for a time be left out of considera- tion just as the inequalities of motion resulting from the attraction of planets were at first passed over in the search for the law of gravitation." After all, absolute cost is to the science of fire-rating what the ultimate atom is to the chemist. No one has ever seen or will see an atom. It is possibly as far beyond the reach of the microscope as the limits of space are beyond the reach of the telescope. There is a wide range of opinion as to what the atom is, but without wasting time in fruitless speculation, the chemist utilizes the theoretical atom he is compelled to assume as the working hypothesis of his science. Our perturbed conception of fire-cost as a something unat- tainable by measurement, becomes clarified when we realize that the thing we call cost, like Epictetus' definition of a syllogism, is ' ^f/ie measuring -rod and not the thing measured. ' ' Drift and Leeway In computing the state diagrams which appear in a previous chapter, a period of thirteen years was selected in order to obtain three years' experience as a starting point, for the purpose of showing by comparison what the annual cost wave would have been in computing each year from the average of the preceding three years, but subsequent investigation showed that a line so constructed would not be the cost line resulting from an intelli- gent control of rates. In any rational system the lines of loss ratio as a cause would logically determine the average rate line as an effect. In the past they have exercised an interacting influence. The loss ratio lines have influenced the rate line, and the rate line has, in obscure and perplexing ways, exercised a reflex influence upon both loss lines. This reciprocal influence has tended to create illusive appearances which in no small meas- ure have helped to cause the welter of unreason from which sooner or later it will be necessary to extricate fire-rating. Of the three lines, the rate line has been a line of expediency, and the line of loss to premiums has been simply a ratio of this expediency. To attempt to trace out a logical rate line from the loss to premium line would be as fruitless as an attempt to inter- pret the laws of causation manifested in the wheeltracks of a buggy hitched to a shying horse. Of the three lines, that of loss to risk alone exhibits a record of the real laws of causation in fire destruction per se^ and while this line is supposed to exhibit a close approximation to the real ratio of loss to amount at risk, it too, has been distorted by obscure influences which would gradually disappear with the introduction of scientific method in rating. Among the influences which have created these illusive appear- ances and which have affected all three of the ratio lines, the most important has been the wide differences year after year in amount at risk. These differences have created deceptive appearances 193 194 Fire-Rating as a Science of underwriting profit or the contrary. While in any long period of years this influence becomes more or less absorbed, it has in the past often exercised an important effect in determining the course of all three of the ratio lines. An analytical comparison of the amount at risk, in the quantitative diagram of a state, with the line of loss to risk in the ratio diagram of the same state would, it is true, enable us to figure out closely the effect of these changes in the annual amount at risk upon the statistics of the succeeding year, but the problem is further complicated by the growth of moral hazard and blanket insurance during periods of rate demoralization. These causes, as well as the quantitative reasons mentioned, all tend to disturb the reliability of both the loss lines as indicative of actual experience. A comparison of the quantitative wave of any state showing the amount at risk each year with the wave of loss to risk, reveals the fact that these waves almost uniformly pulsate in opposite direc- tions. This phenomenon is, of course, subject to exceptions caused by large fires and other unforeseen influences, but the pulsa- tion is so regular as to establish the law that, with normal losses, as amount at risk goes up, loss to risk goes down and vice versa. It follows that a true understanding of relations can be obtained only by expert analysis which takes careful account each year of the proportion of total risks on which losses occur during the succeed- ing year, or what is the same thing in effect, of unearned premiums. An illustration of the deceptive appearances in our annual statistics is found in California. The ratio diagram of this state (page 133) shows a tremendous drop in the rate line and a cor- responding rise in the line of loss to premiums during 1895 and 1896. Had there been a large increase or decrease in the amount of risk during either of these years, there would have been a cor- responding fluctuation in the loss-to-risk line, but as shown by the diagram it varies only four points from 1895 to 1899 inclu- sive. We find, however, that the amount at risk rose about forty per cent in 1898 over 1897. As about half the losses on any given year's business are paid the next year, this naturally would have caused a large drop in the loss-to-risk line during 1898, but the ratio-diagram shows a drop of only two points. This would indicate that under normal conditions loss to risk was increased Drift and Leeway 195 about twenty points by blanket insurance, term risks written during the rate war, and moral hazard resulting from the same cause. In spite of this fact the official figures give no indication of the real phenomena shown by the ratio lines. Illusive appear- ances of this kind permeate the official statistics of fire insurance and are a constant source of illogical inference not only on the part of the public but of fire underwriters as well. This species of astigmatism, caused by deceptive appearances, can be cured only by expert analysis which as far as possible will eliminate from our statistical aggregates these appearances and allow us to see the naked truth. No analysis of this kind has ever been attempted or possibly ever conceived, but it is only through such analyses that we can take into accurate account the **drift and leeway" which enters into the rating problem. This drift and leeway, however, is largely incident to existing methods. With the introduction of scientific rating, with stand- ard cost estimates and flexible rates, the aberrations caused by disturbed conditions would become a diminishing quantity, and those caused by fluctuation in amount at risk would become purely a matter of mathematical computation. It is probable that with the establishment of scientific method, experience would soon show the logic of having no fixed periods for rate modifications, except as judgment might suggest. In some classes or states rates might properly be permitted to remain unchanged indefi- nitely, while in others, changes might seem advisable every year. The all-important thing is that rate changes could be made con- cretely or discretely anywhere or everywhere without delay or expense and without disrupting or even disturbing a vast system of published tariffs. Under such conditions the line of annual loss to premiums would become obsolete. A new line of annual cost would take its place and the difference between this and the line of annual premiums, or underwriting income, would show the margin of underwriting profit or loss each year, pointing out unmistakably after an annual reckoning of drift and leeway just what should be done with the rates of any class in any state.* *There is a constant ebb and flow of hazard resulting from the introduction of new methods of heating, lighting, and motive power, new industrial processes, new structural features in buildings, and improved lire oetecting, extinguishing, and retarding devices. These things, however, properly belong to tariff construction, through which their effects are gradually revealed in statistical aggregates; hence, thev are not legitimately a part of the drift and leeway resulting from illusive appearances in these aggregates. Summary Our inquiry as to the possibilities and limitations of fire-rating as a science began with an investigation of the fundamental principles on which all science is based. As these principles con- stitute the premise on which this inquiry is based, it is proper to state that no principle was enunciated that is in dispute among acknowledged scientific authorities. These generalizations are to-day the common property of manlcind, constituting the founda- tion on which the structure of modern science has been erected. Adopting these definitions which, in substance, express the consensus of modern scientific thought, the way was clear for sub- sequent inquiry into the nature of the phenomena with which the activity known as fire-rating has to deal, in order to determine the possibilities and limitations of this activity as a science under the definitions given. This inquiry revealed that in conformity with the laws governing intelligence, the classifying and reason- ing faculties had empirically accomplished their task up to the barriers imposed by self-interest. As the flat-head Indian's skull and the Chinese woman's foot are the distorted results of com- presses imposed by immemorial custom, so it may be said that fire-rating as an organic growth is the result of an artificial swath- ing imposed upon it by the conventional intellects who deny its birthright as a science, because it is unable to burst the bandages imposed upon it by their motherly care. "Every science may be said to date from the discovery, among the phenomena with which it is concerned, of some fundamental principle which serves to organize into a coherent ratiocinative body of knowledge that which has hitherto been an incoherent empirical body of knowledge."* This fundamental principle in fire-rating lies in the unrecog- nized or at least unacknowledged fact that, as an activity, it is concerned with a specific manifestation of the cosmic law of rhythm ; that it has to do with the properties of waves of fire ♦Outlines of Cosmic Philosophy, John Fiske. 196 Summary 1 97 destruction, and by implication that it must recognize all the properties of the phenomena with which it is concerned. Among these we find the property of destructiveness resulting from amplitude of vibration with its necessary corollary that the real economic end of fire-rating as a science is to temper these waves into dimensions which will be endurable to property interests. Granting that every human industry emanates from the bread- and-butter motive, we are compelled to recognize on the other hand that the community is the universal, if indirect, employer of all industrial activity, and the work must be done to suit the employer rather than the employed. In the logical modification of the wave of annual fire destruc- tion, and the scientific dispersion of its excesses over and above endurable limits through ancillary rate waves, lies the real utility of fire insurance to the community, and in the performance of this duty satisfactorily, the industry is entitled (and no one will dispute its right) to exact its reasonable wage. Under this definition of its raison d'etre^ we find beneath the confused phenomena of fire-rating the fundamental principle which must ultimately change our incoherent empirical body of knowledge into a coherent ratiocinative body of knowledge. But every science which reaches the stage of quantitative measurement needs a symbolic language of its own in order that it may possess an instrumentality for intelligent investigation and discussion of the phenomena with which it deals. We find the possibilities of this symbolic language in the dia- gram, which as a symbol is applicable to all the diverse and com- plicated relations involved in the ratios with which the activity of fire-rating is concerned, and (while the diagram will reveal unerringly the messages hidden in our statistics) as the algebraic equation must in its finality be converted into Arabic numerals if we would learn its concrete meaning, so diagrams must in the end be interpreted through statistical tabulations if we would obtain exact quantitative results. An inherent property of waves is ceaseless motion, and any rating system intended to measure and modify this motion must, like the waves themselves, possess the quality of mobility, a mobility which will admit of instant'" adaptation to existing con- 198 Fire-Rating as a Science ditions. This property in rates is obtained by the simple expedi- ent of classifying every risk in our printed local tariffs, as a means of issuing instructions to agents singly or en masse in the rate modifications, necessitated by experience, an expedient similar to that which enables the military commander to move his army by companies, battalions, regiments, and brigades, and without which his army would be a mob. In the light of a premise which no man of science would ques- tion, in the light of a fundamental generalization defining the phenomena with which it is concerned as a specific manifestation of the all-pervading law of rhythm known as the loss wave, and in the light of a symbolic language which reveals relations among these phenomena which have all these years lain perdu in the bramble-patch of our statistics, there is not only no room to doubt that the activity of fire-rating possesses the potentialities of a science, but no room to believe that these potentialities can be realized through any chain of reasoning that does not start from fundamental principles established by science itself. Admitting this conclusion, however, does not change the fact that every applied science has its distinct utilitarian aims and predestined limitations. Chronology establishes a second as the unit of time, because it answers its needs as a science, in the daily lives of humanity at large, but, as has been said, a second is almost an eternity in comparison with instantaneousness. Acous- tics measures time into thirty odd thousandths of a second, but here its quantitative measurement stops because it has reached the limit of the differentiating capacity of the human ear, but optics must measure time in quantities less than one seven-hun- dred-trillionth of a second before it reaches the borderland of sight. On the other hand, it suffices astronomy in its grosser measurements, to adopt the diameter of the earth's orbit as its unit in estimating star distances. Meteorology and seismology can forecast storms and earthquakes only a short distance in the future, and within broad geographical limits, but as regards the probable violence of these disturbances prevision is extremely indefinite, nevertheless, meteorology as a science is vastly superior in its forecasts to the predictions of Poor Richard's almanac; in fact, to-day it 1s one of the most useful sciences Summary 199 in conserving life and property. So fire-rating as a science must always be a science of indefinite prevision in the con- crete, while it possesses the possibilities of an exact physical science in its ability to measure from fixed standards the sequen- tial motion of loss waves in established property groups located within given territorial limits, either singly or collectively. It can observe and establish generalizations and differentiate and apply quantitative measurement to relations among the phenom- ena found in the waves with which it is concerned as accurately as acoustics and optics can measure the atmospheric and etheric waves with which they have to do. It can estimate the excesses in waves of fire destruction, and transmute them into rate waves harmless to its patrons, according to the dictates of judgment and equity, instead of by haphazard, and this is the real utili- tarian end of fire-rating as a science, as it is also its natural limi- tation, for it can establish quantitative relations among the charges, credits, basis rates, and exposures of specific risks, only through expert estimate. Except in their relational sense, how- ever, these factors which make up the individual rate are practi- cally no more important to the individual owner, than that chronometers should measure time into units smaller than the second for the daily needs of people who wish to catch a train, or know the dinner hour. Science can no more analyze and measure the laws of causation in the atoms which build up the individual rate molecule, than the signal service forecaster can tell what will be the specific damages resulting from an atmos- pheric disturbance traveling eastward in North Dakota, to the gable end of John Doe's barn in Attica, Indiana, but the value of fire-rating as a science is no more disturbed than the value of the weather forecasting science by this fact. The Transition Conceding that fire-rating as a physical science is feasible, and that the change from empirical to scientific method would cure the evils inherent in present conditions, it is important to consider whether this change would cause a train of inconven- iences which would make the remedy worse than the disease. In fine, granting that as a science fire-rating is practicable, would the transition be practicable? f Were it possible to close our doors to business, until we could rerate the country on a basis of estimated cost relations, the problem would be comparatively simple, but this is out of the question — the change if made must be made without "suspension of traffic." It must come through evolution aj>d not revolution. But the man of expedients who prides himself on being practical, will say. Something must be done at once. We cannot wait for- ever for theories. Granting this, it is proper to inquire what the man of expedients himself can do, in view of the wholesale cor- raling of his expedients during recent years by state authorities. He might, it is true, repeat the experiment of a horizontal advance throughout the country as he did in 1893, but this venerable expedient has been tried and found wanting. The practical man is at last constrained to admit this himself, in the face of the unanswerable logic of ousters, fines, and county jails. Or he might investigate the present relations of rates to cost, deter- mine as best he could what classes are unprofitable, and in what degree and where, and then make new basis schedules from which to reconstruct local tariffs of the old rigid pattern in two score states, then set up these tariffs to be again broken because they will not bend. In other words, the self-styled practical man, with all his fertility of expedient has but one expedient left, and that is to emulate the patient pismire and rebuild his frail structure of rates, tariff by tariff and risk by risk, to be again trodden under foot by man, or triturated out of existence by the elements. The Transition 201 Admitting, however, that" this would be tolerated by public sentiment, it would necessitate another period of expense and demoralization, with the certainty of another debacle at the end. Turn which way he may, the man of expedients is confronted with an impasse. Change in any industrial activity means more or less tempo- rary inconvenience, and in confronting the unavoidable results of an inevitable change, the question is to secure as a quid pro quo something that will effect a permanent cure of the evils which make the change necessary. The practical man just now is con- templating new basis schedules. Scientific rating demands the same. When the practical man has made his basis schedules he will have to utilize them in constructing local tariffs. Scientific rating must do the same with its cost estimates, so that in the matter of time, expense, temporary confusion, and all that sort of thing, science asks nothing that is not demanded by empiri- cism, except that science would require that local tariffs show the class number opposite the cost estimate of each risk in order that every rate change in future might not destroy its printed estimate. This necessity would cause neither expense nor delay, hence, from whatever point of view we take, "the practical man" has no practical advantage to offer in his persistent refusal to recognize the scientific necessity for fixed standards in all measurement. But can cost estimates be introduced gradually and mixed in with local tariffs, and used contemporaneously with ordinary rates without breeding confusion during the period of change from the old to the new? This is the real question on which hinges the possibility of change from empirical to scientific rating without a period of upheaval, and this question is solved, not by an expedient or scheme, but by two necessities inherent in the generalization from which scientific rating must start. The first of these is the necessity that the class number of each risk shall appear in tariff, and the second in the fact that scientific rating must be founded upon a system of coexistent tariff rela- tions as an unchanging standard for the measurement of sequential relations. In the past, rates have been percentages of each one hundred 202 Fire-Rating as a Science dollars at risk, instead of each thousand dollars as with the life companies. This has made the unit of measurement of premium so small that a fraction of a cent dropped in a percentage change of rate, often becomes large enough in the premium to enable a shrewd agent to capture a risk through manipulation of the dropped fraction. When we come to the small charges which make up the rate (amounting in many cases to but a few cents) percentage changes become impracticable. If cost estimates are adopted in lieu of rate estimates, there is a logical necessity for basing them upon amount at risk instead of upon the shifting and deceptive ratio of a ratio which exists in the relations between losses and premiums. If based upon one thousand dollars at risk, each estimate would admit of exact percentage change, and two agents figuring the same percentage of profit for the same risk could not reach materially different results. In the face of these necessities it follows that cost estimates appearing in tariffs along with ordinary rates would have two distinct ear-marks; one in their class number and the other in the fact that the estimate would be based upon one thousand instead of one hundred dollars at risk. These ear-marks would make cost estimates distinguishable from ordinary rates at a glance. With the understanding that these estimates should remain unchanged, except for actual change in hazard, and the further understanding that whether written at more or less than cost, the premium would invariably be based upon percentage modifications of cost estimates as directed by the companies, it would be possible for these estimates to appear in the same tariff with rates, without the slightest chance of mixture or confusion, and it would become practicable to formulate basis schedules of estimated cost relations and apply them in local ratings by risks, classes, towns, or states at our convenience or pleasure. Assum- ing, for example, it were decided to apply these estimates first to the flouring-mill class. The fact would be a matter of common knowledge among fire underwriters, and everybody would know that flour-mill rates were to be controlled thereafter by percent- age changes from the cost estimates appearing in tariff. Each The Transition 203 company would announce to its agents that it would write flouring mills at such percentage of profit as might be determined by its own judgment, or by concerted action (where not prohibited by law). After a dozen of the leading classes had been thus rated by cost estimates, we would for practical purposes have all business rated on the new basis and properly classified in our tariffs. Every town needing a rerating would naturally be rated by cost estimates in order to obtain flexible conditions, in lieu of rate suspensions, to meet demoralized conditions, and probably before we fairly realized the fact, the entire country would be rated upon the cost basis. In the meantime, it would be necessary to make rate changes by judgment alone as we have done in the past, with the important difference that these changes could be made system- atically, promptly, and last, but not least, without injury to our estitnates. By this time, however, the companies finding the entire country rated and classed by a uniform classification different from their own, could not fail to see the advantages of making their individual lists conform to the classification by which their business was rated, in order to secure economy, uniformity, and reliability in their own classifications. With this change in the individual classifications of the companies to conform to the uniform classification found in tariffs, would come the ability on the part of the companies adopting this classification to combine their aggregate experience as a basis for the statistical control of rates. Our present local tariffs seldom last longer than five years, when changes necessitate a new tariff, and it may be assumed that, within this time, rating as a science would be on its feet. After the first year the advantages of the change would probably be so obvious that the work would be pushed to a finish within a year or two at most. By thus making a path of least resistance leading toward right methods, fire insurance would effect the most important change in its history, through the imperceptible elimi- nation of dead tissue, and assimilation of live tissue which accom- panies all healthy growth. It would be difficult to find any form of human activity that in adapting itself to its shifting environments is not continuously 204 Flre-Ratlng as a Science undergoing changes which involve greater hardship than would be encountered in transforming fire-rating from an empirical to a scientific activity, but it does not follow that when the change has been accomplished fire underwriters would be able to rest upon their oars through another period of arrested development, for science means growth, progress, finer distinctions, nicer quantifications evermore. Nota Bene The processes of filling mental and dental cavities are not un- like. Both require much hammering, and are accompanied by- nerve disturbances and apprehension on the part of the patient, who, not infrequently, in spite of the logic of personal discomfort elects to keep his cavity — ache and all. When science finds a new idea, it always requires much ham- mering to give it permanent lodgment, for Mind, unlike Nature, does not abhor a vacuum. At the risk of iteration, it seems proper to add a final word, vitally important, because it has to do with our subject from its most practical aspect. Heretofore, a seemingly impassable barrier in the way of a change to scientific fire-rating has existed in the prevalent idea that the first step in this change would be to secure the consent of the companies to maintain uniform and combined classifica- tion. Experience has shown that many companies are as yet far from ready to do this. If science reveals that this is not neces- sary as a preliminary, and that in other respects the change to scientific method requires nothing essentially different, so far as difficulty is concerned, from the necessity for a general rerat- ing which is admitted by everybody, the most serious obstacle vanishes. From this standpoint perhaps the most important message delivered to us by pure science lies in its definition of standards. This definition informs us that all measurement must be by comparison with a standard, that this standard must be a constant quantity, and that the standard itself need not be measured because it precedes measurement. It must be a thing arbitrarily selected by common sense as the most convenient and reliable thing to measure with. In fire-rating, we are called upon to measure the fluctuations in a series of ratios or relations which constitute a form of wave motion, and as in all other measurement, we must use a fixed standard which, itself, "is not the thing measured but the measur- 205 2o6 Fire-Rating as a Science ing rod." In measuring the sequential relations found in wave motion, our standard must be the coexistent relations established by our tariffs. These tariff standards, like all standards, precede measurement. They are the measuring rod and not the thing measured, and any attempt to utilize statistics in measuring these tariffs, whose functions are to measure and not be measured, must be unscientific. To attempt this is as absurd as it would be in a tailor to measure his tape-line by the standard of his customer, instead of his customer by the standard of his tape- line. All tailors use tape measures, and every tailor keeps a book to record his measurements, but the record book would be use- less without the tape measure as a standard. The relations between our tariffs and the individual classification lists kept by companies, is not unlike that between the tailor's tape-line and his book of measurements. The fact that our tariffs, as a system of simultaneous relations, must always be established by estimate, is inherent in the nature of standards. In making these tariffs, our task is simply to make the relations reasonable and then keep them as fixed or constant standards for the measurement of sequential relations. It follows that to attempt to establish tariffs as fixed standards by exact figuring from the statistical data in our possession is to attempt a thing not only impossible but unnecessary. A realization of this important fact not only absolves us from the imaginary necessity of consulting our exceedingly questionable statistical data in establishing a tariff system of co-existent relations, but points out clearly the logic of availing ourselves of established relations in existing state tariffs, which come nearest to our national average as a whole, and then adopting these with the frank admis- sion that they are our standard or mean line, and as necessary to us as the tape-line to the tailor. With this conception of the scientific nature of standards, the perplexing task we have so often vainly essayed, of measuring our measuring rod, becomes entirely unnecessary, and the problem of formulating standard cost relations becomes simply a problem of common sense. The most important revelation found in the definition of standards undoubtedly lies in the fact that this definition suggests that it is not necessary that the companies adopt uniform classification as a preliminary to scientific rating. In seeking this Nota Bene 207 in the past as the first step, we have got the cart before the horse, for these classifications would be useless until the country had been rated by an established system of standard tariffs of cost relations. Uniformity in individual lists of companies would be premature before the statistics entered in their records are based upon standard cost estimates. This brings us to the fact that the only necessary working tools in breaking ground for the foundation of a science of fire-rating are: First — A system of tariffs established by common sense for use as constant standards. Second — A classification list by which every risk shall be designated by its class number in local tariffs. By basing cost estimates upon one thousand dollars at risk instead of one hundred dollars, and printing the class number of each risk in local tariff, each cost estimate would be un- mistakable, and we could proceed to apply these estimates in future rating precisely as we would proceed to apply new rates. This would give us flexible rates, and by the time the country had been so rated, the advantages of adopting this clas- sification might be safely depended upon to induce the companies to fall into line in the use of uniform classification and in com- bining their statistics to learn their average class experience. In this order of procedure, pointed out by science itself, we would begin at the foundation and build upward instead of beginning at the top and building downward. It might possibly have simplified this discussion had we used the name Standard Rates instead of Cost Relations, but it would have been a misnomer. By common usage the word rate has come to mean our changeable selling price, and standard esti- mates of cost relations would be neither selling price nor change- able. By calling these estimates Cost Relations, we not only obtain a truer designation, but are able to retain the word Rate as the name of our selling price, the difference between Cost and Rate being the index of the ratio of underwriting profit. On the whole, the term Estimated Cost Relations serves to designate coexistent relations for what they are, i. e. fixed standards of measurement for establishing our income by com- parison with constant quantities that answer to the definition furnished by science itself as to what constitutes a standard. Conclusion In concluding this protracted inquiry, we are compelled to admit that fire-rating in its broader aspects is not a simple matter; that as a science it embodies more important and more intricate problems than the mere reconstruction, by slap-dash estimate, of basis tariffs as fast as they are knocked over by legislation and competition. It is, perhaps, nothing to the discredit of the aver- age fire insurance official that he knows as little of fire-rating, as a science, as the life insurance official knows of the actuarial science on which life insurance is founded, or the average mer- chant of the science of accounting, without which commerce would be a tu'penny affair. The average managerial function in the past, as it probably always will be in the future, is to earn dividends satisfactory to stock-holders out of established rates, be they what they may. The making of these rates is a separate and distinct activity, which ought to be a science; an activity for which practical underwriters have neither leisure nor neces- sary training. Interdicted from establishing uniform rates ourselves, the work of rating during recent years has passed into the hands of professional raters. Under a system which has never recognized the scientific necessity for standards, the professional rater is expected to make marketable bricks without straw. In the absence of actuarial possibilities he is forced before the public in the suspicious attitude of one naming a common selling price, and while to us his voice may be the voice of Jacob to the pur- blind public his hands are the hands of Esau. Under the circum- stances it is not surprising that the constituted authorities in state after state are enacting codes of outlawry against the profes- sional rater as the minion of a trust. During the era of the professional rater, the younger genera- tion of fire underwriters has had so little opportunity to exercise itself in the work of rating, crude as it has been, that to-day it 208 Conclusion 209 may be said to have become a lost art with fire underwriters. Meanwhile the independent rater — the servant alike of agents, companies, and Ihe public — has been compelled to apply his basis tariffs as faithfully as he could in view of the exactions of his numerous masters, with the result that the one capable of raising the largest amount of Hades has been usually mollified with the most liberal concession. Under the grind of his daily toil, the independent rater has had no opportunity for analytic or synthetic study of the phenomena with which he has dealt, and even with both opportunity and capacity, he could have taken no more certain way to cut off his income than to suggest a new idea involving the necessity for any material departure from prece- dent. Under these conditions, maintained year after year, rates have slowly but surely drifted into "Tohu-ba-Bohuland, the unruly chaos where event stumbles after event, and change jostles change without sequence and without law." To-day we have admittedly lost our bearings, and sundry and divers com- mittees, aided by the insurance press, have turned bell-ringers, and are crying out on the highways for information as to- the whereabouts of our lost, strayed, or stolen rates, to the edifica- tion of the public which has done so much to help us lose them. It must be confessed that fire-rates have not the homing instinct of Little Bo-Peep's sheep, and it is hopeless to expect that, if we "let them alone, they will come home a' wagging their tails behind them." By general consent fire-rates are astray. Such system as we have had, has been turned topsy-turvy, and everyone insists that something must be done. The phraseologists are busy in the manufacture of verbal panaceas. "No more flat advances," "schedule-rating," "class equalization," "justice to the pub- lic," are the catchwords of the hour, and no one seems to realize that these and other euphemisms, if they have any definite mean- ing, imply the necessity for a science of fire-rating. But back of this foreground of perplexity stands grim Authority ready to inflict the penalties of the law for the slightest symptom of con- certed action, and in every tree-top roosts an incorporate buzzard ready for another gorge upon our lost rates when they have been found and properly fattened. It must be confessed that it is hard 2IO Fire-Rating as a Science to see the sun through all the dust aroused by self-interest, but it does not follow that there is no such thing as blue sky and God's sunshine above the dust clouds we have helped to kick up. In its final analysis, science is simply a search for truth in the right way, and all human history shows that human laws based upon error cannot stand before natural laws based upon truth. It has not been many centuries since teachers were forbidden to instruct their pupils regarding the facts revealed by the telescope; since mathematics was declared to be the source of all heresies; geometry an institution of the devil ; chemistry one of the seven devilish arts, and the study of physics, a statutory crime. At the beginning of the present century, fanning-mills for winnowing grain were denounced as an institution of Satan, "Prince of the powers of the air," and a violation of the text, "The wind bloweth where it listeth. " Many people still in the youth of old age can recall the hue and cry against the use of anaesthetics, because "pain is God-given. " It has hardly been two score years since the constituted authorities forbade the Scientific Congress of Italy to meet at Bologna. A little further back we find that lawyers were regarded with almost universal distrust. Further back, doctors were in equally bad odor and were generally for- bidden to practice their art, and if we go back to pagan days, merchants were so generally distrusted that they were assigned the same God with thieves. The present prejudice against fire insurance is doubtless in large measure the result of its being one of the youngest in the sisterhood of human activities, and this prejudice is increased in certain states because of the tremendous waves in loss ratio, which keep the industry in constant and unpleasant evidence before the public. The "wild-and-woolly" legislation of some states is simply another manifestation of prejudice against everything affecting public welfare that is not understood by the public mind. Fire underwriters cannot con- sistently condemn the public for this distrust of things beyond popular comprehension, for they, too, have long manifested pre- cisely the same spirit in resisting "suspicious novelties" and "questionable innovations." These things simply prove the truth of the epigram, "There is no pain equal to the pain of a new idea." Back of this resistance to progress lies the soul of good, Conclusion 21 1 found in most things called evil — an earnest desire for what seems under a mistaken notion to be right. It is a law of nature that there can be no permanent progress where there is no resistance. The present efforts of the authorities to destroy law and order in our industry are an omen of progress to come, for it is only under the stimulus of opposition that men's minds are fitted for the task of grappling complicated problems. It is claimed that if slavery had never existed, the human mind would never have become capable of continued concentration ; that we have emerged from savagery because slaves through countless generations were compelled to concentrate their thoughts upon assigned tasks. If true, this shows that slavery, bad as it was, was simply a phase of human progress, a step upwards from cannibalism. The pricks and goads of populistic legislation are the appetizers, without which, in all probability, we should never have been able to break our cake of custom. In England, where fire insurance has been unmolested by legislation, there has been no publication of statis- tics, and neither underwriters nor the public have any information as to aggregate results. In Eastern states, where fire underwriters have been comparatively free from legislative exactions, they have been unable during the past quarter of a century to reach the stage of progress found in general associations for the regu- lation of commissions. On the other hand, under the constant stimulus of legislative exactions, fire underwriters in the Western and Southern states have been driven into active and comparatively harmonious co-operation, not only as to rates, but as to expenses. Their ideas have been expanded to this extent by the educational process of constant antagonistic forces, for in the effort to adapt themselves to their environments, they have been compelled to resort to experimentation, and experimentation means advance. Viewed from a humanitarian standpoint, the difference between present fire underwriting ideals in America and England, or for that matter Europe, is the difference between progress and stag- nation, and this is said in full recognition of the fact that in a commercialistic sense American underwriters have much to learn from their brethren across the water. The human mind, like the human back, becomes fitted to its burdens; and in the populistic states, underwriters, like the unwilling school-boy whipped to 212 Fire-Rating as a Science school, have been educated by the logic of illogical events into more tolerant and progressive views. Like Rabelais they have been forced to the conclusion that: " It is wise to get knowledge and learning from every source — from a sot, a pot, a fool, a winter mitten, or an old slipper." It is this stimulus, resulting from public dissatisfaction, which will eventually compel fire underwriters into an earnest search for the truth in the right way, which is necessarily the scientific way; and, without doubt, this movement so fraught with impor- tance to the future of the industry, will originate in the United States, where the conflict between counter-forces has raged the longest and hardest. In the face of a determined public senti- ment, the first requisite is that fire underwriters must make their methods conform to law, natural and statutory, and this can be done only by a search for the truth in the right way. Public opinion has demanded and enforced the publication of our aggre- gate experience each year in each state. Any movement of the companies to ascertain their aggregate experience by classes as well as by states would be going farther than the public has yet asked. The publicity in class statistics essential to fire-rating as a science is the publicity exacted by law, only more in detail; more analytical in form. No existing law prohibits the com- panies from ascertaining their combined experience through actuarial estimates of coexistent relations, not intended to be a combined price-list, but a basis of intelligent information in which every citizen is interested. Such information is not interdicted by legislation, and in all probability never will be, for it is in exact line with the popular demand for "the truth, the whole truth, and nothing but the truth." In states where the laws do not interfere there is nothing to prevent underwriters from agreeing upon reasonable ratios of profit; and with the ability to equalize class rates, which we have lacked in the past, the ratio of specific class profit, fixed by competition, would be so surprisingly small that no state could reasonably interfere. In states where the laws do interfere, however, these estimated cost relations based upon statistical data, would ultimately con- stitute a landmark which would command confidence and respect on the part of every underwriter, even without conference or Conclusion 213 restraint other than that dictated by common prudence. Popular opinion would soon crystallize in a sentiment that the selling of indemnity below cost was a disgraceful act, no less inimical to the public than to the underwriting community. Minimum rates would establish themselves as surely as minimum prices establish themselves with the merchant who knows the cost of his goods. The work of independent raters would become purely statistical. It would be no part of their duty to dictate a selling price to companies and agents, or a purchasing price to the public. Their work would be to determine actuarially the cost relations of the thing sold, and it would be for those dealing in the thing to deter- mine their own selling price. Under such conditions, the inde- pendent rater would cease to be like Figaro, the servant of everybody. He would be free to prosecute his duties without keeping a constant eye upon the personal equation, which in the past has done so much to disturb his work. In the past, the tariff rate of a risk has been ostensibly its selling price. This necessarily included the three independent elements of loss ratio, expense ratio, and ratio of underwriting profit, but each of these has been a fluctuating quantity moving under an independent rhythmic law of its own, with waves of expense and underwriting profit hardly less in relative fluctuation than the wave of loss. By eliminating the element of underwriting profit and agreeing upon a reasonable maximum of expense, which some day the public will demand, the commission and brokerage question would become merged in the cut-rate ques- tion, where it belongs. If the fundamental generalization, that fire-rating as an activ- ity has to do with the modification of loss waves, a corollary from this is that as an industry fire insurance with scientific rating and pliable rates would be purged of the element of chance, which has been its bane and reproach in the past, excepting so far as inherent in the mismanagement, which makes chance an element in all commercial emprise. Under the generalization stated, fire insurance would become a clearing house for the transfer of class and state balances resulting from modified waves of loss back and forth between stock-holder and policy-holder, 214 Fire- Rating as a Science through flexible rates. In so far as chance is concerned, there would be no appreciable difference between banks which receive deposits from one to loan to another, and insurance com- panies which under scientific rating would house the excess of premiums during wave minima in order to distribute them during wave maxima. The touchstone of success with the fire company- would lie in a wise discrimination in selection, economic manage- ment, and judicious investments, rather than in the qualities which are supposed to achieve success upon the turf or green baize. The competition on the part of non-associated companies has flourished in the past upon inflexible rates. As the house fly can light upon a bald head and accomplish its purpose before the brain beneath, through the complicated system of sensory and motor nerves, can receive news 'and "wire orders" to the flexor and extensor muscles when and where to slap, so the inde- pendent company has been able to suck its fill before we could smash our cumbrous rating machinery, and let loose fratricidal strife among our agents. Disguise it as we may, our sole remedy for this sort of competition has killed the agent and amused the fly. Pliable rates would enable fire insurance to slap before the fly could unsheathe its suction pump, and this is the only thing that will command the respect of flies. In the light of the foregoing investigation of rating as a science one thing is plain: the enforced abandonment of tariffs which, after the manner of trusts, baldly state a common and inflexible selling price for all companies, would be a blessing in disguise, for fire-rating can never become a science under such tariffs. So long as we continue to use them, all hope of scientific methods must be abandoned. On the other hand, granting the necessity for a general restoration of the rate relations which have been thrown into chaos by the events of recent years, it is surprising and encouraging to note how little of change is involved in the acceptance of fire-rating as a potential science. The change from empirical popular knowledge to exact scientific knowledge is in the line of natural human evolution. It is a change that is constantly occurring in every phase of human progress, a change of natural growth, of integration of live tissue and elimination Conclusion 215 of dead tissue. The change from empirical rating to scientific rating would in the same manner be in the line of a natural growth upon such of system as has been evolved by combined underwriting intelligence in the past; a growth that would result easily and naturally the moment we remove the trammels set by conventionalism and selfishness. All science, theoretical and applied, must avail itself of arbi- trary standards in order to apply quantitative measurement. In fire-rating as a science, numerous standards for various purposes are essential. Most of these standards have been already estab- lished by average intelligence, even if with indefinite value. Our A, B, C and D buildings, our fire departments of first, second, third, and fourth class, our preferred and non-preferred, non-hazardous, hazardous, and extra hazardous stocks are all classified standards loosely defined. That these standards under scientific method will increase in number, and become more definite, with finer shades of distinction, cannot be doubted, for * 'progress toward higher complexity and higher organization is a law that holds good of processes as well as things, and the greater the amount of progress, the more rapidly must progress go on." The classified experience of all companies is not essen- tial to practical results; on the contrary, the experience of some companies would be positively detrimental to the reliability of statistics. Nor need scientific rating be established everywhere at once. It can be started tentatively, class by class, or state by state. No science ever came into existence like Minerva, full grown and panoplied. The search for truth is necessarily a slow search, for the least error necessitates the return to an established fact, and a retracing up to the point of divergence from the right path. Right thinking moves forward by slow stages of experi- mentation and revision. Many sciences which began with the dawn of civilization are still instinct with progress, each pausing from time to time to await the expansion of human intelligence, or the aid of another science to point out the way. There is a world of room for research in fire-rating, if we once set out in quest of Truth, but we can never find her by looking for fixity in a pulsating universe, or by trying to change coexistent relations 2 1 6 Fire-Rating as a Science into sequential relations, or by dealing with fluids by the law of solids, or by trying to change space into time. It was preordained that the harmonies of Cosmos should be modulated from the elemental crash of force and resistance, and the same Will that resolved universal chaos into universal rhythm bequeathed to man the message of the ages, "The truth shall make you free." APPENDIX External Exposures The external exposure charge is the pons asinorum of the fire- rater. Apparently defying all attempts at quantitative analysis it has been in a large measure left to guesswork. No study of fire-rating as a science can ignore this illusive but important factor. In thousands of risks the hazard arising from exterior exposure is larger than the inherent hazard of the risk itself, and after the most careful synthesis of basis rate, charges and credits in establishing a rate, we are often forced into the absurd expedient of ** lumping" an exposure charge which may be three or four times as much as the unexposed rate of the risk itself. In other charges appearing in basis tariffs it is possible to preserve at least reasonably true relations, but hardly any two risks are similarly affected by the same exposure hazard, for as in gunnery we must take into quantitative account the range and dynamics of the attacking exposure both as to structure and con- tents as well as the statical resistance of the exposed structure and contents, along with the retreating ability found in all removable property. What may be a heavy exposure to one risk may be an unimportant exposure to another. Again, it is impossible to determine where exterior exposure ends, for we must reckon not only with the nearest exposure, but with the accumulated hazard resulting from the exposure of expo- sures by other exposures. In the great Chicago fire it was con- clusively demonstrated that every building in the city was exposed by Mrs. O'Leary's barn, and it may be stated as a generalization that in every city and town, every structure is in some degree exposed by every other structure within corporate limits. With factors of causation so numerous and mutually impli- cated, it is, of course, useless to attempt to trace back every remote cause to its source and establish its quantitative relations. Finite powers can never work out an equation so nearly infinite, but even in the problem of exposure, the common sense of fire iii iv Appendix insurance has untangled from the vast plexus of causation a number of strictly logical inferences. In order to understand the equities of the distribution of exposure, it is proper to revert once more to our definition of the word basis rate, as the residuum of unanalyzed or at least unap- praised hazard. This residuum if crudely dissected will be found to be composed largely of the following elements: 1. The surplus indemnity secured for nothing by large property owners through evasion of the spirit of co-insurance. 2. Personal influences which, because unanalyzable, must be distributed among all policy-holders. 3. The residuum of external exposure which escapes appraisement under our present methods of reckoning exposure charges. If we regard the basis rate as a receptacle into which we throw everything we cannot quantitatively estimate, the logic of throwing into this receptacle the residuum of exposure result- ing from remote causes, which cannot be analyzed or estimated, becomes evident. On a rough estimate the entire premiums col- lected for exposure must be about equal to the total premiums collected for the inherent hazards of risks themselves. Deduct- ing from existing basis rates the other factors above enumerated, /. ^., property insured for nothing through our inability to enforce co-insurance, and the aggregate moral hazard, which has been claimed to be about twenty-five per cent of the total hazard of all property, there remains relatively a considerable proportion of this basis rate attributable to the residuum of exposure left after we have applied our present exposure charges, such as they are. While these charges have evidently absorbed a large share of the total exposure hazard of the country, when we come to examine them in our state tariffs we find an utter lack of logical relations. In fine, exposure charges, like other charges in existing tariffs, are established by quantitative estimate, and the relative com- plexity of the exposure factor has caused corresponding incongruities in these charges. It is not the intention of this investigation to discuss the formulation of basis tariffs, because the work of tariff construction is simply the exercise of the esti- mating faculty in establishing coexistent relations, and for this reason is not a legitimate subject of scientific inquiry. Appendix v It is within the scope of scientific investigation, however, to inquire into the possibility of establishing formulae calculated to distribute external exposure charges more exhaustively, con- sistently, and impartially than we have been able to do in the past. All exposures may be divided into internal and external. Many inconsistencies in charges for internal exposures might be enumerated, but they are simply the errors in relation which are found in other charges. At the worst they are established charges and as such free from personal favoritism, and the inequities, such as they may be, are confined to a single building. When we come to external exposure, causation gets out of doors and stands ready to run amuck. For this reason some method of bringing about reasonable uniformity and certainty in our charges for exterior exposure becomes correspondingly more important. Perhaps the secret of this formula might be found in the mathematical relations of the cone. It is a well-known fact that all flame unaffected by atmospheric currents assumes the shape of a perpendicular cone, as seen in the flames of candles and lamps. (The shape of gas jets is an exception to this, because of the shape of the burner and pressure of the gas.) When forced out of the perpendicular by an air current, the flame assumes the shape of a horizontal cone as seen when under the influence of a blow-pipe. In fact, we use the expression "a tongue of flame" to represent the cone-like shape found in all flames. The same phenomenon may be seen in a burning build- ing. The chances of wind forcing a flame directly against a given object within a radius of one hundred feet are, let us assume, as one to one hundred. Allowing for prevailing winds, this propor- tion would increase as the distance diminished until, on a rough estimate, the chances would be, let us say, as one to two. That this is the liberal basis assumed in our frame exposure charges is shown by the fact that when frame buildings adjoin, the exposure charge added to each in our frame row tariffs is about fifty per cent of the inherent rate of the exposing risk. Granting that this exposure gradually diminishes to a vanishing point, after the manner of a cone, the problem is to estimate the average vanish- ing point and reduce the exposure charge by a descending scale la Appendix until this vanishing point is reached.* That the vanishing point varies with the magnitude and character of the exposure is a logical inference, and this inference is carried out in our tariffs which attempt, at times, to make the vanishing point for exposure differ with the size and nature of the exposing hazard. The true average vanishing point, like all other features of tariff construc- tion, is subject to expert estimate. We know that fires are often communicated by burning brands for miles, and not infrequently by direct radiation for several hundred' feet. All these excep- tional results of causation, however, legitimately belong in the residuum of unanalyzed hazard, which, under the law of comity, appears either in the basis rate or in the average rate increase, which we have been in the habit of attempting to spread over wide areas of time and space after exceptional conflagrations. In the light of this explanation it is obvious that our present vanishing point which is the width of an ordinary sixty-foot street, for ordinary one and two story frame mercantile build- ings, and one hundred feet for large frame manufacturing risks and elevators, is a logical, if crude, generalization, which enables us to take up a good share of the immediate or direct exposure hazard in regulated charges, though we have no formula for reck- oning the increment of hazard resulting from secondary exposures. In working out a generalization for exposures, based upon the law of the cone, it is of course necessary to take into consider- ation the nature of the wall of the exposed and exposing build- ings. An analysis, perhaps sufficiently accurate for practical purposes, has been crystallized by usage into the following: 1. Frame. 2. Brick without parapet or with openings, or exposed woodwork, as balconies, awnings, wood cornice, shingle or mansard roof, also brick veneered or iron clad. 3. Brick wall solid, with parapet, with all openings closed by approved doors or shutters. ♦It is possible to reckon the diminishment of a cone, as shown by its solid contents, superficies or diameter, or to establish any desired ratio of diminishment from the approach of its hyperbola to any given asymptote. The ratio of diminishment found in the isosceles triangle, created by the bisection of a cone, is, however, the simplest, and for practical purposes probably the best, in view of the fact that simplicity is desirable in a calculation which at most is only intended to absorb in regulated charges as much as possible of the unknown quantity found in exterior exposures. A careful study of the problem W9uld doubtless reveal the possibility of calculating tables of exposure based upon the relations of the hyperbola to different asymptotes best suited to different degrees of exposure in size, materials, etc., under different degrees of fire department protection. The following formulae, based upon the isosceles triangle as containing the simplest dimensions of the cone, are purely suggestive. Appendix vn This would, in theory, give nine possible combinations of exposure, as follows: 1 by 1 2 by 1 3 by 1 1 by 2 2 by 2 3 by 2 I by 3 2 by 3 3 by 3 Following established usage we may eliminate the combina- tions printed in light type, which would leave five combinations for consideration. Taking for our starting point the present basis (fifty per cent of the rate of exposing hazard) as our exposure charge between frames, and estimating the exposure of the other combinations in proportion as the hazard is less, we may assume for our expo- sure charge where such risks adjoin each other, 1 by I say 50 per cent of exposing hazard. , > say 30 per cent of exposing hazard. 2 by 2 say 20 per cent of exposing hazard. 3 by I say 10 per cent of exposing hazard. Under the law of the cone these percentages would diminish as the distance from exposure increased. Let us suppose the vanishing point of exposure to be as follows : 1 by I 60 feet. , ^ { ___ —40 feet. 2 by I ) ^ 2 by 2 30 feet. 3 by I —20 feet. We would now have four cones, or what is the same, one cone divided as shown in the diagram below: I by I 2byl 2by2 3 by J Vlll Appendix Reckoning from the base of each to the apex, in proportion to the increasing space between exposures, we would have the following results: to apex- --exposure decreases Ye every lo feet. to apex- --exposure decreases % every lo feet. to apex — exposure decreases % every lo feet, to apex- --exposure decreases yi every lo feet. From point i by i From point i by 2 From point 2 by i From point 2 by 2 From point 3 by i From the preceding assumptions it is possible to construct the following table of diminishment in exposure charges for clear spaces applicable say to buildings in unprotected towns, and from this to construct special tables for buildings and contents under different grades of fire department protection. Character of Risk and Exposure. Vanishing Point. Per cent of Exposure Charge to Inherent Rate of Exposure. Decrease of Exposure Charge for Each Five Feet of Clear Space. I by I I by 2 ) 60 feet 40 feet 30 feet 20 feet 50 per cent 30 per cent 20 per cent 10 per cent 8^ percent 12^4. percent 16% percent 25 per cent 2 by I 5 2 by 2 •^ bv I -- The application of the above table might be stated in the following formula: When more than one exposure in a given direction^ begin with the most remote exposure in block^ not separated by space in excess of its vanishing point, reduce exposure charge for space and add result to exposure charge of next exposure; again reduce for space, and so on, until we come to exposed risk, then add the accumulated exposure charge to basis rate of the exposed risk. When risk is exposed in more than one direction, proceed in the same manner for each direction. Space forbids more than a mere outlined suggestion of this theoretical formula, which is capable of being elaborated into graded tables of exposure for a closer classification of exposed and exposing buildings as to size, structure, and hazard, as well as for stocks and buildings, according to grade of fire department protection. These things will readily suggest themselves to those familiar with practical rating. The principal feature for consideration at present being that the theory suggests the con- Appendix ix struction of formulae adaptable to a wide variety of conditions, which would enable us to extend our analyses to secondary or tertiary exposures, often more important than immediate expo- sures. By so doing, we could absorb, in logically regulated charges, a much larger proportion of the residuum of unanalyzed exterior exposure hazard than we have been able to do in the past. The author has utilized this formula in estimating expo- sures for the past twenty years with results that have never failed to commend themselves by the logical exposure relations obtained, though he does not question the possibility of a more perfect formula. The essential point is that a formula is needed for scientific rating which will establish uniform relations in exposure charges in all parts of the country.* ♦Theoretically the importance of exterior exposure diminishes in proportion to efficiency of fire department protection, though when a city fire "gets away" from a fire department, exterior exposure becomes far more important in its effects upon the aggregate loss ratio of the country than in small towns. This, however, is but another illustration of the unrecognized law of comity in fire insurance, which in the end compels the community at large to partake in the disasters of great conflagrations which create unbearable waves in the loss ratios of single classes, cities or states. View the matter as we may, these con- flagrations, in the absence of any acknowledged system for modifying or distributing cost waves, create a standing contest between insurance and the community at large as to which shall foot the bill. PRINTED BY R. R. DONNELLEY AND SONS COMPANY, AT THE LAKESIDE PRESS, CHICAGO, ILL. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Books not returned on time are subject to a fine of 50c per volume after the third day overdue, increasing to $1.00 per volume after the sixth day. Books not in demand may be renewed if application is made before expiration of loan period. 1:0 i tl^. 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