PRACTICAL GUIDE 
 
 FOR COMPENSATION 
 
 OF THE COMPASS 
 
 WITHOUT BEARINGS 
 A.C 
 
 , 2 , v .. .... , 
 
 
GIFT 
 
 Professor of Geography 
 University of California 
 
Compensation of Compasses 
 
 WITHOUT BEARINGS. 
 
PRACTICAL GUIDE 
 
 FOR 
 
 Compensation of Compasses 
 
 WITHOUT BEARINGS, 
 
 BY 
 
 LIEUTENANT COLLET, F.N, 
 
 it 
 
 TUTOR IN THE POLYTECHNIC SCHOOL OF FRANCE 
 
 TRANSLATED BY W. BOTTOMLEY. 
 
 WITH A PREFACE BY 
 
 SIR WILLIAM THOMSON. L.L.D., D.C.L., F.R.S. 
 
 Professor of Natural Philosophy in the University of Glasgow, 
 Fellow of St. Peter's College, Cambridge. 
 
 1885. 
 PORTSMOUTH : 
 
 GRIFFIN & Co., 2, THE HARD, 
 
 (Publishers by Appointment to H.R.H. tJie Duke of Edinburgh) 
 
 LONDON AGENTS: SIMPK1N, MARSHALL & Co. 
 

 A LA MEMOIRE DE MON FERE. 
 
 Mort 
 
 pendant que j'e'tais en service a la mer, 
 ce livre est tres respectueusement de'die'. 
 
 A. COLLET, 
 ler Juillet, 1884. 
 
CONTENTS. 
 
 PREFACE. ... ... ... I. 
 
 INTRODUCTION III. 
 
 CHAPTER I. 
 
 PAGE 
 
 DEFINITIONS. PRINCIPLES OF THE METHOD ... ... 1-9 
 
 THE CORRECTOR MAGNETS. PLACING THE MAGNETS IN POSITION 3 
 
 CORRECTORS OF SOFT IRON. PLACING THEM IN POSITION. EFFECT 
 
 OF THE SPHERES ON THE DIRECTIVE FORCE ... ... 5 
 
 COMPENSATION WITH THE AID OF THE DEFLECTOR ... ... 6 
 
 COMPLICATIONS IN PRACTICE 7 
 
 CHAPTER II. 
 
 THE DEFLECTOR AND THE DIRECTIVE FORCE ...> 10-36 
 
 DESCRIPTION OF THE DEFLECTOR ... ... ... 10 
 
 MEASUREMENT OF THE DIRECTIVE FORCE .. . .,. 12 
 
 MANAGEMENT OF THE DEFLECTOR. ... ... ... 13 
 
 EXERCISES TO BE MADE ON SHORE. ... ... ... 13 
 
 (A). To OBTAIN THE NORMAL DEFLECTION ... ... 13 
 
 (B). To RETURN THE CARD TO ITS ORIGINAL POSITION ... 16 
 
 (C). To ALTER THE READING BY MEANS OF MAGNETS ... ... 17 
 
 PRACTICAL RULES... ... "... ..... 17 
 
 THE WORK IN PRACTICE ... .. ... ... ... 19 
 
 To INCREASE THE READING OF THE DEFLECFOR ... ... 20 
 
 To DIMINISH THE READING OF THE DEFLECTOR . . ... ... 22 
 
 (D). To ALTER THE READING BY MEANS OF SPHERES .. 23 
 
 (E). GRADUATION OF THE DEFLECTOR ... .. ... 25 
 
Contents. 
 
 PAGE 
 
 DEFECT IN THE PROPORTIONALITY OF THE FORCES TO THE DIVISIONS 28 
 
 ADVANTAGES OF THE GRADUATION OF THE DEFLECTOR ... ... 29 
 
 PRELIMINARY EXAMINATION OF THE DEFLECTOR ... ...' 29 
 
 THE ADDITIONAL MAGNETS ... ... ... ... 31 
 
 NUMERICAL EXAMPLES ... ... "... ... .. 32 
 
 GRADUATION OF THE ADDITIONAL MAGNETS ... ... ... 33 
 
 To DIMINISH THE POWER OF THE DEFLECTOR BY THE SCREWS OF THE 
 
 BASE ... ... ... ... 34 
 
 CONCLUSION .. 36 
 
 CHAPTER III. 
 
 COMPENSATION IN PRACTICE ... ... 37-50 
 
 GENERAL REMARKS ... ... ... .. ... 37 
 
 FIRST OR GENERAL CASE ... ... ... ... 39 
 
 PLACING THE MAGNETS IN POSITION PRACTICAL RULES ... 40 
 
 PLACING THE SPHERES IN POSITION ... . ... 42 
 
 VERIFICATION OF THE COMPENSATION ... .!. .... ... 42 
 
 SECOND CASE ... ... ... ... ... 44 
 
 THIRD OR EXCEPTIONAL CASE ... ... .... - 46 
 
 COMPENSATION OF EXCEPTIONAL CASE IN PRACTICE .... 47 
 
 NUMERICAL EXAMPLE ... ... ... ... _ 49 
 
 CHAPTER IV. 
 
 CORRECTION OF THE HEELING ERROR ' ... ... 5159 
 
 VERTICAL FORCE INSTRUMENT ... ... ... ... 52 
 
 PRELIMINARY OBSERVATIONS TO BE MADE ON SHORE ... ... 53 
 
 OBSERVATIONS ON BOARD PLACING IN POSITION THE VERTICAL MAGNETS 53 
 
 PRACTICAL RULE FOR NORTHERN MAGNETIC HEMISPHERE ... ... 55 
 
 NUMERICAL EXAMPLES ... ... ... ... ... 55 
 
 VERIFICATION OF THE COMPENSATION FOR THE HEELING ERROR 56 
 
Contents. 
 
 PAGE 
 
 CORRECTION or THIS COMPENSATION WHEN THE SHIP CHANGES ITS PLACE 57 
 
 NUMERICAL EXAMPLES ... ... ... ... ... 57 
 
 PRACTICAL RULE FOR THE SOUTHERN MAGNETIC HEMISPHERE ... 58 
 
 THE DIRECTIVE FORCE OF THE COMPASS ON BOARD 59 
 
 CHAPTER V. 
 
 CONTROL OF THE COMPENSATION AT SEA 
 
 NUMERICAL EXAMPLE ... 
 
 CONCLUSION 
 
 TABLE FOR THE DISTANCE OF THE SPHERES ..^ 
 
 TABLE OF NATURAL SINES, COSINES, &c. 
 
 CHART OF LINES OF EQUAL HORIZONTAL FORCE 
 
 CHART OF LINES OF EQUAL DIP ... _ 
 
 CHART OF LINES OF EQUAL VARIATION 
 
 6063 
 62 
 63 
 64 
 65 
 
 PLATE I. 
 
 II. 
 
 III. 
 
PREFACE 
 BY SIR WILLIAM THOMSON 
 
 T N his large book on the Mariner's Compass, published 
 * in 1 88 1, LIEUTENANT COLLET gave a very complete 
 account both of the mathematical theory of the action ot 
 the compass in iron ships, and of the theory and practice 
 of the best methods for fully compensating the disturbing 
 influence of the ship's iron. He has now followed up 
 that most important work by a " Practical Guide " 
 in which, without mathematical formulas, he gives clear 
 and simple instructions for practically performing the 
 processes which must be actually gone through by the 
 adjuster and the navigator to correct the compass initially, 
 and to keep it correct at sea, as accurately as the circum- 
 stances allow in practice. I have myself long felt that 
 such a " Practical Guide " is greatly wanted. My own 
 little pamphlet of " Instructions," which is supplied with 
 my compass, is much too meagre an instalment towards 
 the object. I therefore hailed with satisfaction the recent 
 appearance, in French, of Lieutenant Collet's Compass 
 Guide, and I am very glad now, to see it rendered 
 available to the British public in the present translation 
 of it by Mr. W. BOTTOMLEY. 
 
ii. Preface. 
 
 It is particularly gratifying to me to find both in 
 LIEUTENANT COLLET'S great book, and in his Practical 
 Guide, an ample recognition of the practical value of my 
 method of adjusting the compass without bearings by aid 
 of the Deflector. I have myself pointed out on several 
 occasions in public, some of the advantages of this 
 method, and it has been largely used by Mr. BOTTOMLEY 
 and others in the adjustment of my compass, with most 
 satisfactory results. Few practical navigators have 
 however hitherto learned to use it. 
 
 The admirable manner in which LIEUTENANT 
 COLLET has worked out the method theoretically and 
 practically, his earnest advocacy of it as a thing really 
 valuable to the sailor : and now lastly the clear and full 
 practical instructions for the whole operation of adjusting 
 the compass without bearings will, I am sure, have great 
 effect in bringing it into general use at sea. 
 
 W. THOMSON 
 
 The University, 
 
 Glasgow, January, 
 
INTRODUCTION 
 
 TO THE 
 
 PRACTICAL GUIDE FOR COMPENSATION OF 
 COMPASSES WITH OR WITHOUT BEARINGS. 
 
 I must commence by thanking all those who have given so cordial a 
 reception to the " Traite theorique et pratique de Regulation et de 
 Compensation des Compas" a treatise in which I have embodied all 
 the works on the subject previous to 1881, and my own experiences 
 while on board one of the ironclads in 1880. 
 
 It was in the beginning of September, 1881, that I asked for, 
 and obtained authority from the Minister of Marine to publish that 
 book, which appeared on the 20th December of the same year. 
 
 On the 2oth February, 1882, Vice- Admiral Jaureguiberry, then 
 Minister of Marine, sent me a letter from which I quote the last 
 paragraph. 
 
 " I wish at the same time, to express the satisfaction I feel for 
 the attention you have given to a work, which, to its other merits, 
 adds that of being the first complete treatise published in France on 
 the subject." 
 
 In that book I have, in the first place, drawn attention to a 
 result of capital importance for practical purposes which follows 
 from the valuable researches of Poisson in France, and of Archibald 
 Smith and Evans in England, namely : That if, at any place, the 
 deviation of the compass on a ship be determined on 16 points, then 
 at any other place, a table of deviations or a complete curve showing 
 the values of the deviation on all points, can be obtained by only 
 two observations, taken on the two cardinal points which include the 
 course of the ship. 
 
 Thus, provided the weather be clear enough for ten minutes to 
 allow the bearing of a heavenly body, or a known object on shore, 
 to be obtained, the navigator can afterwards in thick fog, in the 
 
IV. Introduction. 
 
 latitude of the place of observation, steer to within 2 or 3 degrees, 
 which is sufficiently accurate in all cases, except when near a 
 dangerous coast. 
 
 It is evident that such a result is of very great importance to 
 the sailor. It might be of daily use for all ships whatever the system 
 of compass employed, provided only that the deviation does not exceed 
 20 degrees, which is the case always with well-placed standard com- 
 passes. This result appeared so important to Vice-Admiral Peyron, 
 then Prefet Maritime at Brest, that he caused instructions to be 
 issued by the Minister of Marine ordering the general adoption of 
 the very simple formulas which allow the result to be obtained. 
 
 But the principal aim of my book was to overthrow the pre- 
 judice which existed against the compensation of the compass. This 
 operation has for its object the annulling of the deviations of the 
 compass by means of masses of soft iron and magnets properly 
 placed. 
 
 In books previously published and in all courses of instruction 
 this important question was very lightly treated, and, if sometimes 
 merited praise was given to some particularly interesting attempt, an 
 invincible reserve was always perceptible under these praises seeming 
 to imply a want of hearty appreciation of the practical problem. 
 
 Three questions stand forward in connection with the subject 
 of the complete compensation of the compass : 
 
 i st. Is the construction .of compasses sufficiently perfect to 
 allow the method to be applied to them with security ? 
 
 2nd. Can they be used with accuracy by observers having 
 limited theoretical knowledge ? 
 
 3rd. Can they be adjusted without any bearings by practical 
 methods, that is to say, by methods not requiring very special instruc- 
 tion and care ? 
 
 I answer each of these questions in the affirmative. 
 
 I am glad to be able to state that events have already con- 
 firmed me in the most important point. 
 
 Compensation of the compass has now fewer and fewer 
 opponents ; on the contrary, the number of compasses in use com- 
 pletely compensated, continually increases and the time is coming 
 when they alone will be used by ship owners and sailors careful of 
 their duties and of their interests 
 
Introduction. 
 
 The importance of this question was soon appreciated 
 and on the 26th December, 1881, the Minister of Marine, upon 
 the demand of the Director General of Charts and Plans, created in 
 that establishment, a course of lectures where all questions relating to 
 the compass and its compensation should be considered. 
 
 On the first point my conclusions were thus adopted without 
 restrictions ; on the other two, notwithstanding my constant efforts. 
 I must acknowledge it has not been so, and since the instru- 
 ments are good and the methods really practical, we must look 
 elsewhere for this temporary failure. 
 
 Since the publication of my book, Vice-Admirals Jaureguiberry 
 and Peyron in according to me praise, for which I am particularly 
 grateful, have both observed that upon several points I had not 
 attained that degree of simplicity which they considered essential if I 
 wished to gain the conviction of all. 
 
 Having recognized at once the justice and force of these remarks, 
 I returned to my studies with the ambition of attaching my name to 
 a definite work. In the Conferences held first at Toulon at the end 
 of March, 1882, and which were attended by a large number of my 
 chiefs and colleagues, and afterwards in another Conference held in the 
 beginning of May at Marseilles, I attempted to resume and further 
 simplify the question. 
 
 I trusted also that the Traite de Regulation would soon be 
 followed by similar works, as my translation of the English Admiralty 
 Manual had already been, which would this time agree with me in 
 pointing out the advantages and even the necessity of the complete 
 compensation, till that time so much disputed and often denied. 
 I thought also that others entering in the new and simplified way 
 which I had opened, taking as a starting point the results which I 
 had obtained, would be able to clear up the points remaining difficult 
 and obscure notwithstanding my efforts, and to approach still nearer 
 the only end which in my opinion remains to be attained, the com- 
 plete popularization of theoretical works which have directed and 
 subsequently passed triumphantly through the trial of experience. 
 
 This hope has not yet been fully realized. If the publications 
 and courses of lectures given in France or other countries, since 
 January, 1882, be examined, it will be seen that they do not differ in 
 any point essential for practice, from the book which I published, and 
 that inspired often by a spirit contrary to that which guided me, they 
 
vi. Introduction. 
 
 accord an importance to theoretical developements which, in my 
 opinion, they do not deserve, except in purely original researches. 
 For, these theoretical developments, although gratifying to the pride 
 of the author, may perhaps, in a popular work or course of lectures, 
 sacrifice somewhat too much the reader or pupil. They dis- 
 courage and perplex him by making him think the question remains 
 complicated and difficult, and they unnecessarily cause him to travel 
 over a road the difficulties of which the author should keep to 
 himself, exerting himself to spare the reader from them as completely 
 as possible. I believe that these tendencies interfere with the com- 
 plete popularization which I wish to accomplish, because by it 
 alone are we able to obtain tangible results. And this is why I 
 return to the question, animated by the same spirit which inspired 
 my book of December, 1881. 
 
 May I flatter myself that I have attained, at last, to the result 
 so long tried for, and have thus completed the task laid out for me by 
 Vice-Admirals Jaureguiberry and Peyron ? The book which I now give 
 to sailors is without formulas ; I believe it is at the same time, suffici- 
 ently detailed and complete to put within the reach of all, and without 
 requiring any considerable amount of work, methods until now 
 considered too difficult and complicated to be used in ordinary 
 practice. 
 
 The following are the three important improvements which seem 
 to me ought to result in a short time from the work which I publish. 
 
 I St. 
 
 The adoption and the general application of the method of 
 compensation without bearings, by means of the Deflector and 
 Dipping-needle of Sir Wm. Thomson, 
 
 At present the work of adjusting the compass is a complicated 
 one. It is so much the longer and more costly when the ships are 
 large, and the tides, winds, and currents, strong. It is not uncommon, 
 especially in winter time, for this work to take up several days, for 
 ships of large tonnage in our northern ports. 
 
 In very unfavourable circumstances as much as six days have 
 been wasted over a large ship. This amount of time is lost from the 
 active service of the ship. 
 
Introduction. vil. 
 
 Moreover, the special expenses of the work may easily amount 
 to 20, and they may attain ^"40 for a large vessel. It 
 exceeds this amount very much if the insurance of the ship during 
 the time occupied be taken into account, or if the ships, as is 
 frequently the case, are obliged to be taken to fixed positions for the 
 work. The only suitable places which afford a good anchorage, 
 facilities for turning, and the necessary bearings to ensure accuracy in 
 the observations, are often at a considerable distance. 
 
 I propose to replace all these troublesome and costly complica- 
 tions by the compensation being made without expense, during the 
 regular and necessary run of the ship to try her engines. One single 
 objection can be urged, namely, that the actual adjustment when it is 
 made with all possible care, can only give, in the most favourable 
 circumstances, the knowledge of the deviations to within about one 
 degree. But I answer this objection. 
 
 On board our modern ships constructed entirely of iron, the 
 direction of turning of the ship ; the retardation of magnetic induction 
 so complex in character, due to the iron ; the mechanical errors 
 inherent in the heavy cards actually employed ; the inevitable errors 
 of observation made on board with instruments necessarily very simple; 
 can easily double or treble the total error, notwithstanding all the 
 skill and care of the observer. This is so true that a navigator 
 prevented by fog from taking observations can never depend on his 
 course within one degree. 
 
 Overtaken by a fog he must remain at anchor or out at sea, or 
 if he is making a passage, he must set his course on the understanding 
 that there may be a difference of 2 or 3 degrees in the real value of 
 the deviation of the compass from that which is given from the last 
 table of deviations. 
 
 But admitting for an instant that the deviation of the compass 
 can be known to within a degree on all points at the place of obser- 
 vation, is it necessary to impose so much expense, delay and labour, 
 to attain an accuracy which will not exist after a day or two at sea, for 
 iron ships, particularly when they run at high speeds ? 
 
 Would it not be better to compensate without expense, without 
 loss of time, the Azimuth Compass to within two or three degrees 
 and draw up afterwards at leisure, at anchor, the table or complete 
 curve of deviations, by means of observations obtained during the 
 
viii. Introduction. 
 
 swinging of the ship under the influence of the wind and tide. If it is 
 necessary to proceed to sea before being able to collect a sufficient num- 
 ber of observations, the ships head can be placed while going out of 
 port on the different points necessary to complete them. 
 
 Besides, the captains of iron ships who are attentive to their 
 compass, never go to sea without turning their ships round while 
 leaving the port and observing the deviations on the eight principal 
 points so as to be able to make a complete curve of deviations. 
 
 The question which I propose will soon force itself on all and 
 will effect savings in time and money which it would be wrong to 
 neglect any longer. 
 
 By what method should the compass be compensated ; by means 
 of bearings or with the deflector ? 
 
 I firmly recommend this last method which can be practised at 
 sea without being embarrassed by the shore, without requiring the sun 
 or clear enough weather to be able to see a distant object. It is 
 only necessary in fact to see far enough to avoid a collision, going at 
 a slow speed. The work thus becomes one of the easiest ; it occupies 
 hardly an hour in the great majority of cases, an hour and a half in 
 unfavourable circumstances, two hours in exceptional circumstances. 
 
 The method of bearings can be employed afterwards to verify 
 the accuracy of this compensation and to draw up the table or curve 
 of deviation ; and the comparison of these with those obtained on other 
 occasions gives valuable information as to the permanency of the 
 magnetic condition of the ship, and consequently as to the amount of 
 accuracy to be expected from the indications of the compass. 
 
 2nd, 
 
 Another important benefit which will spring from this method of 
 working is that the sailor, familiarized with the use of the Deflector, 
 will become master of his course to within two or three degrees, 
 even in times of fog which may last several days; and that will be 
 the case even on a new ship, or on a ship making a voyage on a new 
 route for the first time. 
 
 As soon as this improvement has been realized another one still 
 more important will inevitably follow in a short time. 
 
Introduction. 
 
 3rd. 
 
 Every day public opinion is more excited, not only by the 
 frequency of collisions and shipwrecks, which are increasing annually, 
 but further and above all, by their consequences becoming more and 
 more serious and disastrous. 
 
 The statistics of the Bureau Veritas apply only to ocean going 
 ships, that is to say, to vessels of over 50 tons for sailing ships and 100 
 tons for steamers. At the present time there are 48,000 sailing 
 ships with a total tonnage of 13 J millions, giving an average of 300 
 tons per ship ; 27,764 steamers with a total tonnage of 9,250,000, or 
 an average of 1,200 tons per steamer. Each ton displacement has 
 according to the insurance policies an average value of 12 los. 
 for sailing ships and 21 for steamers. 
 
 We thus find that the floating material, belonging to all civil- 
 ized nations has a value of 360 million pounds. 
 
 In the single year 1883 tne tota ^ loss of ships from collisions 
 and strandings was as follows : 
 
 From collision, 67 sailing ships representing ,250,000 and 31 
 steamers representing ,750,000, making a total of .1,000,000. 
 
 By stranding, 745 sailing ships representing ,2,800,000 and 
 129 steamers representing .3,200,000, making a total of "6,000,000. 
 
 The value of the total losses from these two causes combined 
 amount in round numbers to '7,000,000. Besides this there are 
 the cases of vessels damaged without becoming total wrecks. 
 
 641 sailing ships and 466 steamers have been in collision, 691 
 sailing ships and 307 steamers have been ashore. Taking these 
 extensive damages at J per cent, only, we see that in material alone, 
 2 per cent, of all that floats is destroyed ; moreover the number of 
 lives lost in these catastrophies is not known exactly. These should 
 be taken into account along with the above statistics, if we are to 
 draw from them all the instruction they admit of; and further we 
 do not find either in France or England, the statistics even of the 
 Insurance Companies given in sufficient detail to allow us to subdivide 
 these two large classes of casualties in order to apply to them effective 
 remedies. For example, it is impossible to know in the case of 
 wrecks, what part is due to errors of course. This want is to be 
 regretted and it is important to fill it up as quickly as possible. 
 That is easy because all the information necessary is to be found 
 
Introduction. 
 
 in the proceedings of the Naval Courts. It is only necessary to collect 
 and arrange it. In any case it is evident to all those who interest 
 themselves in these questions, that the majority of wrecks is due to 
 errors of course. These arise from four different causes (i) The 
 impossibility of obtaining astronomical observations ; (2) Their 
 inaccuracy \ (3) The influence of unknown currents, and lastly 
 the errors of the compass. It would be of great interest to know 
 the relative importance of these causes, because we are not help- 
 less except in the case of one of them, the impossibility of obtaining 
 observations. Still it must be admitted that we can limit the danger 
 which this entails by reducing to a minimum the influence of the 
 others, particularly that of the errors of the compass, which we are 
 now able to know and to diminish. 
 
 The inaccuracy of astronomical observations when well estab- 
 lished will indicate to what precise points studies should be directed, 
 and prominence given in the examination of candidates ; upon what 
 other points improvements from makers, and attention from navigators 
 must be demanded. 
 
 The losses due to currents, the localities where they have taken 
 place, would arouse the attention of mariners and would indicate to 
 governments the parts of the world where new and complete hydro- 
 graphic surveys are necessary, and lighthouses, buoys, &c., are 
 required. 
 
 With regard to the losses caused by the errors of the compass, 
 these are certainly the most numerous, and their number must increase 
 unless special attention be given to this subject. In point of fact the 
 economic laws of maritime competition are becoming every day more 
 severe, one might say more cruel. The shipowner must, at any price, 
 keep pace with his rivals in point of speed. This entails going at full 
 speed when the weather is hazy, and the rapid approach to shore in 
 unfavourable circumstances and even in time of fog. It must be borne 
 in mind that the great activity of maritime commerce lies between the 
 Coasts of North America and the North of Europe, latitudes which 
 are frequently invaded by fogs for eight months in the year. 
 And, I should add, that the great speed of the ships can only be 
 obtained by increasing their length and depth. 
 
 All these facts carry with them inevitable consequences. In 
 former times the coast was approached more prudently and more 
 
Introduction. XT. 
 
 slowly ; if a mistake were made, there was a fair chance of finding in 
 time a greater depth of water than the necessary one-and-a-half or two 
 fathoms. Besides, vessels of a small draught had also a small length, 
 they turned quickly in a space of 200 or 300 feet, and could be readily 
 and surely withdrawn from the danger. At present it is necessary to 
 approach the coast rapidly, and with ships drawing 16, 20 or 24 feet. 
 When a mistake is found out the depth of water is wanting on all 
 sides at once. Moreover, to reduce the speed in order to turn these 
 enormously long vessels, requires a space of eight or nine hundred 
 feet, sometimes more, and whilst the ship is doing this, the currents, 
 always strong near the coast, may soon place it in a precarious position ; 
 our large modern ships thus perish even in circumstances where the 
 smaller and more manageable ships of old could easily be saved. 
 
 The statistics which we have to deal with, incomplete as they 
 are, show clearly that our deductions are not vain speculations. In 
 fact, if the total number of sailing vessels and of steamers be compared 
 with the number of wrecks which have occurred in the two classes 
 of ships, it will be seen that the proportion of wrecks is 1.5 per cent, 
 for sailing ships, 1.7 per cent, for steamers. The greater facility 
 of action of steamships ought to reverse the proportions if the causes 
 we have indicated did not intervene in a preponderant way. 
 
 It is not, however, the sailors who are to blame for casualties 
 so frequent and so serious. 
 
 Their knowledge, their skill, their vigilance and their devotion 
 are equal to their responsibilites. I appeal to the recollection of 
 those who have seen them at work. But it is necessary to take great 
 care not to require of them, as so often is done, more than human 
 strength can accomplish with any chance of success. Justice, the 
 interest of all, demands that all facilities should be given for escaping 
 from dangers, the seriousness of which increases every day. 
 
 No sailor is deliberately thoughtless on these important questions 
 but all ask. and the demand is legitimate that they should be given 
 methods simple enough to prove in themselves that they are practical 
 and to spare them work which they have not time to accomplish. 
 
 In our opinion the most effective way of accomplishing this is 
 to employ henceforth properly constructed compasses only, and above 
 all these which can be superintended and adjusted without any 
 bearings. 
 
xii. Introduction. 
 
 Moreover the use of these compasses would have the immense 
 advantage of reducing to a minimum errors of course and the expenses 
 which they entail, expenses all the greater if the ships are very large 
 and the engines very powerful. From 1850 to 1884 we have passed 
 from ships 200 feet long and 16 feet draught and a speed of 8 
 knots to ships with a speed of 16 knots drawing 24 feet of water 
 and attaining a length of 430 feet or even as much as 530 or 550 feet. 
 I can well understand that ships of the latter dimensions are found a 
 little too great, the ships themselves insufficiently studied and in 
 advance of the time, when they are contrasted with the entrances and 
 dock accomodation of the ports designed for their use. But I am 
 convinced that their is an immediate future for those ships on the 
 large lines of traffic and it is necessary at the risk of serious mistakes 
 to prepare the ports to receive them, and to study with the greatest 
 care each one of the details which would assist in the economical 
 and safe management of similar and more costly masses. 
 
 As for wrecks, all the causes which we have just enumerated 
 indicate the increase in their number and importance. The great 
 speed diminishes the time left for captains to avoid danger, the great 
 length, their enormous bulk, render them more difficult of manage- 
 ment. All these causes combine to increase the intensity of the 
 shock and to make it more destructive. 
 
 Sooner or later and the sooner the better, we shall see all civil- 
 ized nations combining to make, with regard to maritime traffic on their 
 common highway, the sea, rules more complete and more detailed 
 than those which at present exist, similar in fact to those which 
 each one has already in force for carriage roads, railroads and water- 
 ways which pass through its Territory. 
 
 These rules would probably indicate during time of peace, 
 courses between two gi\en ports, to be followed by vessels whose 
 speed exceed a certain limit. I say courses, because it is necessary 
 to have two, one for going and one for returning. These two should 
 be separated by a distance sufficiently great to allow for any error of 
 the compass which may be expected, so that a vessel going along one 
 route would not be led across to the other, through this error. Ships 
 would not be allowed to run at full speed at night, except on these 
 courses. They would have to diminish it as soon as they are off this 
 course through unavoidable circumstances, and when they are approach- 
 ing land. Some years ago it would have been impossible to impose 
 such rules, they would have been either delusive or unjust in the state 
 
Introduction. xm. 
 
 of uncertainty and complication of all questions relating to the compass. 
 But the time is passed when the construction of these instruments, 
 based on purely empirical rules was necessarily defective ; as also the 
 accuracy of their indications. Because neither the one, nor the 
 other could be effectively improved, except at the cost of efforts and 
 studies, which it would have been unjust as well as impossible to 
 demand from makers and sailors. Now the theoretical researches 
 which have been going on for half-a-century, have been at last crowned 
 by complete success. The work produced can be separated from 
 those surroundings which conceal from view the simplicity of the 
 investigations. 
 
 My first book was a popular effort, intended to prove that 
 compensation was not only advantageous but necessary. This demon- 
 stration has proved conclusive since compasses compensated entirely 
 have been introduced into practice. But it is still said that compen- 
 sation is an operation too troublesome and complicated for all 
 captains or officers to be able to perform. Further, in my opinion 
 enough evidence has not been brought forward to show the progress, 
 greater still than that of compensation, accomplished lately in the 
 question of compasses ; I speak of the possibility of adjusting in time 
 of fog and without any bearings. 
 
 It is upon these two points which interest me so much, that I 
 wish again to insist, in order to convince sailors that they can if they 
 will make but a small effort, master these methods which still appear 
 to frighten them by their complication ; this complication I believe I 
 have now been successful in dispelling altogether, I ask of any 
 unprejudiced mind only to compare the dryness, the barrenness, the 
 pretended complication of these methods, with the simplified form 
 which I now give to them, and afterwards to decide whether, contrary 
 to general opinion, these simplified methods are not really, as I main- 
 tain, within the comprehension of every sailor who is only attentive 
 and painstaking. All those who will take the trouble to go through 
 these two pamphlets will I hope be of my opinion. I have separated 
 this book into two parts because there are many compasses which are 
 not yet provided with a Deflector and Dipping needle, which it is 
 wrongly believed are too delicate to handle. I hope to assist in intro- 
 ducing the method of compensation without bearings which appears 
 to me important from the obvious simplification produced, in the appli- 
 cation of the method to compensation with bearings, which henceforth 
 all can use. 
 
XIV". Introduction. 
 
 Four or five hours are now sufficient, if one has these instru- 
 ments at his disposal, to teach or to understand all that is necessary 
 for the practical, and certain application of compensation with or 
 without bearings : and that without requiring further mathematical 
 knowledge than the rule of three and the use of the Trigonometrical 
 tables. 
 
 The same amount of time would be sufficient to give the skill 
 necessary for rapidity and accuracy in the operations. 
 
 Insurance Companies might therefore, and in our opinion 
 should, require the exclusive use of compasses properly constructed, 
 and above all, of those which can be superintended, controlled, or 
 compensated in a practical manner, even without any bearings. 
 
 And what would be still more effective, examiners might require 
 for the examination of all candidates for the position of Captain 
 the knowledge necessary for the proper use of these instruments. 
 For, those who are the least familiar with theoretical studies might 
 attain this result much more easily, and with much less trouble, than 
 that which is necessary to learn the use of that indispensable instru- 
 ment, the sextant. This question deserves the attention of all those 
 who interest themselves in the developement of our Naval power. 
 Our Navy cannot be truly powerful if it is not supported by a 
 numerous and prosperous Mercantile Marine. It is necessary there- 
 fore to make every effort to draw to the latter capital and men which 
 appear to abandon it, and we will accomplish this by diminishing the 
 losses which prevent a sufficiently remunerative employment being 
 offered to one and the other. 
 
 If I have been able in thus diminishing the necessary labour to 
 gain for it a greater number, I shall be happy to have contributed to 
 a real progress, and to have thus testified to Vice- Admirals Jaure- 
 guiberry and Peyron the gratitude which I owe to them for the 
 facilities and the encouragement which they have given to my work, 
 for the freedom of action which they have allowed me, the value of 
 which I well appreciate, and have done my best to repay. 
 
 To diminish the cost and the delay which precedes the depar- 
 ture of a vessel in simplifying all that relates to the compass ; to 
 diminish the errors of course and the dangers more and more con- 
 siderable which they entail, and by that to succeed in diminishing the 
 number of wrecks, such are the results which I have pursued ; they 
 appear to me considerable, and it is the hope of attaining them which 
 
introduction. XV. 
 
 has made me persevere in a task too apt to prove thankless, because 
 in appearance so strictly technical and special. 
 
 I earnestly desire to obtain the approval of sailors, because if 
 I do so, I am sure to be able to relieve them of a part of their labours 
 and responsibilities, and thus to diminish the loss of life, by which it 
 seems that all progress must be payed. 
 
 A. COLLET. 
 
 NOTE. This introduction was already in print when the publication of the 
 English Board of Trade returns was brought under my notice, too late unfor- 
 tunately for me to make use of them. The Abstract of sea casualties bear witness 
 to the earnest solicitude of England for all that concerns the interest of her shipping, 
 of " her walls of oak," or of iron, as we must now say. They reflect the greatest 
 honor on all those who have collected, arranged, and published them. I have 
 found that these Statistics partly satisfy the demands made above. 
 
 The number of deaths due to the diverse risks of navigation is given accurately 
 and completely as regards English vessels, and care has been taken to distinguish the 
 particular kind of vessel and the different causes of the disasters. We thus learn 
 that in the year 1881-82 the total number of deaths at sea due to disasters to English 
 ships is composed as follows : onboard sailing ships 2700 ; on board steamers 1276. 
 
 These numbers are further subdivided : 13 per cent, of the total number of 
 deaths are due to stranding of sailing ships, and 2 per cent, to collisions. 
 For steamers the two proportions are 29 per cent, and 4 per cent, respectively. 
 This again sadly confirms that which we have already asserted. These statistics 
 also give for the Coast of England and her Colonies the exact positions where these 
 disasters occur. But similar information for the Coast of Europe does not exist. 
 
 All that concern collisions and the various circumstances connected with them 
 is both very circumstantial and very complete. If I might be allowed to express a 
 wish dictated by the sole desire to see these valuable works yield their full fruit, I 
 would like to have the Chapter on Strandings subdivided as I have suggested. If 
 the statistics from 1878 were gone over again and care taken to indicate the total 
 number of ships with compensated compasses, the number of those which can be 
 compensated in time of fog, and finally the number of disasters that they have been 
 concerned in, we should know exactly by undisputable numbers the real importance 
 of the improvements of the compass, and of bringing the method of compensation 
 within the reach of all. 
 
CHAPTER I. 
 
 DEFINITIONS. PRINCIPLE OF THE SYSTEM. 
 
 /COMPENSATION of compasses is that operation which is 
 effected by placing around the compass card, at proper 
 positions, magnets and masses of soft iron, in such a way as 
 to exercise on the magnetic needle, actions equal and contrary 
 to those which arise from the iron of the ship, and thus to 
 annul on all points the deviation produced by this iron. 
 
 In reality the deviation is not altogether annulled on all 
 points, in consequence of the inevitable errors of observation ; 
 but it is reduced to a very small amount, not exceeding two or 
 three degrees. 
 
 Compensation has another advantage, which is that it 
 renders constant, or nearly so, the directive force which acts 
 on the magnetic needle on different courses. This increases 
 the sensitiveness and accuracy of the compass, and makes it 
 steadier when the ship is rolling. 
 
 The directive force of the compass, or of the card, is the 
 magnetic force which acts on the magnetic needles to bring 
 the card back to its position of equilibrium when it has been 
 diverted from it by any cause. 
 
 The complete compensation of the compass requires two 
 successive operations. 
 
 The first, which we will call horizontal compensation, has 
 for its object the annulling of the deviation of the compass on 
 all points, when the ship is upright. The second, which we will 
 
2 Compensation without Bearings. CHAP. I. 
 
 call compensation for heeling error, is intended to prevent the 
 heeling of the ship, interfering with the horizontal compen- 
 sation. 
 
 We have given in another pamphlet the method of per- 
 forming these two operations by means of bearings of Ter- 
 restrial or Celestial objects. 
 
 We will now give very simple practical rules which allow 
 us to obtain the same result, when it is not possible to get any 
 bearings. 
 
 It is only within the last few years that experience 
 has enabled us to overcome the various difficulties which hindered 
 the adoption of the method of compensation without sights. 
 The title in itself indicates the important service which it is 
 able to render in the most critical circumstances of navigation, 
 
 o 
 
 such as foggy weather, when no observations can be obtained. 
 
 Theory teaches that the iron of the ship increases or 
 diminishes the directive force which acts on the magnetic 
 
 O 
 
 needles by a quantity variable with each position of the ship's 
 head. It teaches, also, that if the directive force is the same 
 on all courses the deviation of the compass will be constant, 
 and reduced to one or two degrees. One single observation 
 of the deviation suffices to determine this constant error, which 
 in all cases, even when unknown, cannot be dangerous. (See 
 " Trait^ de Regulations.") 
 
 Theory also shows that if the directive force be the 
 same on five points, it will be constant on all points. 
 
 It is evident therefore that it is possible to compensate 
 a compass without bearings, provided we have ; 1st a convenient 
 instrument for measuring with sufficient accuracy, on a fixed 
 course, the directive force on the needles. 2nd compensators 
 magnets and soft iron with which we can increase or diminish 
 by convenient amounts, the forces observed on five courses. This 
 method of compensation could be successfully applied to all com- 
 passes, but it is necessary to point out, that it does not readily 
 give results exact enough for practical purposes unless the 
 card is sufficiently light; that it would not be simple, 
 quick, and convenient, in a word practical, unless the card 
 
CHAP. i. Corrector Magnets. 
 
 has a magnetic . moment sufficiently small to allow of Sir 
 W. Thomson's adjustable Deflector being used for measuring the 
 directive force. We will refer to this instrument further on. 
 
 The corrector magnets should be placed, one set parallel Corrector 
 to the keel, which we will call fore-and-aft magnets ; another 
 set perpendicular to the keel, which we will call thwartship 
 magnets. 
 
 The fore-and-aft magnets should be employed in pairs. 
 They are then placed in the same horizontal plane, one on each 
 side of, and at equal distances from, the axis of the compass. 
 
 The plane which passes through the axis of the compass, 
 and the middle of any thwartship magnet should be parallel 
 to the keel, or should include it. 
 
 The plane which passes through the axis of the compass, 
 and the middle of any fore-and-aft magnet should be perpendicu- 
 lar to the keel. 
 
 To distinguish the poles of the corrector magnets, it is Colour of the 
 convenient to colour one half of the magnet red, the other half 
 blue. The end which is attracted towards the north is painted 
 red, that which is attracted towards the south, blue. 
 
 A very easy and inexpensive improvement, would further 
 simplify the compensation of the compass, by keeping continually 
 before the eyes of the observer the convention made for the 
 colouring of the poles. It consists in colouring red the letter 
 N of the card, and the star which surrounds it, and blue the 
 letter S and the perimeter which encloses it. B^ this means all 
 effort of memory would be done away with, and consequently 
 all chance of mistake. This slight alteration might be made 
 by any one for himself, on the card of his own compass. 
 
 In order to make the operation of placing the bar magnets pi ae i n g the 
 in position, convenient, quick and practical, receptacles should 
 be arranged beforehand in the binnacle. These receptacles 
 should satisfy several conditions. The magnets should be easily 
 inserted, they should not be able to move of themselves when 
 once put in position, lastly the receptacles should be able to 
 be locked in such a way that the position of the magnets 
 
Corrector Magnets. CHAP. i. 
 
 cannot be altered, except by the Officer in charge of the compass. 
 The distance of the magnets from the card should be able to 
 be altered by quantities smaller and smaller, as the magnets 
 are brought closer to the card. Finally whether these receptacles 
 have been provided or not, in order to avoid the occurrence 
 of errors more complicated than those which have to be corrected, 
 the following rule should be strictly observed. 
 
 The distance of the corrector magnets from the card 
 should be such that the perpendicular from the middle of the bar 
 magnet to the line which joins this middle to the centre of the 
 needles, may cut the plane of the needles at a distance from the 
 centre, equal at least to six times the length of the magnetic 
 needles. 
 
 Whenever receptacles have been prepared beforehand for 
 the magnets, they should be examined to make sure that this 
 rule has been observed by the maker. When they have not 
 been provided, the limit which must not be passed by either of 
 the two sets of magnets, should be marked beforehand on the 
 bridge or binnacle. 
 
 Instead of the system of many fixed receptacles, in which 
 the magnets are placed successively, we prefer moveable recept- 
 acles in which the correctors are placed once for all, and which 
 move with the magnets themselves, till the latter produce the 
 effect wanted. 
 
 In general, magnets of the same length, but of two different 
 diameters are given out with each compass. The smallest are 
 used when small errors are to be corrected, or to complete 
 the correction made approximately by the larger ones. Only 
 experience can teach the proper position in which the magnets 
 should be placed at first in order to diminish the successive trials 
 of the compensation. This position varies with the compass, 
 and the magnets used, and also with the place in which the 
 work is done. 
 
 The only general advice which can be given to shorten 
 the operation, is to place the magnets, in the first instance, as far 
 as possible from the card, to bring them nearer gradually, but 
 very slowly, stopping at fixed positions, from time to time, 
 
CHAP. i. Soft Iron Compensators. 5 
 
 for several seconds, in order to prevent the compass card getting 
 into a state of oscillation, under their influence. 
 
 The soft iron compensators are generally employed in pairs. Soft Iron 
 The two, exactly similar, are placed one on each side of the tors, 
 compass, and at equal distances from the centre. 
 
 Spheres of different diameters are the compensators most 
 commonly used after the example of Sir W. Thomson ; cylinders 
 of soft iron, may also be used in accordance with the recom- 
 mendation of the Liverpool Compass Committee. 
 
 To place them quickly in position we should be able Placing of 
 easily to ascertain and vary their distance from the centre of 
 the compass. We should have a table showing the effect they 
 produce on the compass, at different distances, and lastly we 
 should be able to fix them securely at the proper distance. 
 
 Let us imagine a magnetized needle and a magnetized Effect of the 
 bar, longer than this needle, and parallel to it, placed so that tfaedirecfc- 
 the line which joins their centres is perpendicular to their ^*^^ of 
 common direction, the magnetized bar diminishes the directive pass, 
 force on the needle, when its poles are set similarly to those of 
 the needle ; it increases it when its poles are set in the contrary 
 direction to those of the needle. 
 
 Imagine a sphere having its centre in the plane of the Effect of the 
 needles of the compass, and whose diameter is longer than them ; the directive 
 think of it as reduced to that horizontal diameter, which is orce ' 
 parallel to the North and South magnetic line. Suppose also 
 this diameter or rod of soft iron, infinitely thin, be at a sufficient 
 distance from the needles of the compass to prevent any 
 reciprocal action being exercised between them ; that is to say, 
 that the rod may be magnetized only by the action of the 
 earth. The magnetic intensity of the two poles of this diameter 
 is greater when it is long, that is, when the sphere is great. 
 The sphere being invariably fixed to the ship, this magnetic 
 diameter, always preserves the same direction in space, and changes 
 in the sphere when the direction of the ship's head changes ; 
 it may be considered as a magnet, the direction of whose 
 poles are variable with the ship's head. A very simple sketch 
 
6 Compensation with the aid of the Deflector. CHAP. i. 
 
 showing the relative positions of the magnetic needle, and of 
 this diameter on the eight principal points teaches, from what we 
 have seen above, that the sphere or the diameter which represents 
 it, increases the directive force of the needles, when the line 
 joining the centre of the sphere with that of the needles coincides 
 with the direction of the needles, on the contrary, it diminishes 
 the directive force when the line joining the centres is perpen- 
 dicular to the direction of the needles. 
 
 COMPENSATION WITH THE AID OF THE DEFLECTOR. 
 
 Statement of Imagine for an instant that the deviation of the compass 
 
 tionsneces- does not exceed 10 degrees on any point. By means of the 
 
 sary. deflector, the directive force is measured on the North and 
 
 South magnetic points, and the magnets placed parallel to 
 
 the keel, that is fore-and-aft, in such a way as to make these 
 
 two forces equal. We ascertain that this result is attained by means 
 
 of the deflector. 
 
 The same thing is done on the East and West magnetic 
 points, but in this case to equalize the two observed directive 
 forces, the magnets perpendicular to the keel, or thwartship ones, 
 are used. 
 
 This being done, the directive force common to the North 
 and South is not generally the same as that common to the 
 East and West. In order to make them equal, keep the ship's 
 head still on the last cardinal point, and place the compensating 
 spheres with the line of their centres either parallel or per- 
 pendicular to the needles, according to circumstances, so that 
 the directive force on this course may be equal to the mean of 
 the two preceeding forces ; thus the same value has been given 
 to the directive force, on the four cardinal points. 
 
 The ship's head must now be put on any quadrantal 
 point, and the directive force measured. If it is the same as the 
 mean value already found for the four cardinal points, the com- 
 pensation is finished. This is the case with almost all ships 
 of the Merchant Service and in the great majority of Ships of 
 War. But if the directive force on the quadrantal point is different 
 from that common to the four cardinal points, it is made equal 
 
CHAP. I. Complications in practice. 7 
 
 to the mean of these two forces by properly setting the line 
 joining the centres of the spheres, and bringing them nearer to 
 the centre of the compass. 
 
 Such is the simplicity of the method in theory. In Uncertainties 
 practice it is a little more complicated, but this complication cations in * 
 cannot cause the method to be set aside, because the whole P racfclce - 
 time required for the complete compensation of the compass 
 does not exceed forty minutes, with an experienced observer, 
 and an hour at most for one less acquainted with the work. 
 
 The various causes of the uncertainties are. First, we have 
 said that it is necessary to observe on the exact magnetic points, 
 and it must be borne in mind that when compensating the 
 compass without bearings, there is nothing but the compass to 
 indicate the proper direction. It is therefore with the ship's head 
 by compass, that the observations are made, but thedeviations being 
 different at each point, when the ship's head is put on opposite 
 points by the compass, the two positions are not actually opposite 
 to one another as they should be, for the rigorous application of 
 the method, and as we have supposed them to be in the elemen- 
 tary explanation which we have just given. 
 
 In the great majority of cases the bridge or Azimuth 
 compass is so well placed, that without compensators, the 
 deviation does not exceed eight or ten degrees on any point. 
 It follows from this that the deviation, and also the directive 
 force, vary slowly with a change of the ship's head. When 
 therefore the directive forces have been equalized with the ship's 
 head North and South by compass, they will also be equal with 
 ship's head North and South magnetic, or on two points diame- 
 trically opposite, as the theory requires. 
 
 The same applies to the other points on which the forces 
 are equalized by means of compensators. Thus in the case of 
 small deviations, it is sufficient to turn the ship round once, to 
 equalize the directive force on all points. 
 
 But when the deviations of the compass without compen- 
 sators exceed that limit, the preceeding reasoning will no 
 longer apply. The equality of the directive forces on the North 
 and South by compass, does not imply that the forces on magnetic 
 
8 Exceptional Cases. CHAP. i. 
 
 North and South are equal, because the two points of the compass 
 may be very different from the magnetic ones. Two turns of the 
 ship must then be made, the first which will serve to restrict the 
 variations of the directive force, and consequently the deviation 
 to a limit which will allow of the proceeding reasoning being 
 applied to the second turn of the ship. 
 
 Lastly there are cases altogether exceptional, which occur 
 when the axis of the compass being in the fore-and-aft plane of 
 the ship, masses of iron, (such as cannons, turrets, iron boats, &c.,) 
 are not symmetrical and equally distributed on each side of 
 the compass. Also when the masses of iron fulfil these two 
 conditions but the axis of the compass has not been placed in 
 the fore-and-aft plane. In such cases it may be necessarv to 
 make a third turn if the second has not been sufficient to restrict 
 the variations of the force within close enough limits so as to 
 obtain sufficiently accurate information to allow of changing 
 the globes and setting the line of their centres at the time. 
 
 But we should not complain of the complication of the 
 method, because we thus find ourselves in circumstances where 
 without it the compass could not be used. Moreover even in this 
 extreme case the complete compensation will require less than two 
 hours or about one-third of the time actually required for the 
 adjustment of the compass of a ship whose length is over 160 
 feet, when the work is done in a little breeze or in a port exposed 
 to the tide. 
 
 In the most general case and that which resembles most 
 the simplicity of the theoretical case, where the directive forces 
 are equalized on all points, by working only on the four cardinal 
 points, we have said that for verifying the constancy of the force, 
 it is sufficient to place the ship on only one quadrantal point to 
 see that the force remains the same. In practice, especially if 
 the observer has not had much experience, or if the ship be new, 
 one single verification is not sufficient. For example, if the last 
 cardinal point is West, the ships head should be placed successively 
 on S.W., N.W., N. and N.E., and the directive force verified on 
 each. The ship will thus have been made to take one complete 
 turn and one-eighth of a turn in addition. In this way the errors 
 
CHAP. I. JErrors of observation. 
 
 of observation or of placing the compensators in position cannot 
 cancel or conceal one another altogether as they occasionally do at 
 a single point. Thus a complete verification has been obtained. 
 
 Theoretically the deviations of a compass thus compensa- 
 ted should be constant on all points, and a single observation of 
 the deviation would allow of its very small value one or two 
 degrees being obtained. Unfortunately each observation carries 
 with it an inevitable error. The result is that the directive forces 
 instead of being strictly equal have still slight differences insen- 
 sible to observation, and arising occasionally only from the 
 complex laws of the magnetic induction of the imperfectly soft 
 iron of the ship. The deviation ins ead of being constant, will 
 vary then with the ship's head, but the compensation will have 
 had the effect of reducing it to a very small amount, in general 
 not exceeding three degrees. This result suffices to insure the 
 safety of the course, and to give it an accuracy which it was 
 impossible to attain before in time of fog. 
 
10 The Deflector. 
 
 CHAP. II. 
 
 CHAPTER II. 
 THE DEFLECTOR. THE DIRECTIVE FORCE. 
 
 Abstract 
 descrip 
 of the 
 Deflector. 
 
 Abstract T^HIS Instrument, which is about 8 or 9 centimetres lono- 7 
 
 description JL 
 
 of the high, and 5 centimetres wide, is represented in the accom- 
 
 panying drawing. 
 
 The essential part of the instrument consists of the four 
 arms, a, which form two Vs on the figure, one before and one 
 behind. 
 
 Each V carries on one of its arms a red pole, and on the 
 other a blue pole. The colours of the poles are set in the same 
 direction on the two Vs, that is to say, the two blue poles are on 
 the two left hand arms, and the two red poles on the two right 
 hand arms. 
 
 These Vs are made to open more or less, and in consequence 
 the ends of the magnets, which they carry, separate or are brought 
 closer, by turning the milled head b of the screw at the upper 
 part of the figure. 
 
 The variable distance between the poles is measured on a 
 little silvered scale placed in the lower framework of the instru- 
 ment, parallel to the rod p. It is divided into 35 divisions of a 
 millimetre each. The index showing the distance between the 
 
CHAP. ii. fhe Deflector. ll 
 
 magnets moves the length of this scale. To estimate the distance 
 between the magnets to one-tenth of a division, as also to see 
 without trouble which way to turn the screw so as to increase or 
 diminish this distance, the disc t connected with the screw b is 
 used. This disc is divided into ten equal parts, and numbered as 
 shown on the figure. 
 
 When the distance between the magnets is to be increased 
 the milled head b must be turned so that the numbers on the disc 
 as they pass round are seen to increase ; when, on the contrary, 
 the distance is to be diminshed, the numbers ought to be seen to 
 diminish. 
 
 To measure the distance between the magnets the index 
 which moves along the scale should be first examined. It will 
 usually be found to be between two divisions, say 15 and 16 to 
 fix the ideas. The lowest of the two, 15, is taken, and a number 
 of tenths added, equal to the number at the highest point of the 
 disc, to measure the distance between the poles. For example, 
 in the drawing, 1 is shown at the top of the disc, and if 
 the index is between 15 and 16 the distance between the poles 
 will be represented by lo'l. 
 
 The base of the instrument is composed of a framework c, 
 divided into two parts. The distance between the two parts can 
 be altered by means of the screws V shown on the figure. This 
 will be referred to further on, see page 34. 
 
 The instrument is supported on three feet, one of which 
 is in the centre, and should rest in a hollow in the centre 
 of the glass of the compass bowl, while the other two rest on 
 the glass itself. The instrument is thus free to turn round a 
 vertical axis, passing through the centre of the compass card. 
 
 Lastly, a rod p is used for turning the instrument round 
 its vertical axis. This rod is called the pointer. 
 
 This complex instrument may be described, with regard to 
 its action on the needles of the card, as a simple magnet with the 
 distance between its poles, and consequently its action on the 
 needles, variable. A fixed power corresponds to each division of 
 the scale, and its action on a magnetized needle, turning round 
 
The Directive Force. CHAP. n. 
 
 the same axis, depends only on the direction in which the poles 
 are set with regard to the needles. It is sufficient to remember, 
 that when the pointer makes a fixed angle with the North and 
 South line of the card, the force of the deflector is greater accord- 
 ing as the index stands at a higher division of the scale. 
 Measurement Suppose, to fix the ideas, that the North of the card is 
 
 of the 
 
 directive opposite to the lubber line of the bowl. 
 
 force. 
 
 Place the central foot of the deflector in the hollow in the 
 centre of the glass, the pointer (that is, the rod p), in the dir- 
 ection of the North of the card and then turn it round to the 
 division E. by N. The North point of the card will immediately 
 be seen to turn towards the pointer. Continue to move the 
 pointer so as to keep it always over the E. by N. of the card. 
 Now suppose that the distance between the magnets of the 
 deflector be such that the card stops at rest and in equilibrium 
 when the North and South line makes an angle of 90, with its 
 original position of equilibrium, that is when the West point 
 is opposite to the lubber line of the bowl. The card is now in 
 equilibrium under the action of two equal and opposite magnetic 
 forces ; the directive force arising from the joint action of the 
 earth and the ship on the one hand, and the disturbing action of the 
 magnets of the deflector on the other. The latter may therefore 
 be used to measure the former and the reading which expresses 
 the distance between the magnets of the deflector, may be taken 
 to represent it. 
 
 For convenience of speaking we will make use of the follow- 
 ing terms in future : 
 
 Natural position of equilibrium of the card, the position 
 which it occupies on any point, under the combined actions of the 
 earth and the ship. 
 
 Position of normal deflection, that which the card occupies 
 when it rests in equilibrium under the influence of the deflector, 
 with the N orth and South line, making an angle of 90 with its 
 original position and the pointer over the E. by N. of the deflected 
 card. 
 
 It is seen then that without requiring to know the absolute 
 value of the directive force, the deflector gives us the means of 
 
CHAP. ii. Management of the Deflector. 13 
 
 making sure of the equality of the forces on the different points, 
 since the equality takes place at all times when the normal 
 deflection is obtained on these points, with the same reading of 
 the deflector. 
 
 In order to use this instrument it is sufficient to know how 
 to obtain the normal deflection of the card. This is completely 
 attained without trouble with three or four hours practice, the 
 trials offering no difficulty. It can be done quickly in the follow- 
 ing way. 
 
 MANAGEMENT OF THE DEFLECTOR. EXERCISES TO BE 
 MADE ON SHORE. 
 
 It should be remembered that the North point of the card 
 always tends to turn towards the pointer. 
 
 (A.) To Obtain the Normal Deflection. On shore, in a 
 place free from iron, place the bowl of the compass with the 
 lubber line opposite to the North of the card. Make sure 
 that the glass of the compass bowl is level by means of a small 
 spirit level. Place the deflector on the glass, the pointer over the 
 North point of the card ; now turn the pointer round over the E. 
 by N. point. The North point of the card commences to turn 
 towards the pointer. The result to be obtained, is that the card 
 shall remain in equilibrium at 90 from its original position, that 
 is, the West point of the card, must be opposite to the lubber line 
 while the pointer is over the E. by N. division of the deviated 
 card. 
 
 In order to complete the observation with the greatest rapi- 
 dity, it is advisable that the normal deflection should never be ex- 
 ceeded by more than 4 or 5 degrees; for this purpose it is necessary 
 that the card should not be turning fast when it approaches the 
 position of normal deflection. On the other hand it is better for 
 thp accuracy of the observation that it should not be going too 
 slow. Practice alone will enable us to stop the card under the 
 most favourable conditions. This may be acquired quickly by 
 paying attention to the following remarks : 
 
 The card follows the pointer with a speed which accelerates 
 rapidly, especially if the index is already at a division near to 
 that which gives the normal deflection. 
 
14 Exercises to be made on shore. CHAP. u. 
 
 When the division N. 60 W. is seen to pass the lubber line 
 the speed of the card should be reduced, by moving the pointer, 
 as instantaneously as possible, through the North towards the 
 West of the card. 
 
 When the speed is sufficiently slackened, which will be at the 
 end of one or two seconds, the pointer should be turned as quickly 
 as possible back to the E. by N. point At the moment when the 
 West point of the card is 4 or 5 degrees from the lubber line, the 
 pointer is turned quickly towards the North of the card, and 
 made to pass through a sufficient number of degrees, so that the 
 card may lose its speed quickly and remain at rest with the West 
 point opposite to the lubber line. 
 
 At this moment the pointer should be turned rapidly to 
 the E. by N. point. 
 
 Three cases a, 6, c, may now occur. 
 
 (a). The card remains in equilibrium. This would indicate 
 that the reading of the deflector is the proper one to represent the 
 directive force on the needle. 
 
 (6). The card inclines to continue to turn in the same 
 direction and in consequence the West point inclines to pass the 
 lubber line. This shows that the reading of the deflector is too 
 strong and that it must be diminished. 
 
 For this purpose, commence by stopping the movement of 
 the card and if the West point has passed the lubber line con- 
 siderably, it will be necessary to bring it back by turning the 
 pointer quickly towards the North, and if that is not sufficient* 
 towards the West of the card. Bring back the pointer towards 
 the E. by N., when the West point is to the left of the lubber 
 line. 
 
 Suppose that the pointer is thus over the N. 60 E., of the 
 deviated card, which is at rest with its N. 70 W., opposite to the 
 lubber line ; now holding the part of the frame- work opposite 
 to the pointer in the left hand, turn the screw of the deflector 
 with the right hand, in such a way that the divisions on the 
 disc are seen to decrease. Each time that the same figure passes 
 the highest point of the disc, the reading is diminished by one 
 
CHAP. II. To obtain the normal deflection. 15 
 
 division of the silvered scale. Dimmish the reading of the 
 deflector thus, by a greater or less number of divisions according 
 as the speed of the West point passing the lubber line, (which 
 speed you have annulled or changed in direction) was more or 
 less great. This done, bring the pointer back towards the E. 
 bv N. The card follows the movement of the pointer. Watch 
 and reduce the movement in such a way as to obtain the result 
 required, namely the West point remaining at rest opposite to 
 the lubber line, whilst the pointer is over the E. by N. of the 
 card. This is attained by moving the pointer alternately back- 
 wards and forwards ; when it is required to reduce the speed of 
 the card, influenced by the deflector, the pointer is turned towards 
 the North of the card ; when it is necessary to increase this speed 
 it is turned towards the E. by N. When the alternate move- 
 ments are not sufficient to attain the result wished for, the reading 
 of the deflector is diminished or increased, and at each reading 
 the attempts to obtain the normal deflection are re-commenced 
 until that has been attained. 
 
 (c). The card remains at rest before the West point 
 reaches the lubber line, and while the pointer is over the E. by 
 N. of the deviated card. In this case increase the reading of the 
 deflector, and at each new division, see if the speed taken by 
 the card seems sufficient for it to reach the position of normal 
 deflection. 
 
 The main point in these observations is : 
 
 1. To increase or diminish the readings methodically, 
 that is to say, to make the difference between two readings, 
 corresponding to two consecutive attempts to obtain the normal 
 deflection, smaller and smaller as the exact result is approached, 
 
 2. Never allow the speed of the card, under the influence of 
 the deflector to become too great ; the speed is increased by quickly 
 moving the pointer towards the North, and if necessary making 
 it even pass the North, towards the West. When the speed is 
 sufficiently diminished the pointer is turned towards the E. by 
 N. of the card, more or less quickly according to circumstances. 
 
 3. Never allow the West point to pass the lubber line, 
 by more than 5 or 6 degrees; when it arrives opposite to the 
 
16 Return the card to its original position. CHAP. n. 
 
 lubber line, the card should be stopped there rather suddenly by 
 a quick movement of the pointer towards the North. This move- 
 ment should be over a greater or less number of degrees according 
 as the speed of the card is greater or less. 
 
 It is necessary to practice to move the deflector with the 
 greatest quickness, and at the same time not to give it a 
 shock which would raise the foot from the hollow, or would 
 cause the instrument to rebound from the glass. The deflector 
 should glide on the glass, it should be moved quickly, and 
 it should be stopped as instantaneous as possible. 
 
 The reading for the normal deflection being obtained the 
 following exercise should be practised : 
 
 (B.) To return the card to its natural position of equili- 
 brium ivith the aid of the deflector. This exercise is indispensable 
 because if the card is left to itself to come to rest it will take 
 several minutes. The operation will thus be lengthened, and 
 further, on board ship it will be impossible to verify again that 
 the ship's head has not changed during the observation, which is 
 essential. For this purpose, the card and pointer being in their 
 respective positions for normal deflection, turn the pointer quickly 
 towards the West point, passing through the North. You thus 
 give a quick return movement of the card towards its original 
 position. When the division N. 60 W., or one near it, passes the 
 lubber line, bring back the pointer to the E. by N. very sharply 
 and keep it over this division while the card continues to return 
 towards its original position. 
 
 The speed of the card gradually diminishes, and it must 
 be made to stop when the North point comes opposite to the 
 lubber line. To obtain this result, if the speed appears too slow, 
 increase it a little by turning the pointer for an instant towards the 
 North, bringing it back at once to the E. by N. 
 
 If the speed be too great, the North point will pass the 
 lubber line, but it will return soon from the action of the earth 
 and the deflector. The oscillations are quickly destroyed by a 
 succession of rapid and alternate movements of the pointer 
 towards the East when the North point is going to the left of the 
 
CHAP. ir. Alteration of 'the Deflector by Magnets. 17 
 
 lubber line, towards the West when it is going towards the right. 
 The oscillations of the card thus diminish very rapidly in ampli- 
 tude ; when it is stopped, opposite the lubber line, the deflector 
 is lifted quickly and vertically to a sufficient height, so that it 
 may not influence the card any more, it is then removed horizon- 
 tally to a distance of about 4 or 5 feet, so that it will not have 
 any influence on the card. 
 
 It is advisable to make the observation of normal deflec- 
 tion with the lubber line coinciding successively with the four 
 cardinal points. In this way the same observations are made 
 on shore as will have to be made on board ship, and further, the 
 observer is able to learn from the four readings the accuracy he 
 can attain to ; they ought to be rigorously equal to one another, 
 if the bowl is kept in the same place and is turned round to 
 make the lubber line correspond with the different cardinal points 
 of the card. 
 
 To increase or diminish by a given amount the reading 
 which produces the normal deflection, by placing magnets and 
 soft iron conveniently round the compass. 
 
 (C.) Alteration of the reading by means of magnets. 
 Place the bowl in position in the binnacle with the lubber line coin- 
 ciding with the North of the card. Suppose that in this position 
 the reading 15 of the deflector is found to give the normal de- 
 flection. It is desired to modify this reading by means of corrector 
 magnets. 
 
 PRACTICAL RULES. 
 
 The direction of the magnets to be employed is given 
 without ambiguity by the direction which the pointer occupies 
 in the position of normal deflection. (We suppose in speaking 
 thus, that it is over the East and not over the E. by N. of the 
 deviated card.) 
 
 When the reading of the deflector is to be diminished, the The direction 
 corrector magnets should be placed with their poles in the same f th g c^. 
 
 direction as those of the magnets of the deflector, when the ^g r Mag " 
 latter is in the position of normal deflection. 
 
18 Practical rules for placing the Magnets. CHAP. 11. 
 
 On the contrary, when the reading is to be increased, the 
 magnets should be placed with their poles in the opposite direction 
 to those of the deflector, in the position of normal deflection. 
 
 We put it briefly. 
 
 When corrector magnets are not already fitted, the 
 reading, to give the normal deflection, is diminished by placing 
 them in such a way, that the poles are similar to those of the 
 deflector; on the contrary, the reading is increased by placing 
 them with the poles contrary to those of the deflector. 
 
 When the magnets are already in position, two cases 
 may occur. 
 
 CASE 1. The corrector magnets already in position, have 
 their poles in the same direction as those of the deflector in the 
 position of normal deflection. In this case if the reading of the 
 deflector is to be increased, the corrector magnets must be moved 
 farther off. If the reading of the deflector is to be diminished 
 the magnets must be brought nearer. 
 
 CASE 2. The corrector magnets, already in position, 
 have their poles contrary to those of the deflector in the position 
 of normal deflection. In this case, if the reading is to be 
 increased, the corrector magnets must be brought nearer. If the 
 reading is to be diminished the magnets must be moved further 
 away. 
 
 In the first compensations which one makes, these practical 
 rules can, if desired, be copied on the abridged form given on 
 page 40, but this aid will, or ought to be, soon useless, if the 
 following very simple reasoning be remembered. 
 
 Let us consider the combined effect of the corrector mag- 
 nets and the deflector. The North point of the compass in the 
 position of normal deflection is in equilibrium, under the influ- 
 ence of the directive force due to the earth and the ship on the 
 one hand, and the combined force of the deflector and the cor- 
 rector magnets on the other hand. 
 
 Now, when the reading is increased, the force of the 
 deflector is increased ; if then, there are no corrector magnets in 
 position yet, they should be placed in such a way as to bring back 
 
CHAP. ii. Practiced rules for placing the Magnets. 19 
 
 the influence of the deflector to what it was previously, that is 
 to say, to reduce this influence. They must therefore be placed 
 with their poles contrary to those of the deflector. 
 
 On the contrary, when the reading is diminished, the 
 force of the deflector is diminished ; if then, there are no corrector 
 magnets in position, they must be placed so as to bring back 
 the influence of the deflector to what it was previously, that is 
 in such a way as to increase this influence ; they must therefore 
 be placed with their poles in the same direction as those of 
 the deflector. 
 
 If there are magnets in position, two cases are to be 
 distinguished. 
 
 1. The magnets have their poles in the same direction 
 as those of the deflector, in the position of normal deflection ; 
 consequently their influence on the card is in the same direction 
 as the deflector, and added to it. 
 
 If the deflector be increased, to keep the combined action 
 the same, the power of the magnets must be diminished, that is, 
 they must be moved further away. 
 
 If the deflector be diminished, the power of the magnets 
 must be increased to keep the combined action the same or the 
 magnets must be brought nearer. 
 
 2. The magnets, have their poles in the contrary direction 
 to those of the deflector in the position of normal deflection ; 
 consequently the influence of the corrector magnets is contrary 
 in direction or sign to that of the deflector, and they act one 
 against the other. 
 
 Now, if the reading of the deflector is increased, the action 
 of the magnets must be increased, that is they must be brought 
 nearer, to keep this difference the same. 
 
 If the reading of the deflector is diminished, the action of 
 the magnets must be diminished, that is they must be removed 
 further off to preserve this difference the same. 
 
 PRACTICE OF THE OPERATION. 
 
 We have obtained the normal deflection with the reading To increase 
 15 ; suppose it is desired to obtain the same deflection with the of e the ead 
 
 Deflector. 
 
20 To increase the reading of the Deflector. CHAP. n. 
 
 reading 19 by means of the corrector magnets. The observer 
 looking at the disc, turns the screw so as to make the numbers on 
 the disc, pass round with the numbers increasing. The screw is 
 turned four times round and when the zero is at the top for the 
 fourth time, the screw is stopped. 
 
 As soon as the screw begins to turn, the card moves so as 
 to increase ifcs distance from the natural position of equilibrium, 
 and to pass the position of the normal deflection. This movement 
 must not be allowed to exceed 4 or 5 degrees. For this purpose the 
 observer must take hold of the part of the framework, opposite 
 to the pointer with his left hand, and turn the pointer gradually 
 towards the N.E., while he continues turning the screw with his 
 right hand to increase the reading of the deflector. With a 
 little practice the reading may thus be increased by any required 
 amount, and the pointer moved towards the N.E. at the same time, 
 in such a way that the card will remain within 3 or 4 degrees of 
 the normal deflection. If the card has passed this position a very 
 slight final movement of the pointer towards the North brings it 
 back altogether, if it has not quite attained the position, the pointer 
 is moved towards the East. 
 
 We thus obtain the card in equilibrium, in the position of 
 normal deflection, whilst the pointer is over a division somewhere 
 between the North-East and East of the deviated card ; and we 
 have to place the corrector magnets in such a manner as to obtain 
 the normal deflection with the pointer over the E. by N. point. 
 
 Three different cases may now present themselves. 
 
 1st Case. There are no corrector magnets in position yet. 
 
 The observer should now introduce them with their poles in 
 the right direction according to the practical rules, which will be 
 in this case, with their poles contrary to those of the deflector. 
 
 In general the bar magnets are of two different diameters. 
 When the reading of the deflector has to be increased by one or 
 two divisions of the scale, magnets of the smallest diameter are 
 used. When it is to be increased by three or more divisions the 
 thicker magnets are used. 
 
 In both cases the magnets ought to be introduced further 
 from the card when the increase of the reading is smaller. 
 
CHAP. ii. To increase the reading with Magnets. 21 
 
 For quickness of observation, especially when the compen- 
 sation is being made by the observer for the first time, it is always 
 best to place the magnets too far off rather than too near. Place 
 the magnets as far as possible from the card. If in this position, 
 they do not exercise any influence on the card, that is, if the 
 card remains at rest, bring them nearer by degrees until the 
 card shows a tendency to return to its natural position of equi- 
 librium. From this time the magnets should be brought nearer 
 very slowly, centimetre by centimetre. At each position which 
 they occupy leave them at rest for a few seconds, iii order to 
 bring the pointer nearer to the E. by N. point of the deviated 
 card. If it seems from the speed of the card which follows this 
 movement, that the position of normal deflection may be passed, 
 turn the pointer back towards the N.E. to check this speed, and 
 then bring the magnets nearer. 
 
 At each new position of the magnets try again to obtain 
 the normal deflection with the pointer over the E. by N. point, 
 until that result is attained. 
 
 2nd Case. The magnets are already in position, and 
 their poles are similar to those of the deflector in the position of 
 normal deflection. 
 
 The card being at the position of normal deflection, or very 
 near it, and the pointer between the East and N.E., remove the 
 magnets gradually until the card shows a tendency to return to 
 its natural position of equilibrium. Check this movement and 
 prevent it from exceeding ten degrees by moving the pointer 
 towards the E. by N. 
 
 Continue to move the magnets further off by degrees. At 
 each of the successive positions leave them at rest for a few 
 seconds, and move the pointer nearer to the E. by N. 
 
 The card follows the movement of the pointer. If you are 
 afraid that it will pass the position of normal deflection, bring the 
 pointer back towards the N.E., then remove the magnets a little 
 more, and thus at each position that they occupy, try again to 
 obtain the normal deflection. 
 
 3rd Case. The magnets are already in position, and their 
 poles are contrary to those of the deflector in the position of 
 normal deflection. 
 
22 To diminish the reading with Magnets. CHAP. n. 
 
 The card being at the position of normal deflection, and the 
 pointer somewhere between the East and N.E., proceed exactly 
 as in the second case, except that now the magnets must be 
 brought nearer successively, and at each position an attempt made 
 to obtain the normal deflection until that result is attained. 
 
 norma ^ deflection has been obtained with the reading 
 of the 15, it is desired to place the corrector magnets in such a way 
 as to obtain the normal deflection with the reading 11. The 
 observer looks at the disc and turns the screw so as to make the 
 numbers pass round in decreasing order ; when the zero comes to 
 the upper part of the disc for the fourth time, he stops the motion. 
 The reading of the deflector will now be what is required. As 
 soon as the screw is turned, the card begins to return towards its 
 natural position of equilibrium. Follow the card with the deflector 
 keeping the pointer over the E. by N. After some oscillations of 
 short duration, which are rapidly stilled, by moving the pointer 
 contrary to the movement of the card, sometimes towards the 
 East and sometimes towards the E.N.E., the card is brought to 
 rest with the pointer over the E. by N., at about 10 degrees 
 from the position of normal deflection, (more or less according 
 as the reading of the deflector is diminished more or less). 
 Three cases may now occur. 
 
 1st Case. There are no magnets in position. 
 
 The observer should introduce them with their poles in 
 the proper^ direction, according to the practical rules. In this 
 case the magnets will have their poles similar to those of the 
 deflector. 
 
 Place the magnets as far off" as possible, and bring them 
 nearer successively until the card shows a tendency to return to 
 the position of normal deflection. From this time bring the 
 magnets gradually nearer, and by smaller and smaller degrees 
 until the normal deflection is obtained, whilst the pointer is over 
 the E, by N. 
 
 2nd case. The magnets are already in position with their 
 poles similar to those of the deflector. 
 
CHAP. IT. Alteration of the reading with the Spheres. 23 
 
 Proceed in the same way as in the first case. The magnets 
 must be gradually brought nearer. ^ 
 
 3rd case. The magnets are in position, but their poles are 
 contrary to those of the deflector. 
 
 The operation is just the same as the first and second 
 cases, except that here the magnets must be removed gradually 
 until the card returns to the position of normal deflection, with 
 the pointer over E. by N. 
 
 If one thwartship magnet or two fore-and-aft magnets 
 placed as near as possible to the card (always observing absolutely 
 the rule which limits this distance) are not sufficient to produce 
 the normal deflection with the desired reading, a sufficient 
 number of magnets must be used to attain the result. 
 
 N.B. In all the preceding cases it is necessary to verify 
 that the magnets are correctly placed. For this purpose with 
 the aid of the deflector, replace the card in the natural position 
 of equilibrium, then, after some seconds make a new observation 
 of the normal deflection. It may then be found that it is 
 necessary to make a slight alteration in the position of the 
 magnets. 
 
 (D.) Alteration of the reading by means of the Spheres. 
 PRACTICAL RULES. 
 
 If there are no spheres in position, and it is desired to TO increase 
 increase the reading by means of the spheres, they should be placed, b^mea^s'o? 
 one on each side of the card, at equal distances, from the centre tlie Spheres 
 of the compass, and in such a way that the line which joins their 
 centres is parallel to the direction of the pointer, in the position 
 of normal deflection, which corresponds to the point of observation. 
 
 If the spheres are already in position, and the line joining 
 their centres is parallel to this direction of the pointer, they 
 must be brought nearer, or larger ones must be applied. 
 
 If the spheres are already in position, and the line joining 
 their centres is perpendicular to this direction of the pointer, 
 they must be moved further off, or smaller ones must be applied. 
 
24 Alteration of the reading with the Spheres. CHAP. IT. 
 
 To diminish ^ there are no spheres in position, and it is desired to 
 
 the reading diminish the reading by means of the spheres, place them in such 
 
 by means 
 
 of the a way that the Hne joining there centres may be perpendicular, 
 to the direction of the pointer, in the position of normal deflection 
 which corresponds to this point. 
 
 If the spheres are in position with the line joining their 
 centres, perpendicular to this direction of the pointer, bring them 
 closer or apply larger ones. 
 
 If the spheres are in position with the line joining their 
 centres parallel to this direction of the pointer, move them further 
 off, or apply smaller ones. 
 
 When a Thomson compass is compensated in any of the 
 ports of France, or more generally of Europe, the necessary delay 
 in placing the spheres is diminished by attending to the following 
 remark : 
 
 Each division of the scale of the deflector corresponds to 
 about one degree of deviation. 
 
 If then, it is desired to vary the reading of the deflector 
 by 3, 4 or 5 divisions, by means of a pair of spheres of fixed 
 diameter, each sphere should be placed at the proper distance to 
 correct 3, 4 or 5 degrees of quadrantal deviation. This distance 
 is given at the end of the book. 
 
 It is only by experience that we can acquire quickness in 
 applying the magnets and spheres at the proper distance approxi- 
 mately, and quickness in altering their distance correctly from 
 the card. 
 
 The work of placing them in position can be carried out 
 in several ways. That which we have indicated must only be 
 considered as a guide, intended to facilitate the first experiments. 
 The observer will be able to choose from experience, the oper- 
 ations which are the easiest for himself. The essential, for rapid 
 work, is to go through the operations always in the same way, 
 so as to be almost mechanical, and to practice to obtain the 
 normal deflection, by giving a sharp and sudden check to the card. 
 It is better not to bring the card to this position with a very 
 gradually diminishing velocity or with successive jerks. 
 
CHAP. ii. Graduation of the Deflector. 25 
 
 Lastly, as a final exercise to make on shore, before making 
 the compensation on board, it is advisable to measure the magnetic 
 force of the deflector which corresponds to each division of the 
 scale, taking the earth's horizontal force at the place of ob- 
 servation for the unit of force. 
 
 This graduation of the deflector is not absolutely necessary 
 for the use of the instrument, but it simplifies remarkably the 
 control of the compensation in times of fog, and besides it is one 
 of the most useful exercises which can be made in order to 
 become master of the management of the deflector. 
 
 (E.) Graduation of the Deflector. On shore, in a place 
 free from iron, make the lubber line coincide with the North 
 point of the card. Make sure that the three screws of the base 
 of the deflector have been screwed up together, so that the two 
 parts of the base coincide. 
 
 Prepare a table with four vertical columns. In the first 
 write the divisions of the scale of the deflector as pointed out below, 
 in the second the observed angles as we will now explain, in 
 the third the sines or the reciprocals of the sines of these angles. 
 
 It is most important to verify that the point and cap 
 are in good order, as on this the accuracy of the observations 
 depend. Change them if it be necessary. Be sure that the 
 card is well centred in the bowl, and that it can turn com- 
 pletely round without sticking on any point. 
 
 This done and the deflector being at the division 0, 
 place the pointer over the E. by N. and proceed as for an 
 observation of normal deflection. Only, here, the deflector will 
 be too weak to obtain a deflection of 90, and when the card 
 is in equilibrium under the opposed influences of the earth and 
 deflector, with the pointer over the E. by N., the North and 
 South line will make with its original position, that is, with 
 the lubber line, an angle of 39 for example, in the particular 
 case we are examining. Put 39 opposite to in one table. 
 
 Then increase successively the reading of the deflector 
 by two divisions, repeating the same observations, and note each 
 time opposite the division the angle of deflection which it 
 produces. We will thus come to the division 14, which will 
 
26 
 
 Graduation of the Deflector. 
 
 CHAP. II. 
 
 give a deflection of 76 '5. If we proceed to the division 16 of 
 the deflector we shall find that it is too strong, and that the 
 card passes the normal deflection. By diminishing it properly 
 we shall see that the division 15*2 will be sufficient to give the 
 normal deflection of 90. Opposite to each of the angles of deflec- 
 tion obtained place the value of its natural sine. 
 
 Each of these sines represents the force of the deflector for 
 the corresponding division of the scale, taking as the unit the 
 earth's horizontal force at the place of observation. 
 
 Now make the reading of the deflector 17. It will be 
 too strong, that is to say, the card will pass the position of nor- 
 mal deflection when the pointer is kept over the E. by N. of 
 the deviated card. In order to stop the card in equilibrium at 
 the normal deflection of 90 the pointer must be turned towards 
 the North, and placed over the division N. 76 E. 
 
 It will then make an angle of 76 with the North and 
 South line, This angle is entered opposite the division 17. 
 
 The same observation is made for the divisions 20, 23, 
 27; 31, 35, and the corresponding angle made by the pointer 
 with the North and South line is entered opposite to each of 
 them. The reciprocal of the natural sine of each of these angles 
 is entered in Col. III. opposite to it. Each of these numbers 
 represents the force of the deflector for the corresponding divi- 
 sion of the scale, taking the same unit of force as above. 
 
 We thus obtain the following table 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 
 
 FORCES. 
 
 FORCES. 
 
 Divisions of 
 the Scale. 
 
 Observed Deflections. 
 
 Taking H at the place 
 of observation for the 
 
 Taking the same unit 
 as that of the Chart 
 
 
 
 unit. 
 
 Plate I. 
 
 
 
 39 
 
 sine 0*62 
 
 076 
 
 2 
 
 43 
 
 0-68 
 
 0-83 
 
 4 
 
 47 
 
 0-73 
 
 0-89 
 
 6 
 
 51 
 
 0-77 
 
 0-94 
 
 8 
 
 56 
 
 0-83 
 
 1-02 
 
 10 
 
 62 
 
 0-88 
 
 1-08 
 
 12 
 
 67. 5 
 
 0-92 
 
 1-13 
 
 14 
 
 76. 5 
 
 0'97 
 
 1-19 
 
 15-2 
 
 90 
 
 1-00 
 
 1-23 
 
 17 
 20 
 
 pointer 76 
 66 -5 
 
 sine 1-03 
 1-09 
 
 26 
 34 
 
 23 
 
 61 
 
 1-14 
 
 40 
 
 27 
 
 58 
 
 1-18 
 
 45 
 
 31 
 
 56 
 
 1-21 
 
 49 
 
 35 
 
 55 
 
 1-22 
 
 50 
 
CHAP. II. Graduation of the Deflector. 27 
 
 The numbers contained in Col. III. represent the forces 
 of the deflector which correspond to the different divisions of 
 the scale when the horizontal force at the place of observation, 
 called H is taken as the unit. 
 
 If it is desired to have the numbers which correspond to the 
 same forces when the unit of force is that taken as unity for the 
 chart of horizontal forces, the numbers in the third column 
 must be multiplied by the numerical value of H given on the 
 chart. 
 
 If we suppose the observations to have been made at 
 Toulon, where H=1'23, all the numbers in Col. III. must be 
 multiplied by T23. and we thus obtain the numbers given in 
 Col. IV. 
 
 Lastly if we wish to have the same forces expressed 
 by taking for the unit the horizontal force corresponding to 
 some other place of observation, and when the numerical 
 value H' is given on the chart, it is sufficient to divide all 
 the numbers in Col. IV. by H', or to multiply them by the 
 reciprocal of this number. The value of this reciprocal is given 
 on the margin of plate I. 
 
 This graduation only applies to the particular instru- 
 ment, and compass, with which it has been obtained. The 
 observer may consider himself sufficiently exercised when, in 
 several succeeding determinations of one division, made with 
 a compass in good order, he does not find a greater difference 
 than 0'015 between the extreme numbers. 
 
 To correct the inevitable errors of observation when they 
 are small, and to detect them when they are large it is advisable 
 to make a curve combining all the observations. The best way 
 of doing this is to take squared paper on which a horizontal line 
 with its divisions will represent the scale of the deflector. The 
 values of the corresponding forces will be represented on the vertical 
 lines springing from the different divisions. Let us suppose for 
 example that each division of the paper represents one- tenth of 
 the earth's horizontal force at the place of observation. In order 
 not to extend the curve too much vertically we may suppose that the 
 horizontal line of the divisions represents the force 0'60 and over 
 
28 Graduation of the Deflector. CHAP. n. 
 
 each division place the amount by which the corresponding force 
 exceeds 0'60. This curve allows us to complete very accurately 
 the table for each of the divisions of the scale. This is convenient 
 for the exceptional cases of compensation. 
 
 N.B. As the magnetic intensity of the magnets of the 
 deflector and that of the needles of the card may vary in time, it 
 is necessary to verify occasionally the accuracy of the graduation 
 by a new set of observations, and to make a new graduation if 
 necessary. Only three observations are required for this, in any 
 particular place, when the numbers which express the force of each 
 division, taking the earth's horizontal force at the place as the unit, 
 have previously been deduced from Col. IV. 
 
 We may ascertain also whether the change in the graduation 
 depends on the deflector or on the card. It is sufficient to have 
 noted on shore at the time of the first graduation, the period of 
 oscillation of the card ; when this period remains the same in the 
 same place with the same value for the earth's horizontal force, it 
 shows that the magnetic intensity of the needles of the card has 
 not altered. 
 
 Defect in the The va l ue f ^ e f rce corresponding to each division of 
 
 proportion- -Q ie deflector, shows us again one of the causes of the successive 
 
 ality of the 
 
 forces to the trials which must be made when using this instrument for placing 
 * nS> the compensators in position. If in fact, we have observed on 
 one cardinal point the reading 35, and on the opposite cardinal 
 point the reading 0. According to the practical rules, we set the 
 deflector at the division 17'5 to give a mean force between the two 
 observed forces, but the graduation shows that the mean of the two 
 forces 0'62 and 1*22, being 0'92 corresponds to the division 12 and 
 not to the division 17'5. 
 
 Again, if we observe on one point the reading and on the 
 opposite point the reading 20, the practical rules say, to set the 
 deflector at the division 10, while in reality the mean between the 
 two observed forces 0'62 and 1-09 being 0'85 corresponds to the 
 division 9 and not to the division 10. 
 
 It is thus seen that the defect in the proportionality of the 
 forces to the divisions is much greater, when there is a greater 
 difference between the two forces which have to be equalized 
 
CHAR ii. Advantages of Graduation. 29 
 
 We are not troubled with this defect at first, because the difference 
 of readings is not much greater than 15 or 16 divisions in ordinary 
 cases and within these limits the proportionality is very nearly 
 rigorous. "When the difference between the two readings exceeds 
 this limit in the exceptional cases it proves that the deviations are 
 very great and that in consequence the observations are taken on 
 points very far removed from the magnetic points on which the 
 observations should be made. The inevitable error proceeding from 
 the substitution of the points by compass, for the magnetic points 
 is combined with the defect in the proportionality and gives rise 
 to errors possibly more considerable which can be annulled by 
 successive trials only. 
 
 If the divisions of the scale of the moveable magnets of 
 the deflector were determined by calculation, an exact proportion- 
 ality might be arrived at, but it is evident why it is unnecessary to 
 attempt this. It would not do away with the successive trials, it 
 would only diminish them in some particular cases, a benefit which 
 would be too dearly bought by a complication of the instrument. 
 
 The graduation of the deflector has numerous advantages. Advantages of 
 1st. It gives at once in terms of the earth's force, the estimate of tion of the 
 the mean directive force (or very nearly so) which acts on the com- Deflector - 
 pass on board after the compensation. 
 
 2nd. It allows of an exact enough calculation of the values 
 of the different co-efficients of the deviation which exist after an 
 imperfect compensation. ; ,; 
 
 3rd. In the exceptional cases where the co-efficient E (see 
 Traite de regulation) has a greater value than 2, it allows of the 
 calculation and the compensation of this co-efficient, in a sufficiently 
 exact way to leave it with a value comparable with those left after 
 the compensation of the other co-efficients. 
 
 4th. It gives all the elements for the compensation of the 
 most important part of the error due to heel and that for all regions 
 of the earth. 
 
 5th. Lastly it remarkably simplifies the control of the com- 
 pensation in the time of fog. 
 
 PRELIMINARY EXAMINATION OF THE DEFLECTOR. Employment 
 
 The deflector is designed to measure the differences which ^ theTeetT 
 exist between the directive forces, on different points. If there was and of the 
 
 additional 
 magnets. 
 
30 Preliminary examination of the Deflector. CHAP. u. 
 
 a strict proportionality between the divisions, and the forces which 
 they represent, the instrument would be most convenient when 
 the mean of the extreme forces of the deflector corres- 
 ponds to a division, approaching closely to the mean division, 
 that is 17*5. For various reasons, this proportionality does not 
 exist, but it is nevertheless essential that the readings correspond- 
 ing to the different heads, should be completely contained within 
 the limits of the scale, in order that the use of the instrument may 
 be truly convenient, and give the results rapidly. 
 
 This is more likely to occur when a very convenient 
 connection exists between the magnetic force of the card, and the 
 deflector. This connection is attained when on shore, in a place 
 free from iron, the normal deflection is obtained with the 
 deflector reading between 13 and 16. 
 
 In fact the mean directive force on board, of a compass well 
 placed, is generally from O85 to O90 of the earth's horizontal force 
 on shore. The result of this is that the reading which corresponds 
 to this mean force will then fall between the divisions 10 and 12. 
 From the table of graduation of the deflector, it will be seen that 
 this is the precise part of the scale, which gives the mean between 
 the two extreme forces of the deflector. 
 
 When now, in the preliminary observations made on shore, 
 it is found that the reading corresponding to the normal deflection 
 is not between 1.3 and 16, the screws of the framework being 
 tightened so that the two parts of the base coincide, it is advisable 
 at first to make the reading come between these limits. This is done 
 either by means of the screws of the framework, which allow of 
 raising the magnets of the deflector, and in consequence of diminish- 
 ing their power on the card, or by means of the additional magnets 
 which can be placed in the grooves of the base prepared for them 
 and which increase or diminish by a constant quantity, the power, 
 of the deflector according as their poles are similar or contrary to 
 those of the magnets of the deflector. 
 
 But, notwithstanding this preliminary adjustment of the 
 deflector, it may be that in difficult or exceptional cases of com- 
 pensation (see case II. and case III. p. 44 & 46) on certain points, the 
 reading corresponding to the normal deflection, goes beyond the 
 
CHAP. ii. Additional Magnets. 31 
 
 limits of the scale. This circumstance does not render the compen- 
 sation impossible, but it may sensibly lengthen it. This inconvenience 
 can be avoided by acting in the following manner. 
 
 When this occurs on the first two cardinal points, place at 
 once, without waiting for further observations, corrector magnets in 
 the proper way, so as to bring the reading within the divisions 
 nearest to the end of the scale, which has been passed. This 
 preliminary placing in position of the corrector magnets is frequently 
 sufficient to bring all the following readings within the limits of 
 the scale. But, when, notwithstanding that, on the third or fourth 
 cardinal point, the reading is still beyond the scale, the position of 
 the corrector magnets must be altered by making an arbitrary 
 estimate, more or less inaccurate of the reading, which would be 
 found for the normal deflection, if the scale were further extended. 
 
 *ADDITIONAL MAGNETS. This estimate, if it is very in- 
 accurate may considerably lengthen the operation. The necessity 
 to do this may be avoided by having at hand a set of additional 
 magnets, graduated beforehand, the magnetic forces of which should 
 be arranged as we will now explain, and which may be placed in 
 position in a convenient way in the grooves of the base. 
 
 The force of the deflector is increased or diminished by means 
 of additional magnets, in such a way, that the reading remains within 
 the limits of the scale. The number on the additional magnets 
 used is noted along with the reading found. 
 
 This number is nothing but the force of the magnet expressed 
 in tenths and hundreths of the earth's force ; the unit being the 
 same as that of the chart. It is written in white on the magnets. 
 The force of the magnets is added to, or subtracted from, the force 
 corresponding to the reading of the deflector, expressed in the same 
 unit, (that is the force given in Col. IV. of the table) according as the 
 poles of the magnet are similar or contrary to those of the deflector. 
 This must also be noted. 
 
 The result thus obtained is compared with the correspond- 
 ing force when the ship is on the opposite cardinal point of the card. 
 The mean of the two forces is taken. It is seen whether this 
 
 * All this relating to additional magnets may be passed over at first. 
 
32 Numerical Examples. CHAP. n. 
 
 mean m comes within the limits of the scale of the deflector. If it 
 does not, an additional magnet is placed properly in the grooves of the 
 deflector, and the index of the deflector is set in such a way that the 
 sum or difference, according to circumstances of the forces of the 
 deflector, and the additional magnets may be equal to m, the mean 
 force found. This done, alter the corrector magnets, or the spheres, 
 so as to obtain the normal deflection, with the index thus fixed. 
 
 Numerical Examples. A. With the head North, the 
 deflector set at zero is found too strong to obtain the normal deflec- 
 tion. Corrector magnets are placed with their poles contrary to 
 those of the Deflector, in order to obtain the normal deflection with 
 the reading 1. 
 
 With the head South, the deflector set at 35 is too weak to 
 obtain the normal deflection. 
 
 The smallest of the additional magnets, that marked 0*20 
 for example, is now placed in the groove of the deflector with the 
 poles similar to those of the deflector. The normal deflection is 
 now obtained with the deflector at 23. 
 
 The force at the North corresponding to the division I. is 
 from Col. IV., page 26, equal to 0-80. 
 
 The force at South is equal to the force corresponding to 
 division 23 which is 1-40, together with 0'20 the force corresponding 
 to the small magnet, equal to 1/60 altogether. 
 
 The sum of the forces at North and South is thus 2'40, and 
 the mean 1/2 which corresponds to the reading 14' 8. The additional 
 magnet is now taken away, the index of the deflector set at 
 14*8 and the fore-and-aft magnets placed so as to obtain the normal 
 deflection with this reading of the deflector. 
 
 B. If, in another case, we have found that the mean force 
 at the North and South is from the calculation 1/85, we should 
 remove the magnet - 20 and replace it by the additional magnet 
 0'40. Now place the index at the division corresponding to 1/85 
 0-40 = 1*45 that is the division 27 ; and we have only to introduce 
 and place the corrector magnets so as to obtain the normal deflection 
 with this reading. 
 
 It is only in very exceptional cases that this small compli- 
 cation is introduced into the method. In the great majority of 
 
CHAP. ii. Graduation of additional magnets. 33 
 
 cases we may not desire to use it and may prefer an additional 
 turn of the ship, to these calculations and the placing of proper 
 additional magnets, although both are very simple. 
 
 Each observer can follow in this respect the method which 
 appears to him most convenient and certain. The second method 
 which consists in taking not the mean of the readings but the 
 mean of the forces they represent, may shorten considerably the 
 compensation in these exceptional cases ; to put it in practice it is 
 only necessary to have a set of additional magnets properly 
 graduated. 
 
 With each deflector at present, there is only one set, con- 
 sisting of two small additional magnets of the same length and the 
 same diameter, 5 centimetres long and 3 millimetres in diameter 
 Each of them varies the power of the deflector by about eight-tenths 
 of the unit of force on the chart. We think that with the great 
 variety of types of iron ships actually afloat, this single set is not 
 sufficient and that two others should be added. 
 
 Each of the magnets of the weakest pair should be made 
 to vary the force of the deflector by two to three-tenths at most. 
 Each of the magnets of the intermediate pair should be made 
 to vary the force of the deflector by four to five-tenths at most. 
 And one of the magnets of the strongest pair should be made to 
 vary the force of the deflector by six to eight-tenths. 
 
 The different combinations of these magnets would be 
 applicable to the most difficult and exceptional cases in practice 
 and would considerably shorten the operations and prevent the 
 time occupied exceeding two hours and a half in any case. 
 
 As soon as the observations for which they are necessary are 
 completed, it is advisable to remove the additional magnets from the 
 grooves of the framework and to place them side by side in their 
 special receptacle with their poles reversed. 
 
 One single observation or better two, the second for a check Graduation of 
 on the first, is sufficient to graduate an additional magnet. onal mag 
 
 nets. 
 
 Example. On shore in a place free from iron, (the same to 
 which the table page 26 corresponds,) the additional magnet which 
 
3i Graduation of additional magnets. CHAP. n. 
 
 is to be graduated is placed in the groove of the framework, with 
 the ends similar to those of the deflector. Now make the observation 
 for normal deflection ; let 6 be the division which corresponds to the 
 normal deflection. 
 
 This division corresponds to 0'94 of the unit of force in 
 plate I. 
 
 Previously the normal deflection was obtained, without the 
 additional magnet, with ike reading 15'2. corresponding to the force 
 1'23. Hence the smallest additional magnet must be 1*23 0'94 
 or - 29. It is this number which is inscribed on the additional 
 magnet. It will increase or diminish the force of the deflector 
 by this constant quantity, according as its poles are similar or 
 contrary to those ol the deflector. 
 
 Taking the same unit as that of the chart, these magnets 
 and their graduation, have another advantage. 
 
 When from some reason of fitting out or new loading, it is 
 required to make or to correct the compensation in a part of the globe 
 where the horizontal force, IT, has a very different value from that 
 which it had at the port of departure, sufficient additional magnets 
 are placed at once in the grooves of the deflector, to maintain the 
 reading for the normal deflection corresponding to this force H 
 between the divisions 13 and 1 6 of the scale. 
 
 For example, if the work is done at a place where H=1'60 
 the small extra magnet marked just now 0-29 is placed in position 
 with the poles, in the same direction as those of the deflector ; 
 there will thus be every chance that all the readings will now fall 
 within the limits of the scale. It is only necessary to think of the 
 mean of the readings without being obliged to have recourse to the 
 forces which they represent, which is more complicated. 
 
 Diminishing ^Y turning each of the three screws, one complete turn in 
 
 the power ^e same direction, the deflector is raised a millimetre or so from 
 
 of the Defl- 
 ector with ^he glass, and its action on the card is thus diminished by a constant 
 
 S quantity. The screw has made a complete turn, when the arrow 
 engraved on its head returns to the same direction. Before each 
 observation, it is necessary that the plane of the poles of the 
 
CHAP. II. The use of the screws of the base. 85 
 
 magnets of the deflector should be quite parallel to the glass of the 
 bowl, and for this it is necessary to make sure that the three screws 
 have been turned through the same number of complete turns. 
 Graduating anew the deflector when the screws of the feet have made 
 five complete turns, and it will be seen in the particular example to 
 which the table of graduation fits, that each of the first five turns of the 
 screw diminishes the force of the deflector, by about three hundreths 
 of its value. If we graduate the deflector again, when the 
 screws have each made ten complete turns, we will ascertain that 
 each turn between 5 and 10 diminishes the force of the deflector 
 by about two and a half hundredths of its value. Lastly, if we 
 again make the graduation when the three screws have made 
 fifteen turns, we ascertain that each of the last five turns diminish 
 on an average, the force of the deflector by two hundredths of its 
 value. 
 
 Thus the fifteen complete turns diminish the force of the 
 deflector by about thirty-seven-hundredths of the original value. 
 
 One single observation of the normal deflection is sufficient 
 in each of the three given positions of the screws, to give the 
 corresponding quantity, by which the deflector is diminished. In 
 each case, the division is found which gives the normal deflection, 
 with the pointer over the E. by N. of the deviated card. In this 
 position of the screws, the reading for normal deflection corresponds 
 to the force 1 of the deflector, the horizontal force at the place being 
 the unit. The difference between the two forces which correspond 
 to the same division of the scale, but at two different positions of 
 the screws of the base, gives the quantity by which the value of the 
 deflector is diminished. It would be well if the maker would perfect 
 this instrument by adding to each screw an arrangement, which 
 would show at once the number of turns which had been given to it. 
 
 When, having raised the deflector as much as possible by 
 means of the screws, it is still too strong to allow of the directive forces 
 being observed remaining within the limits of the scale, proper extra 
 magnets must be placed in the grooves of the base, with their poles 
 contrary to those of the deflector. 
 
 We repeat again, that in the great majority of cases it is not 
 necessary to be troubled with these slight complications. We 
 
36 Conclusion. CHAP. II. 
 
 have only mentioned them to allow of all the difficulties which may 
 occur in exceptional cases in practice, being overcome. 
 
 Conclusion. The deflector, as at present constructed, is an 
 excellent and practical instrument. We would in the meanwhile 
 wish to see the three following improvements carried out. 
 
 1. An indicator for the number of turns given successively 
 to the screw. 
 
 2. Three sets of extra magnets, instead of one. 
 
 3. Lastly, and the most important of all, the small increase 
 of about one tenth of the total force of the four fixed magnets, on 
 the moveable parts. In this way, by reducing a little the distance 
 which actually exists between the poles of these magnets, when the 
 deflector is at zero, the scale of the deflector would have an extended 
 range beyond the actual limits of the scale. The number of 
 ships or of compasses which would be found in the exceptional 
 cases of compensation, would be still further reduced. 
 
 We will show the application of the preceding rules in 
 three particular cases, types of all those which may occur in 
 practice. Besides it is unnecessary to be troubled to know which 
 case occurs in practice. The readings of the deflector will show 
 without any ambiguity, and in consequence without allowing of any 
 uncertainty in the necessary operations. 
 
CHAP. in. Compensation in Practice. 37 
 
 CHAPTEE III. 
 
 COMPENSATION IN PRACTICE. GENERAL REMARKS. 
 
 1. Preliminary examination of the compass. 
 
 (a.) The accuracy of the compensation depends above all 
 things, on the cap and point being in good order. It is therefore 
 necessary to commence by making an attentive and minute exami- 
 nation of these two parts with a magnifying glass. They should 
 be changed if a scratch or crack is perceived on their surface. 
 
 (6.) Afterwards it must be ascertained that the card is pro- 
 perly centred in the bowl, that is to say, that it can make a complete 
 turn of 360 degrees without rubbing at any part, on the casing 
 which surrounds it. 
 
 (c.) To have an idea of the accuracy of the indications it 
 is advisable to determine that which is called the frictional error. 
 To do this the bowl and card are taken on shore to a place free 
 from iron and the lubber line is made to coincide with the North 
 and South line of the card. Then the card is deflected repeatedly 
 from its position of equilibrium by means of an auxiliary magnet or 
 another card. Care should be taken to apply the disturbing magnet 
 in the same plane as the needles, to remove it afterwards in the 
 same plane, in such a way that the card may not have any oscilla- 
 tion in a vertical direction, but only turn in a horizontal 
 plane. The card is deflected to different angles between 30 
 and 1 or 2 degrees, first on one side, then on the other ; two at 
 least of the deflections should be less than 5 degrees. After each 
 deflection the card is allowed to return freely to its position of 
 equilibrium and the degree opposite to the lubber line noted 
 when the card comes to rest. The distance between the two 
 positions most distant from one another when the card is at rest 
 s erves to measure the error due to friction. The compass is par- 
 ticularly good when this error is very small. For the compass to 
 be considered good this error should not exceed one degree. 
 
 (d.) Compass cards behave better in rolling, other things 
 being equal, when the period of oscillation is great. This time of 
 
38 General Remarks. CHAP. in. 
 
 going from one side to the other, should be fourteen or fifteen 
 seconds at least, and better, eighteen or twenty seconds. 
 
 2. The Ship. 
 
 The accuracy of the compensation is greater when the 
 magnetic condition of the ship is more nearly in equilibrium. 
 
 The compensation gives better and more exact results when 
 the previous history of the ship is considered. In this respect, it is 
 better not to proceed with the compensation immediately after the 
 ship leaves the dock, or any other position in which it has been 
 kept with its head in the same direction for many days. This rule 
 should be more strictly observed when the ship is new and contains 
 large masses of iron, when the same direction of the ship's head 
 has been maintained for a long time and when that direction 
 approaches near to the magnetic East or West. 
 
 Tt is advisable then, if it is possible to wait until the ship 
 has been at anchor in a roadstead and has made several turns in 
 both directions under the influence of wind and sea, before pro- 
 ceeding with the compensation. When time is so pressing that 
 such delay cannot be allowed, before proceeding to the compen- 
 sation and while the ship is having a trial of the machinery she 
 should be made to take several complete turns alternately to 
 port and starboard. Two turns at least, one to port and the other 
 to starboard, are necessary. 
 
 In these conditions an accurate compensation can now be 
 obtained. When it is made under the most favourable conditions, 
 a good observer should not leave a greater error than three degrees 
 on any point of the compass. 
 
 If it is necessary to do the work hastily, or in less favour- 
 able circumstances as regards weather, the greatest error on any 
 point may amount to as much as four degrees. The newer the 
 vessel is the more essential is it to attend to every possible precau- 
 tion to ensure the accuracy of the compensation. 
 
 3. The Weather. 
 
 The weather should be fine, the sea calm, the trim sufficiently 
 accurate so that the ship may be considered on an even keel during 
 the whole time of the observations. On any point whatever, the 
 
CHAP. in. General Remarks. 39 
 
 final observation, which is used for placing the magnets (whether of 
 deviation if the work is carried out by bearings, or of directive 
 force, if without bearings) must not be made without ascertaining 
 that the ship's head has not altered in direction by more than four 
 or five degrees after having kept her on the same course for four or 
 five minutes. 
 
 The ship should be placed as correctly as possible on the 
 different points, and should be steered as straight as possible, by 
 means of another compass placed 8 feet or more from the compass 
 to be compensated. In all cases the greatest care should be taken 
 to see that the ship does not get off her course by more than 
 four or five degrees while waiting for the observation, and to steer 
 very straight at the time the observation is being made. When 
 these instructions have not been carried out the observation must 
 be made over again. 
 
 When the work is done without bearings, as soon as the 
 normal deflection has been obtained, the card must be returned 
 to its original position, with the assistance of the deflector (in 
 order to make sure that the ship's head has not changed during 
 the observations) and the latter raised vertically above the card. 
 When it is sufficiently high to have no influence on the card, it 
 is taken away horizontally to a considerable distance (6 feet or 
 so) from the card, and the latter is allowed to come freely to rest. 
 If the ship's head as shown by it now differs by more than four 
 or five degrees from what it was before, the observation for the 
 normal deflection must be repeated. 
 
 The ship's head should be placed successfully on the four 
 cardinal points by the compass to be compensated. To fix the 
 ideas, suppose we start with the ship's head north, and that the 
 ship swings to starboard. 
 
 FIEST OR GENERAL CASE. 
 
 This is the one which occurs in almost all Merchant ships, 
 and in the great majority of ships of war for the Azimuth compass 
 or for the bridge compass properly placed. We mean henceforth 
 by this expression a compass placed in the central third of the 
 length of the ship, and with its axis placed in the fore-and-aft 
 plane. It is necessary also that the iron on the two sides should be 
 
40 Practical Rules. 
 
 CHAP. III. 
 
 symmetrical and sensibly equal, and lastly that there should not 
 be any very large masses of iron in the immediate neighbourhood 
 of the compass. 
 
 For such a compass the difference of the readings to be 
 equalized will not exceed eight or ten divisions, if the readings 
 fall in the first half of the scale ; 12 or 15 divisions if they fall 
 in the upper half. In this case it is sufficient, in order to carry out 
 the compensation to within 2 or 3 degrees, to place the ship 
 successively on the four cardinal points, and as a check to observe 
 the normal deflection on three quadrantal points. 
 
 PRACTICAL RULES. 
 
 Placing the With the ship's head North or South the fore-and-aft 
 
 ma g n et S are used. 
 
 With the ship's head East or West the thwartship magnets 
 are used. 
 
 When the reading of the deflector is to be increased, if 
 there are no magnets in position, place them with their poles set 
 in the opposite direction to those of the deflector in the position 
 of normal deflection corresponding to the ship's head for the 
 observation. 
 
 If there are magnets in position, bring them nearer, if their 
 poles are set in the opposite direction to those of the deflector, in 
 the position of normal deflection. Remove them farther off if their 
 poles are set similarly to those of the deflector in the position of 
 normal deflection. 
 
 When the reading is to be diminished, if there are no magnets 
 in position, place them with their poles set in the same direction 
 as those of the deflector in the position of normal deflection. 
 
 If magnets are in position, bring them nearer, if their poles 
 are similarly set to those of the deflector in the position of 
 normal deflection. Remove them farther off, on the contrary, if 
 their poles are set in the opposite direction to those of the deflec- 
 tor in the position of normal deflection. 
 
 1 Ships head North by compass. Make the observation 
 for normal deflection, suppose the corresponding reading to be 
 20'2. Return the card with the help of the deflector to its 
 
CHAP. in. Compensation in most general case. 41 
 
 original position ; then take the latter away, and satisfy yourself 
 that the ship's head has remained within 4 or 5 degrees of the 
 same direction during the time of observation. 
 
 2. Ship's head East by compass. Make the observation 
 for normal deflection. Let the reading corresponding be 8'4. 
 Return the card to its original position with the help of the 
 deflector, and verify that the ship's head has not changed. 
 
 3. Ship's head South by compass. Make the observation 
 for normal deflection. Let the reading be 14 '8. Return the card 
 to its original position, &c., as before. 
 
 The reading found with the ship's head North was 20'2. 
 
 The reading found with the ship's head South was 14 '8. 
 
 The sum of the two readings is 35. 
 And the Mean 17' 5. 
 
 By means of the screw, set the index at 17*5. Place the 
 deflector on the compass bowl with the pointer over the North. 
 Now, keeping the ship as exactly as possible in the same direction 
 by means of the auxiliary compass, place the fore-and-aft corrector 
 magnets in such a way as to obtain the normal deflection with 
 the reading 17'5. 
 
 The deflector reading has been increased, and there are no 
 magnets in position, therefore they must be placed with their 
 poles in the opposite direction to those of the deflector. The 
 magnets are brought nearer until the normal deflection is obtained. 
 They are then fixed in the position they occupy. 
 
 Make a second observation for the normal deflection to 
 make sure of the accuracy of the position of the magnets. Alter 
 the position if necessary. Then note the position of the magnets. 
 
 4. Ship's head West by compass. Make the observation 
 for normal deflection. Let it be 12 6. Return the card to its 
 original position as before. 
 
 The reading with ship's head East was 8*4. 
 
 The reading with ship's head West was 12'6. '..-v ; 
 
 The Sum is 21'0 
 And the Mean 10 '5 
 
 Set the index of the deflector at 10'5. Place the deflector 
 on the bowl with the pointer over the North of the card. Now, 
 
42 Placing the spheres in position. CHAP. in. 
 
 keeping the ship's head as accurately as possible in the same 
 position, place the thwartship corrector magnets so as to obtain 
 the normal deflection with the reading 10'5. The reading of the 
 deflector has been diminished, and there are no magnets in position, 
 they must therefore be placed with their poles set in the same 
 direction as those of the deflector in the position for normal 
 deflection. Place the magnets at the proper distance and fix them. 
 Return the card to its original position, and ascertain that the 
 direction of the ship's head has not changed. 
 
 Make a second observation for normal deflection to verify 
 that the magnets have been accurately placed. Alter the position 
 if necessary, and note the position of the magnets. 
 
 Placing the The mean of the reading for the North and South, which 
 
 position we will call the common reading for these two points, is 17'5. 
 
 The common reading for the East and West is 10'5. The 
 sum of these two readings is 28, and the mean 14. Set the index 
 of the deflector at 14, and place the deflector on the bowl. Now, 
 keeping the ship's head as accurately as possible on the West 
 point of the compass, place the spheres so as to obtain the normal 
 deflection with the reading 14. 
 
 In this case the reading has been increased, the spheres 
 must therefore be placed so that the line joining their centres 
 coincides with the direction of the pointer in the position of normal 
 deflection, that is athwartship. Fix the spheres at the proper 
 distance. Return the card to its original position. Make a second 
 observation of normal deflection to verify the accuracy of the 
 position, alter it if necessary, and note the position of the spheres. 
 
 Before leaving the West Point, it is advisable to make the 
 observations necessary for the compensation of the heeling error, 
 (see p. 54). 
 
 After the preceding operations, the horizontal compensa- 
 tion is finished in the great majority of cases. It is verified in 
 the following way. 
 
 Place the ship's head successively S.W., N.W., N. and N.E. 
 by the compass. On each of these courses note the reading 
 corresponding to the normal deflection. 
 
CHAP. in. Accuracy of the Compensation. 43 
 
 Theoretically, if the compensation has been properly made, 
 these four readings should be identical with the reading obtained 
 on the last cardinal point, after having placed the spheres. But 
 practically, we must not expect that an inexperienced observer will 
 be able to measure the directive force of the compass with the 
 deflector to a closer approximation than one and a half per cent 
 of the value of the earth's horizontal force. The table of gradua- 
 tion shows that five divisions of the disc in the lower part of the 
 scale and six divisions in the upper part, correspond to one and 
 a half per cent, of this force. We may consider, therefore, 
 that the readings are nearly enough equal to one another, when 
 the differences, in the different parts of the scale, are within these 
 limits. 
 
 If then, the differences of the five readings indicated above 
 are comprised within these limits (and this is the case in general) 
 the compensation may be considered well done, and the deviation 
 reduced to 2 or 3 degrees in amount. 
 
 A practised observer, working in very fine weather, can 
 obtain a much closer approximation, that is to say, the equality 
 of the readings to within two or three divisions of the disc in the 
 lower part of the scale, and within 4 or 5 divisions in the upper 
 part. 
 
 If it has been possible to carry out the*" preceding opera- 
 tions with strict accuracy, if above all the retardation of magnetic 
 induction in the iron of the ship does not introduce an almost 
 inevitable error, particularly on board ships constructed com- 
 pletely of iron as in our time, the deviation will be constant on 
 all points and will not exceed two degrees. Unfortunately the 
 magnetic condition of an iron ship varies in a very complex 
 manner, and when combined with all the inevitable errors of 
 observation, we can only say that the compensation reduces the 
 deviation to a very small amount, 2 to 3 degrees, which is com- 
 posed of two parts, one constant, the other variable. The latter 
 does not exceed 1 or 2 degrees in compensations properly made. 
 
 When by means of good Astronomical observations, the 
 value of this constant part has been determined, and it has been 
 ascertained by several observations that it does not change with 
 
44 Second Case. CHAP. in. 
 
 time, we can, after correcting the indications of the compass by 
 this amount, navigate to within 2 degrees. But even when this 
 determination has not been made, or when the magnetic condition 
 of the ship is shown to be variable so that the constancy of this 
 quantity cannot be counted upon, nevertheless we may rest 
 assured that, in time of fog, we can know the course to within 
 three degrees, and navigate with all security except in approach- 
 ing a dangerous coast. 
 
 This constant quantity A is determined approximately by 
 observing the deviations in the same place on four cardinal points 
 or on the eight principal points of the card. The sum of the 
 deviations is taken, and A is obtained by dividing this number 
 in the first case by 4, and in the second case by 8. (For further 
 information see " Traite de la Regulation.") 
 
 It is only by astronomical observations, carefully made, 
 and by verifying the indications of a good compass, on each new 
 course, that it is possible to navigate to within one degree of error. 
 
 SECOND CASE. 
 
 The axis of the compass is still in the fore-and-aft plane 
 of the ship. The masses of iron round about it are also quite 
 symmetrical and sensibly equal on both sides, but the deviations 
 of the compass without compensators are large and exceed 15 
 degrees. 
 
 We are aware that we are dealing with the second case, 
 cither because the differences of the successive readings which we 
 have been obliged to correct on the four cardinal points exceed 
 the limits indicated above, or because, after placing the spheres 
 at West, the readings found on S.W., on N.W., then on N.E., 
 differ between themselves, and from the last reading obtained on 
 West by more than half a division of the scale. In this case a 
 second turn of the ship is necessary. 
 
 To fix the ideas suppose that for normal deflection 
 
 With ship's head North the reading is 35. 
 
 With ship's head East the reading is 0'5. 
 
 With ship's head South the reading is 5. 
 
 With ship's head West the reading is 13. 
 
CHAP. III. Second Case. 45 
 
 The mean of the two readings on North and South being 
 20, the fore-and-aft magnets are placed so as to obtain the normal 
 deflection with the reading 20. 
 
 The mean of the two readings on East and West is 67, 
 and the thwartship magnets are placed so as to obtain the normal 
 deflection with the reading 67. 
 
 The mean of the readings on North and South is 20. 
 The mean of the readings on East and West is 67. 
 The sum is 267 and the mean 13'3. 
 
 The deflector is set at this reading of 13 '3, and the spheres 
 adjusted so as to obtain the normal deflection. 
 
 After this the ship's head is brought to S.W. and it is 
 found that the reading which gives the normal deflection is 11. 
 
 With the ship's head N.W. the reading for the normal 
 deflection is found to be 14. Each of these two readings indicate 
 by themselves that it is necessary to make a second turn with 
 the ship because they differ from the last reading 13 '3, obtained 
 after fixing the compensators, by more than half a division. 
 
 Now place the ship's head North and suppose we find that 
 the reading for normal deflection is 15. The last reading obtained 
 on the South is by hypothesis 13'3. The mean of 13'3 and 15 
 is 141. Set the index at 14'1 and alter the fore-and aft magnets 
 so as to obtain the normal deflection with this reading. 
 
 Now put the ship's head East and suppose the reading 
 which gives the normal deflection is found to be 10. This added 
 to the last reading on West is 23'3, and the mean is 11 '6. Set the 
 deflector to this reading and alter the magnets so as to obtain the 
 normal deflection with the reading 11 '6. 
 
 Now the ship's head is brought to South. Let 10*8 be the 
 reading which gives normal deflection. The last reading found 
 on North was 14*1. The mean of these two readings is 12'5. Set 
 the deflector to 12 -5 and alter the fore-and-aft magnets so as to 
 obtain the normal deflection with this reading. 
 
 Now put the ship's head West. Let 10 be the reading 
 found to give normal deflection. The mean of this reading and 
 
46 Exceptional Case. CHAP. in. 
 
 that found on East is 10*8. Set the deflector to 10'8 and alter 
 the thwartship magnets so as to obtain the normal deflection with 
 this reading. 
 
 The common reading for North and South is 12 '5, and 
 the common reading for East and West is 10'8. The mean 
 of these two is 1T7. Set the deflector to this reading and alter 
 the globes so as to obtain the normal deflection with the deflector 
 at 117. 
 
 Now place the ship's head successively on S.W., N.W. and 
 N., and find the readings which give the normal deflection with 
 the ship's head on these points. Let these readings be respect- 
 ively 11 '5, 12 - 1, and 11*9. These three readings show that the 
 compensation has been done accurately. 
 
 If these three readings had been found to differ among 
 themselves and from that last obtained on West by more than 
 half a division of the scale, this would indicate that the case was 
 one of the exceptional ones, where the co-efficient called E (See 
 " Traite de Regulation,") must be taken into account. This 
 occurs when the axis of the compass being in the fore-and-aft 
 plane of the ship, masses of soft iron (such as cannons, turrets, iron 
 boats) are not symmetrical or sensibly equal on each side, or 
 again, when these masses of iron comply with these two con- 
 ditions, but the axis of the compass has not been placed in the 
 central fore-and-aft plane of the ship, which makes the iron 
 situated on the side nearest to the compass have a greater effect 
 than that on the other side. 
 
 THIKD CASE, OR EXCEPTIONAL CASE. 
 
 In which E cannot be neglected. To correct this co-efficient 
 it is necessary to bring the spheres nearer, and at the same time 
 to set the line joining their centres at a certain angle with regard 
 to the thwartship line. These two operations would be very 
 long and difficult to accomplish by trials alone. To carry this 
 out with accuracy and quickness the ship must be made to take 
 a third turn, and care must be taken to graduate the deflector 
 previously, as we have described. 
 
 Besides, when such a case occurs and the ship is a new 
 one of large draught of water and of considerable value, it would 
 
CHAP. ill. Compensation of exceptional case. 47 
 
 be advisable to take advantage of the time of fitting out, and the 
 trial trips to compensate the compass approximately by bearings, 
 and to collect all the elements to construct a good curve or table 
 of deviations. This curve or table may vary with time, even 
 while remaining in the same place, because the magnetic condition 
 of such a ship will not remain permanent for any length of time. 
 But when the ship is already old and the principal facts of its 
 magnetic condition are known from previous adjustments, when 
 especially the difference between the two extreme readings for 
 the normal deflection, obtained in the third turn of the ship on 
 the eight principal points of the compass, does not exceed seven 
 or eight divisions of the scale, even in these completely exceptional 
 cases when it is required for an urgent mission the compass can 
 be compensated with the deflector alone, (provided the latter has 
 been graduated) and the ship can proceed to sea with a certainty 
 that the deviations of the compass do not exceed 4 or 5 degrees. 
 This is sufficient to secure safety and the proper setting of the 
 course until the fog has cleared off, and the compensation can be 
 completed and verified by turning the ship round and taking 
 bearings of a heavenly body. 
 
 THE COMPENSATION OF THESE EXCEPTIONAL CASES 
 IN PRACTICE. 
 
 Preliminary observations. In these cases it is not un- 
 common that, on some of the cardinal points, the reading corres- 
 ponding to the normal deflection may not be contained within 
 the limits of the scale. It is necessary then, without waiting for 
 further observations, to bring it within the limits by placing at 
 once corrector magnets in a proper manner. 
 
 Suppose for example that on North the deflector set at 
 zero is still too strong to obtain the normal deflection, the pointer 
 being over the E. by N. In this case fore-and-aft magnets are 
 introduced at once, with their poles contrary to those of the 
 deflector, and at such a distance that the normal deflection is 
 obtained with the reading between and 1 on the scale. 
 
 Suppose, in the next place, that at East the deflector set 
 at 35 is too weak to obtain the normal deflection. The thwart- 
 ship magnets should at once be placed in position with their poles 
 
48 Compensation of exceptional cases. CHAP. in. 
 
 similar to those of the deflector, and at such a distance that the 
 normal deflection may be obtained with the deflector set at a 
 reading between 30 and 35. 
 
 The placing of the magnets thus in the first instance is 
 often sufficient to bring all the following readings within the 
 limits of the scale. When this is not so it is necessary to adjust 
 the screws of the base, or to use the additional magnets as 
 described on page 31. 
 
 A third turn of the ship is now made, and at each of the 
 eight principal points the reading corresponding to the normal 
 deflection is found. 
 
 From the table of graduation the value of the force corres- 
 ponding to each of these readings is taken. The corresponding 
 numbers in either of the last two columns may be used, but when 
 one of them is chosen all the values of the forces must be taken 
 from that column in order not to change the unit of measurement. 
 
 Calling Fn, Fne, Fe, &c., the directive forces corresponding 
 to North, N.E., East, &c., we have the following equations 
 
 = !>~!! s 
 
 -bn+Jb s 
 
 Sin D x - Fn + Fs ~( Fe + Fw ) Sin E - Fse 4 Fuw ~ ( Fne + Fsw ) 
 
 Fn + Fe + Fs + F w Fse + F sw + Fnw + Fne 
 
 (See " Traite de Regulation " for the definitions of these 
 quantities). The smaller the value of B the more correctly are 
 the fore and-aft magnets placed. Similarly the smaller the value 
 of C the more correctly are the transverse magnets placed. 
 
 Correction of E. Take from the Table, page 64, the value 
 of D corresponding to the position of the spheres actually applied 
 to the compass. This quantity is marked + if the line joining 
 the centre of the spheres is thwartship, and if this line is fore- 
 and-aft. This value of D, expressed in degrees and tenths of a 
 degree, is added algebraically to the value of D' expressed in 
 degrees and tenths of a degree, as found from the above formula. 
 Call D J the algebriac sum of these two quantities. 
 
 Let E be the angle expressed in degrees and tenths of a 
 degree found from the above formula, calculate the quantity 
 
(JHAP. in. Exceptional Cases. 49 
 
 i 2 -t-E 2 . This gives the amount of error to be corrected by 
 the spheres, and the corresponding distances at which they must 
 be placed is found from Table, page 64. If the spheres already 
 in position cannot be brought close enough, larger ones must be 
 used and placed at th* proper distance to correct this error. 
 
 To set the line joining their centres in the proper direction 
 
 E 
 
 the angle 2m given by the formula tan '2m - ~- must be found. 
 
 The angle 2 m is counted from the centre of the compass, 
 from to 90, commencing from the thwartship line on the star- 
 board side, positive towards the stern, negative towards the bow. 
 
 TT 
 
 Whatever be the value of - there is always an angle 
 
 positive or negative, the tangent of which corresponds to this 
 value. Let 2 m be this angle. A direction corresponds to m the 
 half of this angle. Let us consider this direction and the perpen- 
 dicular to it. It is in one of these directions that the line joining 
 the centres of the spheres mu.st be set One or other is chosen 
 according as D l is positive or negative. If D t is negative, the 
 direction which approaches nearest to the fore-and-aft line is 
 chosen. IfDj is positive the direction which is nearest to the 
 thwarlship line is taken. 
 
 Numerical Example. Suppose that, after having placed 
 the corrector magnets by steering successively on the four cardinal 
 points, and having placed the spheres on the last point steered, 
 say West, the last reading for the normal deflection, with all the 
 correctors in position, is found to be 8 '5. 
 
 Suppose the 8J- inch spheres are placed at 84 inches with 
 the line joining the centres thwartship. These will correct 
 a D= +G'5. 
 
 The ship is placed successively on the eight principal 
 points, and the following readings are found to give the normal 
 deflection. 
 
 Ship's Head. Heading of Deflector. Corresponding Force. 
 
 S.W. 11-3 0-905. 
 
 N.W. 9 0-87 
 
 North 7 0-80 
 
 N.E. G 0-77 
 
 East 8-5 0-85 
 
 S.E. 10-5 0-89 
 
 South 11 DO 
 
50 Exceptional Case. * CHAP. in. 
 
 From the formulas given above we have the following 
 values with the forces in this particular case. 
 
 . -D 0800-90 . 0-85085 
 fem 13- bin I p^ 
 
 Sin D'- 17 7- 17 8inE _ 0-89 + 0-87-(077 + 0-905) 
 
 3'4 o'45 
 
 Sin B = 0-06. Sin = 0. Sin V =0. Sin E - + 0'026. 
 
 The table, page 65, gives the values of the angles corres- 
 ponding to these sines. 
 
 B = 3-5. C = 0. E=+27. 
 
 Therefore the fore-and-aft magnets are not properly placed. 
 While still on the last course steered, the South, we can make use 
 of these calculations (which only occupy about ten minutes, when 
 a curve of the graduation of the deflector has been constructed 
 beforehand) to place them properly. Adding together the eight 
 forces corresponding to the eight principal points, we find the 
 sum to be 6 '8. Now divide this by 8 and we find the mean 
 force to be 0'85, which corresponds to the division 8'5 of the 
 deflector. Place the index at this reading, and alter the fore-and- 
 aft magnets so as to obtain the normal deflection with the ship's 
 head South, and the deflector set at this reading. Now we are 
 sure that the quantity B has been annulled altogether or very 
 early so. 
 
 Alteration and setting of the Spheres. In this particular 
 ease. 
 
 ^/Djf+E 2 = N /D a +E 2 = +7 1 = +706' 
 Therefore the spheres instead of remaining at the distance 
 8'4 inches ought to be placed at 81 inches. 
 
 The line joining the centres of the spheres should make 
 
 with the thwartship line an angle m such that tan 2m-|j = 
 9.7 
 ^= +0-415. Hence 2w = + 2230' and m= + 1115', w + 90 = 
 
 10115'. D being positive, we must choose the angle which gives 
 a direction nearest to the thwartship line, that is m+ = 1115' 
 
 The line joining the centres must therefore be turned so 
 as to make an angle of 1115' with the thwartship line. The 
 sphere on the starboard side should be nearest the stern. 
 
CHAP. iv. Correction for the heeling error. 51 
 
 CHAPTER TV. 
 CORRECTION FOR THE HEELING ERROR. 
 
 T 
 
 'HE horizontal compensation annuls, or very nearly so, the 
 influence of the iron of the ship on the compass, when she 
 is upright. But when the ship heels over the position of the 
 iron is changed with regard to the compass, and in consequence 
 the deviations which it produces are changed also. 
 
 The heeling error on any point is the difference between 
 the deviation on that point when the ship is upright and when 
 she heels over. A ship which rolls or heels over easily should 
 never be sent to sea without having previously had the greater 
 part of this error compensated by vertical magnets. This error, 
 on courses approaching the North and South, attains or some- 
 times exceeds five or six degrees for ten degrees of heel of the 
 ship. 
 
 This error depends on the ship's head, on the amount of 
 heel, and also on the direction of the latter, whether it is to port 
 or starboard. It consists of three important terms, generally 
 very unequal. 
 
 That which is usually much the greatest arises partly 
 from the permanent magnetism of the ship, and partly from 
 magnetism induced in the soft iron of the beams, and of the iron 
 deck. It is to this term only that attention is ordinarily directed 
 and as it is corrected by vertical magnets. The correction is 
 not strictly accurate, except for the place where it has been made 
 and it ought to be re-corrected when the ship goes to other 
 latitudes. 
 
 The placing of corrector magnets in position generally 
 keeps the heeling error within limits sufficiently small so that it 
 can never be dangerous or produce much inaccuracy in the setting 
 of the course 
 
52 The dipping needle instrument. CHAP. iv. 
 
 But even when the ship does not change her place, there 
 are two cases where it is necessary to seize the first favourable 
 opportunity for astronomical observations to verify the efficiency 
 of the correction thus made. 
 
 These two cases occur, when the two other terms of the 
 heeling error, which are neglected usually, have a considerable 
 value, and this takes place when large masses of iron either 
 horizontal or vertical are found in the neighbourhood of the 
 compass, the axis of which is in the fore-and-aft plane of the ship 
 or also when the compass is not placed as usual, in the central 
 third of the length of the ship, but very close to one of the two 
 extremities. 
 
 Vertical bar magnets which will correct the most import- 
 ant term of the heeling error can be placed in position in a few 
 minutes, with the ship remaining upright, without any bearings 
 whe the deflector and also another instrument invented by 
 Sir William Thomson, which he calls the dipping noedle instru- 
 ment are available. 
 
 The dipping This instrument consists of a cylinder 3 inches long and 
 
 strument. 2 inches in diameter, which contains a magnetic needle, d 
 moveable round an axis a a perpendicular to it. 
 
 The angle which this needle makes with the horizontal 
 line is measured on two graduated circles, one of which is shown 
 at b. 
 
 To use this instrument it is placed in the magnetic meridian 
 and the needle is brought back to the horizontal position from which 
 
CHAP. IV. Observations on shore. 53 
 
 it is deflected, on shore by the earth's vertical magnetic force, and 
 on board ship by the combined magnetic forces of the earth and 
 ship. To accomplish this on shore, in the Northern hemisphere, a 
 counterpoise of paper or thin cardboard, shown on the figure 
 below a a, is placed on the end of the needle which is attracted 
 towards the South. This counterpoise is moved along the needle 
 until the latter is horizontal. The distance of the centre of the 
 paper from the axis a a is then measured by means of the inclined 
 scale which is shown at c. 
 
 To make the observation accurate it is necessary that the 
 axis a a should be horizontal, or very nearly so, at the time of 
 observation. This condition is accomplished when the air bubble 
 contained in the small level n is in the middle of this level. This 
 can be done with a few minutes practice by simply holding the 
 instrument in the hand. 
 
 The platform p is raised or lowered according as it is 
 desired to keep the needle at rest, or to free it for the observa- 
 tion. 
 
 Observations on shore. 1st. The deflector should be grad- p re ii m i n ary 
 uated on shore in a place free from iron. A single glance at the observations 
 
 1 to be made 
 
 table give's the division of this scale, which corresponds to the on shore, 
 horizontal force of the place on shore and the normal deflection. 
 
 2nd. At the same place on shore the dipping needle is set 
 as exactly as possible in the magnetic North and South line 
 without the counterpoise. This line is obtained from the known 
 value of the declination at the place and for the particular year. 
 
 An error of 2 or 3 degrees in the setting does not produce 
 any sensible error. The lowest end of the needle should be turned 
 towards the North. 
 
 The paper counterpoise is then placed on the highest end 
 of the needle, and slided along it until the needle is horizon- 
 tal. By means of the inclined scale its distance a from the axis 
 of rotation is measured. 
 
 After having completed the horizontal compensation on ^n^oarlT 
 board, the reading which gives the normal deflection on all points Placing the 
 
 is noted. The table of graduation, Col. III., gives the correspond- magnets in 
 
 position. 
 
54 Compensation for heeling error. CHAP. iv. 
 
 ing force. This number shows the ratio between the directive 
 force of the compass on board and on shore. 
 
 It is a fact of great importance to have, because it 
 allows us to know at once whether the compass is placed in a 
 favourable condition or not, for proper working (see p. 59). The 
 compass is, other things being equal, in the most favourable con- 
 ditions, when this ratio is large. Let X be its value which is 
 usually less than 1. 
 
 The paper counterpoise is moved along the dipping needle 
 so as to make its distance along the axis 6 = X a. 
 
 For a compass placed in a good position this quantity X 
 varies between 0'80 and 0'95. When for any reason this quantity 
 has not been exactly determined as we have described, it may 
 be assumed to be equal to 0'90. An error of only a few 
 hundred ths will thus be made. In the ports of England and 
 France an error of four or five per cent, on this quantity, will 
 riot give rise to more than one and a half degrees of error for ten 
 degrees of heel of the ship. 
 
 The ship is now placed on the magnetic East or West, 
 that is, on East or West by compass, since it has been completely 
 compensated. 
 
 This course is kept as correctly as possible by means of an 
 auxiliary compass placed about 8 feet away. 
 
 The bowl and card of the compass to be compensated, is 
 removed from the binnacle to a distance of 5 feet or so. 
 
 The dipping needle instrument is then placed with its axis 
 of rotation in the same plane as that occupied by the needles 01 
 the card, its centre being in the vertical axis of the compass. It 
 is then turned round till the needle is in the magnetic meridian, 
 and the end with the counterpoise towards the South. As the 
 ship's head is supposed to be magnetic East or West, the needle 
 of the dipping instrument will thus be thwartship. When the 
 dipping needle is at rest, the bubble of the level being in the 
 centre of the glass, the position which it occupies is noticed. 
 
 If the needle is horizontal there would be no heeling error 
 to correct. 
 
CHAP. iv. Compensation for heeling error. 55 
 
 If it is not horizontal, which is generally the case, it is 
 made so by placing a magnet, set in the proper direction, in the 
 vertical cylindrical 'case which is found in the centre of the 
 binnacle. This case should be as far as possible from the card at 
 the commencement of the operation. 
 
 If, on board, the end with the paper weight is too high, Practical 
 
 rules for the 
 the vertical magnet must have its red pole up. Northern 
 
 magnetic 
 
 If, on board, the end with the paper weight is too low, the hemisphere 
 vertical magnet must have its blue end up. 
 
 In the Southern magnetic hemisphere the poles must be 
 reversed, since the paper weight is placed on the end which 
 points towards the North. 
 
 Having placed the vertical magnet in the case, it is 
 gradually raised towards the card, until the needle set and 
 weighted, as we have described, becomes horizontal. 
 
 When this result is obtained the case is fixed in the 
 position which it then occupies. 
 
 If one magnet is not sufficient a second one is introduced, 
 and the case lowered to the bottom. It is then raised little by 
 little and fixed in the position it occupies when the needle is 
 horizontal. 
 
 Numerical Example. At Toulon, with the compass and 
 deflector to which the table of graduation applies, suppose that the 
 normal deflection is obtained on shore with the reading 15'2 ; 
 and the same deflection is obtained on board after the complete 
 compensation with the reading at the division 7. 
 
 The table of graduation of the deflector shows in the 
 third vertical column, that the ratio of the horizontal forces 
 which act on the compass on board and on shore is 080; because 
 the deflector set at the division 7 corresponds to the force O'SO. 
 
 On shore suppose that the dipping needle set North and 
 South is horizontal, when the paper weight is at a distance from 
 the axis of rotation equal to i'9. 
 
 On board the rule given above shows that the weight 
 should be set at J/9 * 08 = T52. 
 
56 Verification of the Compensation for heeling error. CHAP. iv. 
 
 By means of the scale the paper weight is placed at this 
 distance from the axis of rotation. 
 
 The ship is placed East or West magnetic, that is East or 
 West by the compass, since it has been already completely com- 
 pensated; and the bowl and card of the compass is removed. 
 The ship is steered by an auxiliary compass ; the dipping needle 
 instrument is placed in position with the needle in the North 
 and South line, and the paper weight at T52 from the axis. 
 
 Suppose that, the axis of rotation being horizontal, the 
 end of the needle with the paper weight is higher than the other 
 end. A magnet with its red pole up must be placed in the case 
 and raised gradually, until the needle becomes horizontal. When 
 this result is obtained the case is fixed in the position it then 
 occupies and this position noted. 
 
 ^i 8 com P ensa ^ on i s sufficient in the great majority of 
 
 pensation cases. When one of the two exceptional cases described in the 
 
 of the heel- . 
 
 ing error, last chapter occur, it is necessary to verify the accuracy of 
 
 the compensation thus made, which can be done by means of 
 astronomical observations. 
 
 To do this in a roadstead, the ship is made to heel over from 
 7 to 8 degrees, or better 10 degrees according to the facilities at 
 hand, or at sea the time may be chosen when the ship has such 
 a heel without rolling more than 2 or 3 degrees. 
 
 Then proceed thus : 
 
 1st. If there are masses of fore-and-aft iron close to the 
 compass, place the ships head North or South by the compass and 
 observe the deviation, compare it with the value found on the 
 same point with the ship upright. If the two values of the 
 deviation differ by less than ] degree the conpensation is sufficiently 
 good ; if it is greater than this amount divide the difference by 
 the number of degrees of heel. This gives the correction which 
 must be applied to courses near the North and South for each 
 degree of heel of the ship. For the other courses multiply the 
 number thus found by tho iqnftro of the cosine of the an^le 
 between the course and the North and South line by the compass. 
 
 2nd. When there are some large pieces of vertical iron 
 near to the compass, place the ships head East or West and 
 
CHAP. iv. Correction of the Compensation for heel. 
 
 57 
 
 proceed exactly as before. Only the correction found, for each 
 degree of heel for the East and West points should be multiplied 
 by -thai aqmtre-^f the sine of the angle between this point and the 
 North or South of the compass. 
 
 It is not necessary to take account of this second minor 
 error, when the corrector called the Flinder's bar has been properly 
 placed. (See Traite de Regulation). 
 
 To correct the compensation for the heel when the ship Correction of 
 
 i - i ...... , T the corn- 
 
 changes its geographical position, it is necessary to have charts 
 
 giving the values of the horizontal force and of the dip in different 
 parts of the globe. These charts are given at plates I. & II. at 
 the end of the book. 
 
 Suppose in the first place that the ship has gone to 
 another place without changing the hemisphere. 
 
 Numerical Examples. 1st case. In the same hemisphere. 
 The compensation for the heeling error having been made at 
 Toulon, it is desired to correct this compensation in order that 
 it may annul the errors at a place situated in lat, 20 N., and 
 long. 20 W. 
 
 At Toulon the paper weight was at 1*9, and the vertical 
 magnetic force at the same place Z - H tan 6 = 2'25 because at 
 Toulon, H - 1-3 ; tan = tan 61 '30 = T83. 
 
 At the place 20 N., latitude, and 20 W., longitude, the 
 value of the vertical force Z' = H' tan = 1'6; since H' = r(j and 
 tan 6 = tan 45 1. 
 
 It is necessary to determine the arm of the lever of the 
 counterpoise which corresponds to the new value of the vertical 
 force : that is to say, the distance from the axis of rotation at 
 which the counterpoise ought to be placed to make the needle 
 horizontal, when subject to the terrestrial force of the second 
 place of observation alone. 
 
 Calling x this arm of the lever we will evidently have 
 
 = =r x = 1*9 x __ 1'2 about. 
 a & ^'25 
 
 On board, on the East or West point, and in the second 
 place of observation the needle is subject to the force X Z' X 
 being the factor determined as we have described, 
 
 pensation 
 for the heel 
 when the 
 ship chan- 
 ges its geog- 
 raphical 
 position. 
 
58 Correction of the Compensation. CHAP, iv 
 
 This factor, for a ship which has been at sea for sometime 
 may be considered as constant, and for a new ship it varies by 
 insensible amounts; in two or three months one or two hundredths 
 of its value. We may therefore take for X the number deter- 
 mined at the first place. 
 
 The result is that the arm of the lever of the paper weight, 
 for the second place of observation in the particular case we are 
 examining should be 1'2 x 0'8 = 0'96. The weight is placed at 
 this distance. 
 
 The ships head is placed East or West magnetic, and the 
 dipping needle in the North and South line is put in the same 
 position as that occupied by the needles of the card, when in the 
 binnacle. The needle is made horizontal by means of the vertical 
 magnet. 
 
 2nd case. The ship has gone to the Southern hemisphere. 
 
 The same reasoning and the same calculations apply here 
 also ; only it must be remembered that the dip is of different 
 sign in one hemisphere from the other. In consequence tan 0' 
 will be negative and also Z' and x, which shows that the counter- 
 poise must be passed from one end of the needle to the other. 
 
 For a place where we have 
 
 H'-l-6; 0' = 45; ban 0' = 1 ; x will be equal to- 1-2, and 
 the counterpoise should be placed at 0'96 from the axis of 
 rotation, that is to say, on the other half of the needle from that 
 which it occupied in the Northern hemisphere. 
 
 Practical rule ^ n ^ ne Southern hemisphere the vertical magnet is set 
 
 sTutlTrn according to the following rule. 
 
 hemisphere j f Qn j^^ fae paper weight is too high, place the vertical 
 
 magnet with the blue end up. 
 
 If on the contrary the paper weight is too low place the 
 vertical magnet with the red end up 
 
 THE DIRECTIVE FORCE OF THE COMPASS ON BOARD. 
 
 When the horizontal and complete compensation is finished 
 when moreover the deflector has been graduated on shore, the ratio 
 which exists between the directive force on board, which is constant 
 
CHAP. IV. The directive force of the compass on board. 59 
 
 now on all points, and that on shore is at once obtained ; the 
 numerical value of this ratio is given by the number in the third 
 column of the table which corresponds to the reading of the 
 deflector common to all directions of the ship's head. (See p. 55). It 
 is the quantity which we have called X. It is very important to 
 know this quantity because by means of it an idea can be formed 
 of the accuracy, and precision of the indications which the 
 compass will give in practice. The accuracy of the compass will 
 be greater when X is larger. In general this number is smaller 
 than 1. For an azimuth compass well placed, it is generally 
 between 0'950 and O800. This ratio varies very gradually, and 
 very little during the first months the ship is at sea, and remains 
 therefore strictly constant, or extremely nearly so. It keeps the 
 same value in all parts of the globe. 
 
 For steering compasses, not so favourably placed as the 
 Azimuth compass, it varies from O900 to 0750. 
 
 The compasses at present in use generally give accurate 
 enough indications when they are acted upon by directive forces 
 between 0'6 of the directive force taken as unity on the chart, 
 Plate 1, and the unit force. 
 
 In a place where the horizontal force taken from the chart 
 is expressed by H the directive force of the compass on board is 
 equal to X H. 
 
 It is necessary to watch the compass more carefully when 
 the directive force on board is small ; when it is smaller than 
 0'6, the compass is in unfavourable conditions, and if it is lower 
 still the indications of the compass cannot be relied on to give 
 great accuracy, because the frictional error is generally very 
 nearly inversely proportional to the directive force which acts 
 on the compass. 
 
60 Verification of the Compensation at Sea. CHAP. v. 
 
 CHAPTER V. 
 VERIFICATION OF THE COMPENSATION AT SEA. 
 
 nPHE compensation thus made is only exact tor the place 
 where it has been carried out. 
 
 Whenever the ship goes along a course at right angles, 
 either to the lines of equal horizontal force or to the lines of equal 
 dip, it is necessary to pay particular attention to the compass. 
 We have shown how this watchfulness should be carried out 
 when bearings can be obtained, (see " Traite de Regulation") 
 
 In the majority of ships, it is the fore-and-aft magnets 
 which must be watched with the greatest care. Consequently, 
 in times of fog, it is on the North and South points of the com- 
 pass, that it is specially necessary to make frequent observations 
 of the normal deflection, to see if the two corresponding readings 
 continue to be equal to one another. 
 
 The compass may be conveniently verified, in times of fog, 
 in the following way : 
 
 The observation for normal deflection is made successively 
 on the three following points. On the course of the ship and on 
 the two cardinal points of the compass, which are adjacent to 
 this course, commencing with the ship's head North or South. 
 Note the reading found on each of three courses. 
 
 If the same reading is found, (within the limits adopted) 
 on the three points, and if, besides, the numerical value of the 
 force, taken from the fourth vertical column of the table (page 26) 
 corresponding to this common reading is equa) within one or 
 two hundredths to the product X H' (X being the ratio determined 
 before, and H' being the horizontal force at the place, taken 
 from the chart, plate I ) it is not necessary to alter the compen- 
 sation. 
 
 If the three readings are equal but the corresponding 
 force has not the proper value, X H', or again, if these throe 
 readings differ by a greater amount than that which is allowed, 
 it is necessary to alter the compensation in the following manner. 
 
CHAP. v. Verification of the Compensation at Sea. 61 
 
 The normal deflection is obtained with the ship's head on 
 one of the points, North or South ; the one on which the normal 
 deflection was not obtained previously. 
 
 If this reading is equal to that already found, with the 
 ship's head on the opposite point, the fore-and-aft magnets are 
 correct ; but if it is different these magnets must be altered (see 
 p. 40) so as to obtain the normal deflection with the deflector set 
 at the mean of the readings, with the ship's head North and South. 
 
 In the majority of ships, the reading for the normal defle- 
 tion thus made to agree for the North and South points by the 
 magnets is generally equal to the reading found on the East or 
 West point within the limits allowed. 
 
 If this is so, and if the ship is not new, it is not necessary 
 to verify the accuracy of the position of the thwartship magnets. 
 But if these readings are different, or if the ship is new, the 
 normal deflection must be found with the ship's head on the East 
 or West point, whichever has not been tried yet. If the reading 
 of the deflector thus found, differs from that obtained on the 
 opposite point, the thwartship magnets must be altered so as 
 to obtain the normal deflection with the deflector set at the 
 mean of the two readings obtained with the ship's head East and 
 West. 
 
 When the ship has been some time at sea, the readings 
 thus obtained on the one hand, with the ship's head North and 
 South, and on the other hand, with the ship's head East and West, 
 after altering one or both sets of corrector magnets if necessary, 
 will generally be equal to one another, and it will not be necessary 
 to alter the position of the spheres. 
 
 When they are not equal, which may happen in new ships 
 constructed entirely of iron, the spheres must be altered on the 
 last course, steered so as to obtain the normal deflection, with the 
 deflector set at the mean of the two readings, the one common to 
 the North and South points, and the other, common to the East 
 and West points. 
 
 The correction of the horizontal compensation being finish- 
 ed, the correction of the compensation for the heeling error must 
 afterwards be proceeded with, (see p. 57) 
 
62 Verification of the Compensation at Sea. CHAP. v. 
 
 When the ship has been at sea for one or two years, and 
 when besides the soft iron compensator called the Flinders bar has 
 been placed in position, the correction of the horizontal compen- 
 sation is very simple. It is limited to verifying from time to 
 time, that the three readings found on the course of the ship, and 
 on the two adjacent cardinal points are really equal to one another 
 within the limits allowed, (see " Traite de Regulation") 
 
 N.B. When the ship has remained or remains for a long 
 time on the same course and when this course is close to East or 
 West magnetic, then the inspection of the compass should be 
 frequent, particularly if the ship is new, or is making this voyage 
 for the first time The inspection should be made daily, and to 
 carry it out, the ship should be steered on three cardinal points, 
 at least, on the North and South on the one hand, and on the 
 other hand, on the East or West, whichever of these two points 
 is nearest to the course of the ship. 
 
 When the course does not make an angle of more than 30 3 
 with one of the two lines, North and South or East and West, it 
 is necessary to take a fourth reading on the intermediate quad- 
 rantal point. 
 
 Numerical Example. Leaving Toulon, after the complete 
 compensation is finished, the reading common for all points was 
 the division 10. The number taken from the third vertical column 
 corresponding to this division is 0'88. This is the value of X. 
 
 It is desired to check the compensation of the compass at 
 a placed 20 N. Lat and 20 W. Long. Here H'=l-6. therefore 
 XH' = 1-4-1. 
 
 The reading for normal deflection on the course being 
 steered, say N. 35 E. is found. Let this reading be 24 ; let the 
 reading with ship's head East be 23'5 and with the ship's head 
 North 24-5. 
 
 Since these three readings agree among themselves within 
 the limits allowed, and also correspond to the force 141 of the 
 fourth vertical column it is not necessary to proceed further 
 with the correction of the compensation. 
 
CHAP. v. Conclusion. 63 
 
 CONCLUSION. 
 
 When from the impossibility of getting astronomical obser- 
 vations it is necessary to navigate after correcting the compen- 
 sation by means of the deflector alone, the first opportunity which 
 occurs to verify the accuracy of the correction by means of 
 bearings should be taken advantage of and the correctors should be 
 altered if necessary. This verification is all the more indispensa- 
 ble when the ship is new, the masses of iron in the neighbourhood 
 of the compass very great and lastly when the mean directive 
 force on board, that is the quantity X is very small. 
 
Distances of Spheres for quadrantal correction. 
 
 TABLE FOR THE DISTANCE OF 
 THE SPHERES. 
 
 Error 
 to be 
 Cor- 
 
 Distance of Nearest Points of Globes from Centre of Compass 
 
 lo-inch 
 
 9-inch 
 
 8^-inch 
 
 8-inch 
 
 7^-inch 
 
 7-inch 
 
 6|-inch 
 
 6-inch 
 
 5^-inch 
 
 rected. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 Globes. 
 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 inches. 
 
 1 
 
 22-80 
 
 20-52 
 
 19-38 
 
 18-24 
 
 17-10 
 
 15-96 
 
 14-82 
 
 13-68 
 
 12-54 
 
 H 
 
 19-30 
 
 17-56 
 
 16-40 
 
 15-44 
 
 14-47 
 
 13-51 
 
 12-54 
 
 11-58 
 
 10-61 
 
 2 
 
 17-06 
 
 15-36 
 
 14-50 
 
 13-65 
 
 12-80 
 
 11-94 
 
 11-09 
 
 10-23 
 
 9-39 
 
 2i 
 
 15-48 
 
 13-93 
 
 13-16 
 
 12-38 
 
 11-61 
 
 10-84 
 
 10-C6 
 
 9-29 
 
 8-51 
 
 3 
 
 14-28 
 
 12-85 
 
 12-14 
 
 11-42 
 
 10-71 
 
 9-99 
 
 9-28 
 
 8-57 
 
 7-85 
 
 3i 
 
 13-32 
 
 11-99 
 
 11-32 
 
 10-65 
 
 9-99 
 
 9-32 
 
 8-66 
 
 7-99 
 
 7-33 
 
 4 
 
 12-52 
 
 11-26 
 
 10-64 
 
 10-02 
 
 9-39 
 
 8-76 
 
 8-14 
 
 7-51 
 
 6-88 
 
 <i 
 
 11 84 
 
 10-66 
 
 10-06 
 
 947 
 
 8-88 
 
 8-29 
 
 7-70 
 
 7-10 
 
 6-51 
 
 5 
 
 11-28 
 
 10-15 
 
 9-57 
 
 9-00 
 
 8-46 
 
 7-90 
 
 7'33 
 
 6-77 
 
 6-20 
 
 5i 
 
 10-77 
 
 9-69 
 
 9-15 
 
 8-62 
 
 8-07 
 
 7-53 
 
 7-00 
 
 6-46 
 
 5-92 
 
 6 
 
 10-31 
 
 9-28 
 
 8-76 
 
 8-24 
 
 7-73 
 
 7-21 
 
 6-70 
 
 6-18 
 
 5-67 
 
 ( 'i 
 
 9-90 
 
 8-91 
 
 8-41 
 
 7-92 
 
 7-42 
 
 6-93 
 
 6-44 
 
 5-94 
 
 5-44 
 
 
 9-54 
 
 8-58 
 
 8-11 
 
 7-63 
 
 7-15 
 
 6-68 
 
 6-20 
 
 5-72 
 
 5-25 
 
 7i 
 
 9-19 
 
 8-28 
 
 7-81 
 
 7-35 
 
 6-90 
 
 6-43 
 
 5-97 
 
 5-51 
 
 5-06 
 
 8 
 
 8-92 
 
 8-03 
 
 7-58 
 
 7-14 
 
 6-69 
 
 6-24 
 
 5-80 
 
 5-35 
 
 4-91 
 
 8i 
 
 8-64 
 
 7-77 
 
 734 
 
 6-91 
 
 6-48 
 
 6-05 
 
 5-62 
 
 5-18 
 
 4-75 
 
 9 
 
 8-39 
 
 7-55 
 
 7-13 
 
 6-71 
 
 6-29 
 
 5-87 
 
 5-45 
 
 5-03 
 
 4-61 
 
 4 
 
 8-14 
 
 7'33 
 
 6-92 
 
 6-51 
 
 6-10 
 
 5-70 
 
 5-29 
 
 4-88 
 
 4-48 
 
 10 
 
 7-93 
 
 7-13 
 
 6-74 
 
 6-34 
 
 5-95 
 
 5-55 
 
 5-15 
 
 4-76 
 
 4-36 
 
 10i 
 
 7-72 
 
 6-95 
 
 6-56 
 
 6-18 
 
 5-79 
 
 5-40 
 
 5-02 
 
 4-63 
 
 4-25 
 
 11 
 
 7-51 
 
 6-76 
 
 6-38 
 
 6-01 
 
 5-63 
 
 5-26 
 
 4-88 
 
 4-51 
 
 4-13 
 
 iii 
 
 7-35 
 
 6-61 
 
 6-25 
 
 5-88 
 
 5-51 
 
 5-14 
 
 4-78 
 
 4-41 
 
 4-04 
 
 12 
 
 7-17 
 
 6-45 
 
 6-09 
 
 5-74 
 
 5-38 
 
 5-02 
 
 4-66 
 
 4-30 
 
 3-94 
 
 The first column, intitled " Error to be corrected," gives 
 the different values of the quantity we have called D. 
 
 When this quantity is positive, the line joining the cent res 
 of the spheres must be thwartship. 
 
 When this value is negative, the line joining the centres 
 of the spheres must be fore and aft. 
 
 See " Trait^ de Regulation," p. 234, for the table giving 
 the exceptional values of D, from 12 to 16 
 
Natural Joints, Cosines, 
 
 TABLE 
 
 OF NATURAL SINES, COSINES, TANGENTS, &c. 
 
 
 
 
 
 
 
 
 
 
 Angle. 
 
 Sine. 
 
 Difference 
 for 10' 
 
 Arc. 
 
 Tangent. 
 
 Cotan. 
 
 Vers-sin. 
 
 Cosine. 
 
 
 
 
 
 o-oooo 
 
 
 o-oooo 
 
 o-oooo 
 
 infini. 
 
 o-oooo 
 
 1-0000 
 
 90 
 
 1 
 
 0-0175 
 
 
 0-0175 
 
 0-0175 
 
 57-290 
 
 0-0002 
 
 0-9998 
 
 89 
 
 2 
 
 0-0349 
 
 
 0-0349 
 
 0-0349 
 
 28-636 
 
 0-0006 
 
 0-9994 
 
 S8 
 
 3 
 
 0-0523 
 
 
 0-0524 
 
 0-0524 
 
 19-081 
 
 0-0014 
 
 0-9986 
 
 87 
 
 4 
 
 0-0698 
 
 
 0-0698 
 
 0-0700 
 
 14-301 
 
 0-0024 
 
 0-9976 
 
 86 
 
 5 
 
 0-0872 
 
 0-0029 
 
 0-0873 
 
 0-0875 
 
 11-430 
 
 0-0038 
 
 0-9962 
 
 85 
 
 6 
 
 0-1045 
 
 
 0-1047 
 
 0-1051 
 
 9-514 
 
 9-0055 
 
 0-9945 
 
 84 
 
 7 
 
 0-1219 
 
 
 0-1222 
 
 0-1228 
 
 8-144 
 
 0-0075 
 
 0-9925 
 
 83 
 
 8 
 
 0-1392 
 
 
 0-1396 
 
 0-1405 
 
 7-115 
 
 0-0097 
 
 0-9903 
 
 82 
 
 9 
 
 0-1564 
 
 
 0-1571 
 
 0-1584 
 
 6-314 
 
 0-0123 
 
 0-9877 
 
 81 
 
 10 
 
 0-1736 
 
 
 0-1745 
 
 0-1763 
 
 5-671 
 
 0-0152 
 
 0-9848 
 
 80 
 
 11 
 
 0-1908 
 
 
 0-1920 
 
 0-1944 
 
 5-145 
 
 0-0184 
 
 0-9816 
 
 79 
 
 12 
 
 0-2079 
 
 
 0-2094 
 
 0-2126 
 
 4-705 
 
 0-0219 
 
 0-9781 
 
 78 
 
 13 
 
 0-2250 
 
 
 0-2269 
 
 0-2309 
 
 4-331 
 
 0-0256 
 
 0-9744 
 
 77 
 
 14 
 
 0-2419 
 
 
 0-2443 
 
 0-2493 
 
 4-011 
 
 0-0297 
 
 0-9703 
 
 76 
 
 15 
 
 0-2588 
 
 
 0-2618 
 
 0-2679 
 
 3732 
 
 0-0341 
 
 0-9659 
 
 75 
 
 16 
 
 0-2756 
 
 0-0028 
 
 0-2793 
 
 0-2867 
 
 3-487 
 
 0-0387 
 
 0-9613 
 
 74 
 
 17 
 
 0-2924 
 
 
 0-2967 
 
 0-3057 
 
 3-271 
 
 0-0437 
 
 0-9563 
 
 73 
 
 18 
 
 0-3090 
 
 
 0-3142 
 
 0-3249 
 
 3-078 
 
 0-0489 
 
 0-9511 
 
 72 
 
 19 
 
 0-3256 
 
 
 0-3316 
 
 0-3443 
 
 2-904 
 
 0-0545 
 
 0-9455 
 
 71 
 
 20 
 
 0-3420 
 
 
 0-3491 
 
 0-3640 
 
 2-747 
 
 0-0603 
 
 0-9397 
 
 70 
 
 21 
 
 0*3584 
 
 
 0-3665 
 
 0-3839 
 
 2-605 
 
 0-0664 
 
 0-9336 
 
 69 
 
 22 
 
 0-3746 
 
 0-0027 
 
 0-3840 
 
 0-4040 
 
 2-475 
 
 0-0728 
 
 0-9272 
 
 68 
 
 23 
 
 0-3907 
 
 
 0-4014 
 
 0-4245 
 
 2-356 
 
 0-0795 
 
 0-9205 
 
 67 
 
 24 
 
 0-4067 
 
 
 0-4189 
 
 0-4452 
 
 2-246 
 
 0-0865 
 
 0-9135 
 
 66 
 
 25 
 
 0-4226 
 
 
 0-4363 
 
 0-4663 
 
 2.145 
 
 0-0937 
 
 0-9063 
 
 65 
 
 26 
 
 0-4384 
 
 
 0-4538 
 
 0-4877 
 
 2-050 
 
 0-1012 
 
 0-8988 
 
 64 
 
 27 
 
 0-4540 
 
 0-0026 
 
 0-4712 
 
 0-5095 
 
 1-963 
 
 0-1090 
 
 0-8910 
 
 63 
 
 28 
 
 0-4695 
 
 
 0-4887 
 
 0-5317 
 
 1-881 
 
 0-1171 
 
 0-8829 
 
 62 
 
 29 
 
 0-4848 
 
 
 0-5061 
 
 0-5543 
 
 1-804 
 
 0-1254 
 
 0-8746 
 
 61 
 
 30 
 
 0-5000 
 
 
 0-5236 
 
 0-5774 
 
 1-732 
 
 0-1340 
 
 0-8660 
 
 60 
 
 31 
 
 0-5150 
 
 0-0025 
 
 0-5411 
 
 0-6009 
 
 1-664 
 
 0-1428 
 
 0-8572 
 
 59 
 
 32 
 
 0-5299 
 
 
 0-5585 
 
 0-6249 
 
 1-600 
 
 0-1520 
 
 0-8480 
 
 58 
 
 33 
 
 0-5446 
 
 
 0-5760 
 
 0-6494 
 
 1-540 
 
 0-1613 
 
 0-8387 
 
 57 
 
 34 
 
 0-5592 
 
 0-0024 
 
 0-5934 
 
 0-6745 
 
 1-483 
 
 0-1710 
 
 0-8290 
 
 56 
 
 35 
 
 0-5736 
 
 
 0-6109 
 
 0-7002 
 
 1-428 
 
 0-1808 
 
 0-8192 
 
 55 
 
 36 
 
 0-5878 
 
 
 0-6283 
 
 ;>-7265 
 
 1-376 
 
 0-1910 
 
 0-8090 
 
 54 
 
 37 
 
 0-6018 
 
 0-0023 
 
 0-6458 
 
 0-7536 
 
 1-327 
 
 0-2014 
 
 0-7986 
 
 53 
 
 38 
 
 0-6157 
 
 
 0-6632 
 
 0-7813 
 
 1-280 
 
 0-2120 
 
 0-7880 
 
 52 
 
 39 
 
 0-6293 
 
 
 0-6807 
 
 0-8098 
 
 1-235 
 
 0-2229 
 
 0-7771 
 
 51 
 
 40 
 
 0-6428 
 
 0-0022 
 
 0-6981 
 
 0-8391 
 
 1-192 
 
 0-2340 
 
 0-7660 
 
 50 
 
 41 
 
 0-6561 
 
 
 0-7156 
 
 0-8693 1-150 
 
 0-2453 
 
 0-7547 
 
 49 
 
 42 
 
 0-6691 
 
 
 0-7330 
 
 0-9004 l-lll 
 
 0-2569 
 
 0-7431 
 
 48 
 
 48 
 
 0-6820 
 
 0-0021 
 
 0-7505 
 
 0-9325 1-072 
 
 0-2686 
 
 0-7314 
 
 47 
 
 44 
 
 6-6947 
 
 
 0-7679 
 
 0-9657 
 
 1-036 
 
 0-2807 
 
 0-7193 
 
 46 
 
 45 
 
 0-7071 
 
 
 0-7854 
 
 1-0000 
 
 1-000 
 
 0-2929 
 
 0-7071 
 
 45 
 
 - 
 
 Cosine. 
 
 Difference 
 for 10'. 
 
 - 
 
 Cotan. Tangent. 
 
 - 
 
 Sine. 
 
 Angle. 
 
THE following Charts which have been constructed by Staff 
 
 Commander Creak, R.N., for the Admiralty Compass Manual, 
 
 are given by permission of the Hydrographer. 
 
g S 
 
 PH 
 
 3 
 
WORKS BY M. COLLET, 
 
 Traite Theorique et Pratique de la Regulation 
 
 et de la Compensation des Compas. 
 One Volume with 6 Plates. Price 1O francs. 
 
 SUMMARY OF THE WORK. 
 
 Historical account of the works relating to the 
 Deviation of the Compass. Elementary, mechanical and 
 physical notions which serve as the basis for the construction 
 and for the trials which have to be made with a Compass. 
 Steadiness and Sensibility of the Compass. Choice of a 
 good Compass. 
 
 REGULATION OF COMPASSES. 
 
 Table and complete curve of the deviations. Cal- 
 culation of the five co-efficients of the deviation. The 
 magnetic forces on board. 
 
 COMPENSATION OF THE COMPASS. 
 
 Its utility, advantages and necessity on vessels 
 constructed of iron. Different Instruments for measuring 
 horizontal forces. Different systems of compensated Com- 
 passes actually in use. 
 
 II. 
 
 Practical Guide for Compensation of the 
 Compass with Bearings. 
 
 A translation of this by W. Bottomley will shortly 
 be published. 
 
 SUMMARY. 
 
 Placing the corrector magnets and soft iron correctors 
 in position. Compensation of the heeling error. Numerical 
 examples. Correction of the compensation at sea. Placing 
 in position the Flinders bar which generally makes the 
 horizontal compensation accurate for all latitudes. 
 
 PARIS: CHALLEMEL AINE, 5, RUE JACOB. 
 

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